Price Competition between International Airline Alliances

Price Competition between International Airline Alliances Volodymyr Bilotkach1 February 9, 2004 Abstract This paper develops a model of price competition between two international airline alliances, with consumers’ preferences vertically differentiated by the number of stops. Alliances benefit the interline passengers. Alliances with antitrust immunity do not benefit interline passengers more than those without antitrust immunity, in contrast to the Cournot-type settings. While antitrust immunity leads to higher fares for non-stop travel between hubs of alliance partners, granting it might be necessary to induce consolidation between carriers. Formation of alliances with antitrust immunity is consistent with the proposed model, even though such is likely to decrease individual carriers’ profit. Keywords: Airline Alliances, Antitrust Immunity, Vertical Differentiation, Price Competition, Hub-and-Spoke Networks JEL Codes: D43, D49, L13, L29, L40, L93 Acknowledgements: I thank Stan Reynolds, seminar participants at The University of Arizona, and conference participants in Seattle and Madrid for helpful comments. I am solely responsible for any remaining errors and omissions. 1 Department of Economics, The University of Arizona, McClelland Hall 401, P.O. Box 210108, Tucson, AZ 85721; e-mail: bilotkac@u.arizona.edu 1 I. Introduction Consolidation or formation of international airline alliances is an important phenomenon currently reshaping the international airline industry. Airline consolidation can and does take various forms, from shared use of facilities at a single airport to agreements covering (and in effect uniting) large portions of partner airlines’ networks. Yet, the most noticeable feature of consolidating efforts between airlines is uniting of the alliance members’ networks, referred to as code-sharing. A code-sharing agreement between airlines A and B involves inclusion of flights, serviced by, say, airline A, into the airline B's schedule, and vise versa. This form of partnership allows airlines to jointly market each other’s flights, expand their networks, and sell seats on partner airline’s flights. While Doganis (2001) claims that code-sharing is little more than a kind of potentially unstable marketing alliance, it is common for the media to start talking about serious partnership between the carriers when they start (or even propose to start) uniting their networks and selling seats on each other’s flights. Also, this is typically the point where regulatory authorities step in to examine possible effects of a partnership between airlines. Formation of international airline alliances raises questions concerning effects of such partnerships on competition and welfare on the market. Answers to these questions are of great interest to both scholars and regulatory authorities. In general, the question regulators ask is not whether airlines should be allowed to cooperate, but rather how they should be allowed to do it. Possibly the most important issue is the granting of antitrust immunity (explicit right to jointly set fares) to alliance partners. For example, the problems with the code-sharing agreement between American Airlines (AA) and British Airways (BA), discussed below, were directly related to the regulators' concerns that the alliance thus formed would obtain market power on the largest London - US markets, which is an important factor, given that a significant share of transatlantic travel passes through London. The model developed in this paper proposes a different approach to examining airline consolidation, by departing from Cournot-type models, used in previous research 2 to address the issue, to a differentiated product Bertrand setting. This departure results in a model that allows a coherent formal comparison of price effects of airline alliances with and without the antitrust immunity, an important issue Cournot-type models have been able to address only indirectly. To date, the issue of welfare and competition effects of airline alliances has received some attention of scholars. The theoretical models of international airline consolidation include works by Park (1997), Brueckner (2001 a) and Brueckner and Whalen (2000). The common feature of the three models is that they all assume Cournottype competition. Also, Park assumes that alliance members equally share revenue from interline passengers. Brueckner and Brueckner and Whalen only model the cases of alliances where partner carriers are allowed to jointly set fares for interline trips (i.e., alliances with antitrust immunity). Park looks at the two categories of code-sharing agreements: complementary and parallel. The difference between the two is that, while the former does not involve overlapping partner carriers’ networks, the latter one does. The general findings of Park’s analysis is that while complementary alliance is likely to be welfare-increasing (due to removal of double marginalization present otherwise), the parallel alliance tends to be welfare-decreasing, as it reduces competition on routes, where alliance partners’ networks overlap. Brueckner (2001 a) models welfare effects of formation of a single alliance with antitrust immunity, where partner airlines operate simple overlapping hub-and-spoke networks. He finds that alliance with antitrust immunity will benefit interline passengers, but fares for travel between partner airlines hubs will increase. On the balance, Brueckner suggests such an alliance will be welfareincreasing. Brueckner and Whalen (2000) construct a model of competition between two international alliances with some horizontal product differentiation (through brand loyalty). However, the setup of that model only allows determining the impact of alliances on interline fares, since the network structure does not include hub-to-hub routes. Also, the model assumes antitrust immunity. None of the models discussed in the previous paragraph has allowed a coherent theoretical comparison of effects of alliances with and without the antitrust immunity, primarily because it is not very clear how to model the latter within the Cournot-type setups. Instead, researchers simply suggest that, since no explicit fare coordination is 3 allowed without antitrust immunity, double marginalization should persist. Thus, Cournot-type models conclude that code-sharing with antitrust immunity will lead to decrease in interline fares. Yet, no formal distinction between the cases of alliances without immunity and no alliances has been made. While some general arguments have been proposed to suggest the existence of forces2, which should make interline fares under code-sharing without immunity lower than in the case of no alliances, no coherent model giving such a result in Cournot-type setting has been offered. Empirical analysis of effects of international airline alliances has been offered by Park and Zhang (2000), Brueckner and Whalen (2000), and Brueckner (2003). All of these papers confirm that airline alliances benefit interline passengers by offering lower fares. Park and Zhang also find evidence for increasing market power of the alliance members at their hubs, even though they suggest that this effect is offset by cost savings that alliance brings about to result in lower fares for departures from those hubs. While finding that alliances decrease interline fares, Brueckner and Whalen fail to observe statistically significant increase in fares due to establishment of an alliance for non-stop travel on routes where such appears to decrease the number of competitors. Brueckner’s empirical research shows that antitrust immunity decreases fares for interline trips to the greater extent, as compared to the case of code-sharing without such immunity. Our model takes a different approach to analyzing international airline alliances in several dimensions. First, we use a more realistic model of the airlines transportation network, which mirrors that of the transatlantic market, around which major alliances are formed and compete (yet, the analysis can be applied to any arbitrary network). The demand for airline flights is cast as a vertical differentiation model, in which all consumers are willing to pay a premium for flights with fewer stops, other things equal. Competition between airlines offering flights with different number of connections is an important feature of international air travel. Another diversion from the previous literature is stepping away from quantity competition to price competition. 2 The primary such force referred to in the literature is the unanimity rule, required previously for setting of the IATA fares. However, Doganis (1991) states that unanimity has been largely abandoned in the 80s, which makes this argument less convincing, especially given that the empirical research uses data from late 90s. 4 The approach taken here allows us to directly model competition between alliances with and without antitrust immunity and compare the equilibria thus obtained to the one without alliances. Results of the analysis show that, unlike in the Cournot-type models, granting partner airlines antitrust immunity does not lead to additional gains to interline passengers, as compared to alliances without immunity. Thus, the differentiated Bertrand approach adopted in this paper yields different predictions concerning antitrust immunity, while keeping previous results regarding gains to interline passengers due to establishment of the alliance. It is also shown that an alliance with antitrust immunity leads to higher fares for travel between hub airports of the alliance members, also consistent with the previous results. In addition to that, we offer an argument for why airlines are inclined to enter alliances even though such may decrease profits of individual alliance member (thus, formation of two alliances is consistent with our model). The rest of the paper is organized as follows. Section II describes airlines’ consolidation efforts, with emphasis on the transatlantic market. Section III develops and analyses the model of price competition between alliances; cases of alliances with antitrust immunity, alliances without antitrust immunity, and no alliance case are considered separately. Section IV provides discussion of the model’s results, featuring arguments for why airlines form alliances even when this decreases profits of individual alliance members, as well as considering implications of our analysis for future research and competition policy. Section V concludes. Proofs of Propositions are in the Appendix. II. Airline Consolidation on International Markets The “fashion” for consolidation among airlines started in the second half of 1990s. According to Doganis (2001), over 500 various partnerships between airlines have been recorded in 1998. These alliances take various forms, and differ in terms of scope and (perceived) stability. Describing all possible forms of cooperation on international airline markets is not the purpose of this paper (especially after it was well done by Doganis). We will only take a brief look at the four major alliances that currently exist. The 5 common feature of all these partnerships is that all of them started with cooperation between a major US carrier and a European airline, each operating a hub-and-spoke network. Also, establishments of these partnerships coincided with further opening of the transatlantic market. In fact, signing of an “open-skies” agreement between the United States and the respective European country was a pre-requisite for approval of the codesharing agreement between the carriers. The first of the currently existing alliances started with a major code-sharing agreement between KLM Royal Dutch Airlines and the Northwest Airlines in 1993 (see, for instance, Economist, 2001, Transportation Research Board, 2000). This agreement covered most of the networks serviced by those two airlines, allowing for coordination of schedules and fares (backed by the antitrust immunity the alliance was able to obtain). Presently, KLM and Northwest form the core of a growing alliance, including such carriers as Continental Airlines (not including transatlantic flights of this carrier), and Air China. The core of the second alliance is formed by Lufthansa and United Airlines (the so-called Star Alliance). British Airways and American Airlines are at the core of the Oneworld alliance (total of eight airlines from Europe, Asia, North and South America, and Australia). However, American Airlines and British Airways were known to have problems trying to establish a comprehensive code-sharing agreement and obtain anti-trust immunity for their transatlantic routes3. The youngest of those alliances is the Skyteam group, core of which is formed by Delta Airlines4 and Air France (currently five airlines, with Aeroflot Russian International Airlines in the process of joining the team). Note that while alliances can consist of as many airlines as the alliance management deems appropriate, antitrust immunity is given (by the US Department of Transportation, in case a US carrier is involved5) to pairs of carriers within the alliance. On the transatlantic market, in addition to KLM – Northwest pair, antitrust immunity has 3 The problem the regulators saw was that proposed alliance between American Airlines and British Airways could effectively lead to those airlines establishing market power on some of the busiest and the most important transatlantic routes, like London to New York and London to Chicago. Eventually, a limited code-sharing agreement between the carriers was approved, yet no antitrust immunity was granted. 4 During the 1990s, Delta Airlines entertained the idea of entering into alliances with various European carriers, but these attempts were unsuccessful. Yet, the alliance with Air France appears to be (at least to the external observer) a serious commitment on part of the carriers involved. 5 I am not aware of antitrust immunity being granted to alliance groupings outside of international markets involving United States. 6 been granted to Lufthansa – United, United – SAS Scandinavian Airlines, American Airlines – Finnair and Delta Air Lines – Air France pairs. This means that in all of the major alliances there are pairs of carriers with ability to coordinate their fares. Finally, it is not as yet clear where alliances currently observed will lead to. One can say that to some extent airline industry currently offers a test to Porter's (1990) claim that "Alliances are frequently transitional devices. They proliferate in industries undergoing change and escalating competition, where managers fear that they cannot cope." Evidence to this effect has been mixed. On one hand, we have seen seemingly serious partnerships break down in a matter of weeks; on the other hand, stability and rapid development of the currently established world-wide alliances prompted some to suggest that they will in the future turn into major "mega-airlines" (Economist, 2001). In either case, understanding how consolidation between airlines works and influences economic welfare will help us answer some of the current and future competition policy questions in the airline industry. III. 1 Model Model Setup The purpose of this section is to develop a model of price competition between two alliances, as well as to analyze and compare properties of equilibria under three different scenarios. This sub-section provides the setup of the model, including description of the network, demand and airlines’ cost structure. Sub-section 2 analyzes properties of equilibrium in case of two competing alliances with antitrust immunity. Afterwards, a discussion of the equilibrium without cooperation between airlines is offered, followed by the analysis of price competition between two alliances without antitrust immunity. Finally, results of analysis under these different scenarios are compared and suggestions regarding the welfare impacts of alliances are made. We begin with description of the network, which is presented in the Figure below. 7 S3 S1 H2 H1 H3 H4 S2 Alliance I: airline 1 has its hub at H1 and airline 2 with hub at H2 Alliance II: airline 3 with hub at H3 and airline 4 with hub at H4 S4 Figure 1. Network structure This network is set up in such a way as to mirror the transatlantic market. If we suppose that H1 airport is Detroit Wayne Country International, H3 corresponds to Chicago O’Hare, and further assume that H2 corresponds to Amsterdam Schiphol and consider H4 to be Frankfurt airport, we will obtain a model of networks offered by Northwest – KLM alliance and the Star Alliance (the reader can choose specific spoke airports S1 through S4 from among the US and European destinations to complete the picture). Thus, we obtain a network of four distinct airlines (two on each side of the ocean). Each of the airlines operates a single-hub network. Airline 1’s routes are shown as solid lines; airline 2’s routes are represented as dashed lines. Thick solid and thick dashed lines denote routes, serviced by airlines 3 and 4, respectively. In the analysis that follows, two alliances are formed (airlines 1 and 2 form alliance I, while airlines 3 and 4 enter into alliance II), linking the end points on both sides of the ocean through hub airports of the carriers. It should be noted that we will apply the Bertrand model as an approximation to competition in the airline industry, even though Hendricks et al. (1999) find that hub-and- 8 spoke networks cannot be a long-run equilibrium in case of pure Bertrand type competition. Close examination of the networks US carriers have established since deregulation reveals that usually US carriers operate multi-hub networks6, which is not ruled out in the above mentioned paper as a possible result of Bertrand competition. Another issue not considered by Hendricks et al. is a possible premium associated with size of the network, which can also play some role in establishing the hub-and-spoke network consistent with price competition7. Thus, nothing seems to suggest that the network structure we observe on the market is inconsistent with price competition. The network structure that will be used in the model can be thought of as a general representation of the naturally occurring structure, which bears all major features of the latter and simplifies the analysis. Among other reasons for adopting price competition, the following can be stated. Some research has been done to determine whether competition in the airline industry is closer to Bertrand or Cournot model. Brander and Zhang (1990) conclude that there is Cournot type competition in the airline industry, but their conclusion stems only from the analysis of the non-stop flights on select duopolistic markets originating from the congested O'Hare airport. Neven, Roeller and Zhang (1998) provide the industry-wide analysis of the European market and conclude that the pattern is consistent with Bertrand competition. Some recent evidence suggests fierce price competition is very characteristic of the deregulated airline markets. For example, Busse (2002) provides an empirical analysis of price wars in the US airline industry, and discovers that over the time period the paper considers (1985-1992) price cuts by one airline were always matched by the competitors8. Besides, rather narrow observed profit margins in the industry are not consistent with the Cournot-type competition, which clearly predicts positive mark-ups. Note also that our network structure is different from those used in the previous research in the following important ways. First, unlike in Brueckner (2001 a), our 6 Actually, all major carriers on the US market operate networks with several hubs, and Southwest does not have a clearly identified hub. Single hub networks are served by some low-cost carriers not playing any role on the transatlantic market, such as Frontier Airlines, Sun Country Airlines and JetBlue. 7 The issue of whether or not these premiums can play a role will be discussed in the next section. 8 I realize that this evidence could be attributed to the “kinked demand curve” theory, but price wars in the industry appear to be a too common phenomenon, which should weaken this suggestion, as the “kinked demand curve” hypothesis suggest certain degree of price stability, enforced by the fear that competitors will slash their prices in response to your price cut. 9 network allows for two alliances; thus, we can explore the issue of competition between airline partnerships. Second, even though network structure in Brueckner and Whalen (2000) does allow for two alliances, it does not include routes between hub airports (in their model all airlines operate out of a single hub). In summary, unlike previously analyzed networks, ours allows to look at impact of airline alliances on all possible kinds of routes. Demand is modeled as follows. Consider a representative consumer, choosing among the available ways to fly between the two cities. Without loss of generality, consider a case, where the only options available to the consumer involve travel using one or the other of the two alliances. In this case, a consumer using alliance J on a market between cities i and j (all this analysis is easily applicable to the case with no alliances) obtains the (indirect) utility: VijJ = θ ij − (αpijJ + βnijJ ) (1) where pijJ is the fare charged by airline(s) in alliance J; nijJ is the number of segments9 to be flown when traveling with alliance J on a city-pair market under consideration; θ ij is consumer’s reservation utility, which is a random variable with cumulative distribution function F (θ ij ) ; α and β are positive parameters (without loss of generality, α can be normalized to one). Also assume that the (indirect) utility of an outside alternative (not flying) is equal to zero. Note that implicit in the indirect utility function above is the vertical differentiation of the product: other things equal, flights with fewer segments are strictly preferred to flights with more segments. Facing two competing alliances on a city-pair market, a consumer will prefer services of alliance J over those of alliance K if VijJ ≥ 0 and VijJ > VijK (in case these indirect utilities are equal, we will assume that a consumer will be equally likely to choose service of either of the two alliances). It can be easily seen that VijJ > VijK implies: 9 A flight segment is defined as a take-off and landing. 10 pijJ < pijK + β K ( nij − nijJ ) α (2) Given that θ ij is a random variable with cumulative distribution function F (θ ij ) we obtain the following expression for the probability of consumer receiving the nonnegative indirect utility given that flying with alliance J is preferred to flying with alliance K. ( ) ( P V ijJ ≥ 0 = 1 − F αp ijJ + βn ijJ ) [ ] (3) in a specific case where θ ij is distributed uniformly over the support θ ,θ we can write the above expression as: ( ) P V ≥ 0 = 1− J ij ∫ αpijJ + βnijJ θ θ − αpijJ − βnijJ dθ = θ −θ θ −θ (4) Assuming two alliances competing for N potential consumers on the city-pair market ij, the expected demand alliance J will face under the price competition with product differentiation can be written as: ⎧ ⎪0 ⎪⎪ qijJ = ⎨ 12 N 1 − F αpijJ + βnijJ ⎪ ⎪ N 1 − F αp J + βn J ij ij ⎪⎩ ( ( ( ( )) )) β K (nij − nijJ ) α β if pijJ = pijK + (nijK − nijJ ) α β if pijJ < pijK + (nijK − nijJ ) α if pijJ > pijK + (5) Note that in case nijK = nijJ the textbook Bertrand competition case obtains. ( ( Now let q~ij = N 1 − F αpijJ + βnijJ )) be the total expected demand on a city-pair market ij. β pijJ ( pijK ) denote the price at which pijJ = pijK + (nijK − nijJ ) . Using this new Further, let ~ α 11 notation, we can now write the following expression for demand faced by alliance J on a given city-pair market. ⎧0 ⎪ qijJ = ⎨ 12 q~ij ⎪q~ ⎩ ij if pijJ > ~ pijJ ( pijK ) if p J = ~ pJ ( pK ) (6) if p < ~ pijJ ( pijK ) ij J ij ij ij One can easily verify that (6) will be true irrespective of whether alliance J offers travel with more, fewer, or the same number of stops than does alliance K. As a final touch, let π ( pijJ ) denote the difference between pijJ and ~pijJ ( pijK ) for the cases where nijJ < nijK . This difference, which will always be positive, will be called the premium for travel with less stops. This completes general description of the demand side of the market. The main assumptions related to the cost structure over the network are constant returns to scale and separability of costs across the segments of the network. Note that Winston (1985) states that one of the general conclusions from research on cost structure of airlines is that the industry is characterized by constant returns to scale. Further, for the purposes of tractability of the analysis, some cost symmetry assumptions will be introduced. First, costs of carrying a passenger between hubs across the ocean are assumed the same for all carriers: O C H1 1H 2 = C H2 1H 2 = C H3 3 H 4 = C H4 3 H 4 = C HH (7) where the superscript O means ‘overseas route’. Similar symmetry will be assumed about costs of flying between ‘domestic’ hubs10: D C H1 1H 3 = C H2 2 H 4 = C H3 1H 3 = C H4 2 H 4 = C HH 10 (8) Note that ‘domestic’ refers more to the side of the ocean than to a country. That is, Amsterdam – Frankfurt route will be considered ‘domestic’ for our purposes, even though the cities are actually in different countries. 12 Finally, we will assume the same costs for non-stop flights between any of the hubs and D any of the spokes (we will denote this cost through C SH ). Note that it is sufficient for all the analysis that follows to assume that cost of carrying a passenger on a non-stop flight between a hub and a spoke on each side of the ocean (that is, it is sufficient to assume that all such costs are the same across the European routes and across the US routes, while European cost need not be equal to the US cost), but the simplified assumption adopted here does not change the results in any fundamental way. Adopting these assumptions, we can write the airline’s total cost function as: ( D D C i = 2C SH * QSH ) +C i D HH ( D * QHH ) +C i O HH ( O * QHH ) i (9) It must be noted that quantities in (9) refer to the total traffic on the segments of the network, and not to the number of passengers traveling between particular cities. 2 Alliance Competition Equilibrium with Antitrust Immunity The first scenario to be considered is the one of competition between two alliances, with both competitors enjoying antitrust immunity. This means that alliance members will jointly set fares for the routes, on which their networks overlap (which includes all the overseas trips). To make the problem more tractable for the reader we will assume that alliance members will equally divide their traffic on the routes between hubs of the two carriers forming an alliance. Also, revenue, obtained by alliance members on overseas spoke-to-spoke routes and on routes from domestic spokes to overseas hub of the competing alliance (the routes, travel on which actually requires change of carrier) will be equally divided by the two carriers. Another assumption in line with previous literature is that the travel from domestic hubs to overseas spokes will not require change of the carrier within an alliance. These assumptions provide a little simplification to the cumbersome notation that follows. For the current scenario, we can identify two parts of the airline’s revenue function, depending on whether the prices are set independently by the carrier or jointly with an alliance partner. Thus, for a carrier i within an alliance J the total revenue will be given by: 13 TRi = R i + R J (10) where: R J = p SJD SO 2q Si D SO + p SJ + p SJ i OHD 2q Si i OHD J DHO 2q Si J DHO + p SJ K DHO q Si K D HO + p HJ J H J q Hi J H J + p HJ K H J q Hi K H J R i = p Si D S D q Si D S D + p Si D i DHD O 2q Si i DHD D O D + p Si j DHD O 2q Si D j DHD (11) O + p Hi J H K q Hi J H K D D D (12) D Obviously, the airline’s total profit will be given by the difference between (10) and (9), and demands for individual routes will be determined according to (6). Subscripts and superscripts in (11) and (12) have the following meaning. Subscript S stands for 'spoke', subscript H for 'hub'. Subscripts D and O stand for 'domestic' and 'overseas', respectively. Uppercase J denotes alliance to which airline belongs, while uppercase K - other alliance; lowercase j denotes airline belonging to a different alliance, but operating a domestic hub. Thus, for example, q Si K DHO would be read: 'airline i's traffic from a domestic spoke to an overseas hub operated by a member of the competing alliance'. The first term in (11) includes two of the four overseas spoke-to-spoke routes, and the third term includes one of the two respective routes, due to equal division of revenue on those routes between alliance members. First, let us see whether the problem can be simplified by deleting some routes, where traffic will be zero in equilibrium. This can in fact be done, as suggested by the following proposition. Proposition 1: Under price competition with no capacity constraints, vertical product differentiation and cost symmetry as defined above, if nijJ < nijK , then alliance K will have zero traffic on the route. Further, in equilibrium for each alliance there will be positive mark-ups for the routes between its hubs, as well as between any of its hubs and any of the spokes. 14 The proof is in the Appendix. From Figure 1 it is evident that routes mentioned in Proposition 1 are the ones where each alliance provides travel with fewer stops and will therefore make positive profit. For the routes, where both alliances offer flights with the same number of connections, the classical Bertrand result will apply (owing to the cost symmetry), as generalized in the following Proposition, which, together with Proposition 1, complete description of price competition equilibrium between two alliances with antitrust immunity. Proposition 2: All spoke-to-spoke markets and all markets for travel between hubs of different alliances will be equally divided among the alliances, provided the above cost symmetry assumptions are satisfied. Again, the proof is in the Appendix. Before we consider other scenarios, let us review a simple case of totally symmetric cost and demand structure to see what the profit of a single alliance member will be. Assume that average cost for each flight segment is c across the network (that is, cost of a trip involving n segments is cn) and premiums for travel with less stops are kπ , where k = nijK − nijJ , in case alliance J is offering travel with fewer stops. Proposition 2 implies that in equilibrium, if nijJ = nijK , then pijJ = pijK = nc , so no positive profit will be made on those routes. Consider the cases where nijJ < nijK . On those routes the price will be set at the level pijJ = cnijK + kπ = c(nijJ + k ) + kπ = cnijJ + k (c + π ) . So, the profit airline j will get from each passenger on such route will be equal to k (c + π ) . The specific routes where profit will be positive are the following: 1) Domestic spoke - domestic hub. The total profit an airline j from an alliance J will make on such routes will be 2(c + π )q SjD H D (where q SjD H D is the expected demand, as defined by (6)). The coefficient 2 represents two such routes. Note that here k is equal to one. 15 2) Domestic spoke - overseas hub. The profit here is again 2(c + π )q SjD H O (k is equal to one, as before). 3) Domestic hub - overseas hub of the same alliance. The profit on this route will be just (π + c)q HJ D H O . The constant here is equal to one because, while the price charged will be pijJ = 3c + 2π (note that here k is equal to two), the airline will only serve half of the total traffic on this route. Domestic hub to overseas spoke routes are not considered here, since according to what has been previously assumed those passengers will be carried by the other alliance member. So the total profit of airline j from alliance J under these circumstances will be: j Π Alliance = (π + c)[2q SjD H D + 2q SjD H O + q HJ D H O ] (13) Or, we can also write this in terms of the total demands: j Π Alliance = (π + c)[2q~SD H D + 2q~S D H O + q~H D H O ] 3 (14) Price Competition Equilibrium without Alliances In order to assess effects of emergence of airline alliances on fares and traffic on the market in question, we need to see what the situation will look like when alliances are absent, and all four carriers compete with each other. Now the fares are determined not within an alliance but separately by each carrier. Analyzing the no-alliance equilibrium requires imposing certain assumptions on fare setting on the routes, requiring change of carrier. Since there is no cooperation between airlines, a customer on such routes will be required to purchase separate tickets for travel within the network of each of the airlines, included into his itinerary11. The 11 For example, when traveling from spoke 1 to spoke 3 using airlines 1 and 2, the customer will have to either purchase a ticket for travel from spoke 1 to hub 2 on airline 1, and then another ticket from hub 2 to spoke 3 on airline 2; or, the customer can purchase the ticket for travel from spoke 1 to hub 1 on airline 1, and continue on another ticket from hub 1 to spoke 3 on airline 2. 16 question is how airlines will treat passengers, for whom travel within the carrier’s network is only part of the journey. Doganis (1991) indicates there essentially are two ways for airlines to deal with the interline passengers in case the actions are not coordinated. The airline providing a portion of the interline traffic on the ticket sold by a different carrier can specify the portion of total fare it wishes to receive to agree to carry such a passenger. This arrangement is termed pro-rating. One can see that such an arrangement does implicitly assume some degree of coordination between the carriers involved. According to Brueckner, and Bamberger et al., such arrangements are taking place in cases when codesharing partners do not have antitrust immunity, which would allow them to charge a single fare for the interline trip. The second approach to setting interline fares is for the airline to charge a corresponding full fare for its portion of the journey, that is acting as if it were not able to distinguish interline passengers. Besides, airlines are often unable to sell tickets for travel to the end points outside of their network (or, network of the respective alliance). Thus, for travel between some end-points on some airlines one might have to buy two separate tickets, whether from the airlines or through a travel agent. The point is that in case there are no alliances and no coordination of interline fares is taking place, we can work with the assumption that carriers will not distinguish interline passengers from those traveling entirely within their networks. In this case, an airline’s revenue function will be of the form: TRi = pSi DSD qˆ Si DSD + pSi +p i HDi HO qˆ i HDi HO i D HD +p 2qˆ Si i HDi HDj i D HD qˆ + pSi i HDi HDj j D HD +p 2qˆ Si i HDj HO j D HD qˆ + pSi i HDj HO D HO 2qˆ Si D HO (15) Note several things in which this revenue function is different from the one for the alliance case. First, the fares entering the function are now determined by the airline itself, and not by the alliance. Second, q̂ is different from q in case of the alliance equilibrium, since q̂ also includes passengers continuing their travel on other carriers after using service of airline i (or, passengers, continuing travel on airline i after using services of other carriers). Third, demand for interline trips will be determined as a 17 function of the total price (which is just the sum of prices of different carriers for separate portions of the journey), and a consumer will have more than two options to choose from; yet, this does not affect the final results in any fundamental way. The equilibrium for the case of no alliances is summarized in the following Proposition. Proposition 3: For the case of price competition without alliances, assuming the demand and cost symmetries as above, the following will be true: a) All non-stop hub-to-hub routes will be equally divided by airlines offering service between the respective hubs, and carriers will earn normal profit; b) Domestic spoke-to-spoke markets will be equally divided by servicing airlines and carriers will earn normal profit on those markets; c) All traffic on domestic spoke-to-hub markets will be performed by an airline operating the hub, and this carrier will earn positive profit on the route; d) All traffic on domestic spoke to overseas hub markets will be performed by an airline operating the domestic hub and offering travel with less connections; the carrier will earn economic profit on the route; e) Overseas spoke-to-spoke markets will be equally divided between the airlines, but fares on those market will be higher than under the alliance competition equilibrium and all carriers will make positive profit; f) The division of traffic on one-stop hub-to-hub markets is not determined unambiguously, but carriers do not earn positive profit on those markets. Proof is included into Appendix. Let us compare the case of no alliances to the alliance competition with antitrust immunity. Results presented here suggest that creation of alliances increases fares for travel between hubs of the alliance partners, decreases fares for travel on the international spoke-to-spoke markets and leaves all other fares unchanged. This basic conclusion is the same as reached by Brueckner (2001 a). It is reasonable to suggest, in fact, that Cournot competition over our network would lead to similar results, when it comes to comparing no alliance equilibrium to that of competition between two alliances with antitrust immunity (even though the analysis itself would likely be more complicated). In both cases, alliances lead to lower interline fares due to removal of double marginalization, but the sources of the double marginalization in this and Brueckner’s models are different. Also, approach employed here can be more easily applied to networks of any configuration to make predictions on the movement of fares and traffic volume as a result of proposed partnerships. 18 Let us now return to our hypothetical example developed in the previous subsection, to determine individual carrier’s profit in equilibrium without alliances, as well as to compare it with that under the previously studied scenario. The routes on which an airline j will be making positive profits are: 1) Domestic spoke - domestic hub. The total profit an airline j will make on such routes will be 2(π + c)q~S D H D . The coefficient 2 represents two such routes. 2) Domestic spoke - overseas hub to which an airline offers service. The profit here is again 2(π + c)q~S D H O 3) Domestic spoke - overseas spoke. The total profit on these routes will be 2(π + c)q~SD SO . The airline will charge the fare equal to 2c + π to those passengers on this market using an airline for only one segment of their journey, and 3c + π to passengers using airline's services for two segments of their journey. In either case, the per passenger profit will be equal to π + c and each of the airlines will be serving half of the total traffic on the domestic spoke to overseas spoke market. Then, the total profit on an airline in the no alliance equilibrium will be: j Π NoAlliance = 2(π + c)[q~SD H D + q~SD H O + q~S D SO ] (16) and further: j j Π Alliance − Π NoAlliance = (π + c)[q~H D HO − 2q~S D SO ] (17) or, in the more general case of N spokes on each side of the ocean: j j Π Alliance − Π NoAlliance = (π + c)[q~H D H O − Nq~S D SO ] 19 (18) Note that our model allows us to easily incorporate hub-and-spoke networks of any size (not just consisting of two spokes on each side of the ocean) into our analysis. 4 Alliance Competition Equilibrium without Antitrust Immunity The final scenario to be considered is the one of competition between two alliances without antitrust immunity. We assume in this sub-section that two alliances are formed (i.e., partner airlines’ networks are connected through code-sharing agreements), while none of the alliances obtains antitrust immunity (i.e., alliance members are not allowed to set fares jointly). This scenario will be modeled by relaxing the critical assumption of the no alliance case that carriers are unable to distinguish between passengers traveling within their network. That is, instead of charging on-line and interline passengers the same fares for travel within their network, each carrier will now select separate fares for passengers traveling within their network, and those continuing their trips using services of the alliance partner. The key distinctions between this scenario and the one with the antitrust immunity are the following. First, interline fares are not set by alliance members cooperatively, but rather are composed as the sum of sub-fares, charged by individual alliance members. And second, alliance members are not allowed to cooperate in setting fares for trips between their hub airports. To analyze properties of price competition equilibrium under this scenario, previously obtained results can be employed. First, since alliance partners are not allowed to coordinate their actions on routes between their hubs, the result from part (a) of Proposition 3 applies. Also, results from parts (b) through (d) from the same Proposition hold in this scenario, as does result from part (f). All this is true, since there are no institutional differences between the scenario, analyzed in this sub-section, and the case of price competition without alliances. These result suggest, at this point, only one difference between alliance competition equilibria with and without antitrust immunity: fares for non-stop travel between hubs of alliance members will be higher under the scenario with antitrust immunity. Thus, the only routes left are the overseas spoke-to-spoke routes, travel on which will require change of carrier. It can in fact be shown that in this case the fares set for interline trips will be the same as the ones observed under the alliance competition 20 framework with the antitrust immunity. In fact, even though no explicit coordination of fares is allowed, all carriers will still have strong incentive to undercut their sub-fares for the interline trips to the marginal (and average, in our case) cost level. Indeed, if we consider a situation, where sub-fares are set at the level above average cost in such a way that the total interline fare is the same for both alliances, any fare undercutting by any of the airlines (provided the resulting fare is still at or above the airline’s average cost) will channel the entire traffic on a given overseas spoke-to-spoke route through the network of the alliance, of which the undercutting airline is a member. That is, the logic of fierce price competition applies to this case. Naturally, since both alliances offer services with the same number of connections and also have the same costs, this undercutting of subfares will lead to average (and marginal under the cost structure imposed here) cost pricing and no economic profit for airlines. Thus, interline fares in case of alliance competition equilibrium will be the same, regardless of whether carriers have the antitrust immunity. Finally, let us return to the hypothetical example we worked with previously to analyze individual carrier’s profit under the scenario of alliance competition without antitrust immunity. Note that under this scenario positive profits will be made only on the following routes: 1) Domestic spoke - domestic hub. The total profit an airline j will make on such routes will be 2(π + c)q~S D H D . The coefficient 2 represents two such routes. 2) Domestic spoke - overseas hub to which an airline offers service. The profit here is again 2(π + c)q~S D H O Which yields total profit under this scenario, equal to: j Π Noimmunity = 2(π + c)[q~S D H D + q~S D H O ] which clearly yields: 21 (19) j j Π Alliance − Π Noimmunity = q~H D H O (π + c) (20) j j Π NoAlliance − Π Noimmunity = 2q~S D SO (π + c) (21) and: That is, if we have two alliances with no antitrust immunity, price competition between them will yield the lowest profit to an individual carrier, as compared to both other scenarios, considered here. 5 Concluding Comments Analysis of the three different scenarios can allow us to make the following conclusions concerning the effect of establishment of alliances on fares charged on different routes. First, establishment of alliances clearly benefits interline passengers, whether or not carriers involved obtain antitrust immunity. This conclusion mirrors results of the previous theoretical and empirical research. Second, the extent of the benefits to interline passengers does not appear to depend on whether or not alliance partners enjoy antitrust immunity. This conclusion is different from results of Cournot-type competition models. While both this model and the previously developed ones rely on removal of double marginalization due to cooperation between carriers, Cournot type models suggest that absence of antitrust immunity only results in partial removal of double marginalization. Whereas under price competition formation of two competing alliances completely removes rents, previously extracted from interline passengers, regardless of whether or not allied carriers are allowed to coordinate setting of fares. Third, establishment of alliances with antitrust immunity makes passengers on the routes between hubs of alliance members worse off12, whereas this adverse effect is absent for alliances without antitrust immunity. 12 In fact, establishment of Northwest – KLM alliance did not raise many such concerns, since this alliance actually created non-stop flights between Amsterdam and Northwest’s hub airports (Detroit, Minneapolis and Memphis), thus creating benefits for some passengers, who previously had to make connecting flights. 22 The table below describes main findings of the analysis, paying specific attention to changes that occur as we move from the no alliance case to competition between alliances with and without antitrust immunity. Table 1. Main findings of the analysis. Route No Alliances (Baseline Scenario) Changes due to Establishment of Alliances without Antitrust Immunity Changes due to Establishment of Alliances with Antitrust Immunity Domestic Spoke Domestic Hub (e.g., Spoke 1 - Hub 1) Monopolized by the airline opera ting the hub No change No change No change No change No change No change No change No change Traffic increases, fares decrease; no positive mark-ups Traffic increases, fares decrease; no positive mark-ups No change Traffic decreases, fares increase; allied carriers earn positive mark-ups No change No change Domestic Spoke Overseas Hub (Spoke 1 – Hub 2) Domestic Spoke Domestic Spoke (Spoke 1 – Spoke 2) Domestic Hub Domestic Hub (Hub 1 – Hub 3) Domestic Spoke Overseas Spoke (Spoke 1 – Spoke 3) Monopolized by the domestic airline operating the non-stop route from its hub to the overseas hub Divided by the two domestic airlines. No positive mark-ups Divided by the two domestic airlines. No positive mark-ups Equally divided by all airlines. However, there are positive mark-ups, accruing to each of the airlines providing portion of service on this interline trip Equally divided by the airlines providing such non-stop service. No positive mark-ups Overseas hub-to-hub routes, on which non-stop service is possible (Hub 1 – Hub 2) Overseas hub-to-hub No positive mark-ups. routes, on which no nonDivision of traffic between stop service is possible airlines not clear (Hub 3 – Hub 2) Note that establishment of alliances with antitrust immunity will decrease traffic on the overseas hub-to-hub routes operated by the alliance partners. But it does not necessarily imply that total traffic on that segment of the network will decrease. Total traffic can change in either direction, depending on the magnitude of decrease in the number of passengers traveling between hubs of the alliance members, relative to the increase in the number of interline passengers, which will use this segment of the network as part of their itinerary. 23 Regarding welfare impact of establishment of alliances, the following general conclusions can be made. Since establishment of alliances without antitrust immunity decreases fares on some routes, leaving all other fares unchanged, we can say that such development will be welfare-increasing, even though airlines are not likely to be willing to enter into such partnerships. Welfare impact of alliances with antitrust immunity (as compared to the case without alliances) is ambiguous. However, we can suggest that such alliances will be more likely to increase total welfare, the larger the overseas spoketo-spoke markets are relative to the market for travel between hubs of alliance partners. If we consider actual cases from the transatlantic market, recall that proposed alliance with antitrust immunity between American Airlines and British Airways was eventually stopped by the regulators due to fears that the carriers would obtain dominant position on London – New York and London – Chicago markets. That is, it was believed that potential losses to consumers on markets between hubs of the proposed alliance partners would not be offset by potential gains to interline customers. Further, on being denied the antitrust immunity American Airlines and British Airways decided not to enter into a code-sharing agreement at all, which appears to be a wise choice according to our model. Second case concerns the Northwest – KLM alliance. This partnership did not meet much resistance from regulators. Indeed, traffic on Amsterdam – Detroit and Amsterdam – Minneapolis routes is rather small, so possible losses to passengers on these routes are more likely to be offset by gains to interline passengers. Further, Northwest – KLM partnership actually created non-stop services between KLM and Northwest hubs, so it can even be claimed that passengers on these hub-to-hub routes lost very little if at all from this development. 24 IV. Discussion and Implications of the Model's Results This section discusses implications of the model, developed in the previous section of the paper. We begin by considering a seeming paradox that comes from (18). Entering the international alliance can reduce carrier’s profit (provided two alliances are present). The next subsection establishes that it is optimal for carriers to act so as to form two alliances and for each alliance to seek antitrust immunity. We also outline implications for research and antitrust policy, consistent with the model developed in this paper. 1 Carriers’ Incentives to Form International Alliances Result (18) above suggests that, when two alliances compete with each other, there is a possibility that a carrier’s profit will be reduced as a result of entry to the alliance13. Moreover, the possibility that the profit will decline is higher the larger the network the carrier has to offer on its side of the ocean. And from Section II we will notice that at the core of all of the airline alliances are the big network carriers. This fact obviously demands explanation. Several explanations to the above mentioned empirical fact can be offered. The first explanation that comes to mind is related to the economies of traffic density. This argument suggests that by increasing traffic on the transoceanic spoke-to-spoke routes an airline will be able to utilize its capacity more fully and thus decrease average cost of carrying passengers. This can be true, and it has been noted as a reason (and in some cases – the reason) for entering an international alliance. However, we need to find a justification, consistent with our model’s assumption. Another possible explanation relates to other dimensions of the product differentiation, not captured by the model. There can be some other premiums, associated with the alliance travel. For example, all alliances (in fact, all airlines) offer frequent flier programs. Establishment of alliance expands the network, over which frequent flier miles can be collected and redeemed, thus making allied frequent flier program more attractive to customers. Our model might also have failed to consider the 13 Further, entering alliance without antitrust immunity definitely leaves the carrier worse off, when two such alliances compete. 25 premium for seamless travel: when choosing between the two airlines offering the same fare you will prefer the one that checks your luggage to the final destination to the one that does not. However seemingly appealing, the above-described premiums are not convincing arguments. If the issue were just in the scope of the frequent flier programs (seamless travel), the carriers could simply unite their frequent flier programs (sign a trough luggage-checking agreement), and not effectively unite their networks, putting their profits at risk. Yet, there is no need to consider any additional premiums to show that it is individually rational for each carrier to enter an alliance with an overseas airline to the hub of which the airline under consideration offers non-stop service, as well as to seek antitrust immunity for such an alliance. Consider a simple game played between two airlines on one side of the ocean: airlines 1 and 3. Without loss of generality, we will work with the same hypothetical example as before. Suppose that airline 1 is considering an alliance with airline 2 and airline 3 is considering an alliance with airline 4, with both pairs of carriers seeking antitrust immunity for their partnerships14. The idea of the analysis that follows is that payoff of a carrier within an alliance depends on whether or not its competitor on the domestic market entered an alliance with the other overseas carrier. That is, there is a clear case for setting up a simple game between, for example, airline 1 and airline 3. Each of the airlines can either enter the alliance (and seek immunity) or stay away from the alliance. The payoff matrix of the game can be written as follows: Enter Alliance Airline 1 Stay Away Airline 3 Enter Alliance Stay Away 1 3 1 Π Alliance Π Alliance Π Allied Π 3NonAllied Π 1NonAllied 14 Π 3Allied Π1No Alliance Π 3No Alliance It can be easily shown that entering into alliance without the antitrust immunity is strictly dominated by entering into alliance and seeking antitrust immunity. Profit of a member of the ‘immune’ alliance will be greater than that of a member of the alliance without immunity by the amount the former makes on the route between hubs of the two alliance members, no matter what the other player does. See (20). 26 j j Where Π Alliance and Π No Alliance are as calculated before. The terms not defined and which j j will need to be explained are Π Allied and Π NonAllied . The former corresponds to the payoff of the carrier which entered an alliance provided the other player remained non-allied. The latter is the payoff of the non-allied carrier provided the other player entered the international alliance with a respective overseas airline. Let us see what those payoffs are. j j To calculate Π Allied and Π NonAllied , we need to determine what will happen when a single alliance is formed. Suppose that airline 1 enters into an alliance with airline 2. The first effect of such an alliance is the monopolization of the route between hub 1 and hub 2. As shown before, on that market the alliance will be able to charge the fare of up to 3c + 2π dividing the traffic between the two allied carriers. The other routes to consider are overseas spoke-to-spoke routes. Here the alliance is able to set a single fare, which will allow it to effectively attract all of the traffic on those routes15. As shown above, without an alliance, the fares on the overseas spoke-to-spoke routes are equal to 5c + 2π , with each of the airlines making a premium of π + c on half of the traffic, making a single carrier’s profit from all of such routes equal to 2(π + c)q~SD SO . The alliance partners can thus easily set the fare equal to 5c + π 16, attract the entire traffic on the market, and allow each carrier to extract the average profit of 0.5π + c from each passenger. The total alliance member’s expected profit across the four markets is ~ 2(π + 2c)q~S D SO > 2(π + c)q~S D SO , with the traffic increasing due to the lower fare. Note that ~ q~ is different from (to be more exact – larger than) q~ . Obviously, the non-allied carrier loses its profits from the overseas spoke-to-spoke markets. Then, we can write the j j following expressions for Π Allied and Π NonAllied : ~ j j Π Allied = 2(π + c)[q~S D H D + q~S D H O + 0.5q~H D H O ] + 2(π + 2c)q~S D SO > Π No Alliance 15 (22) In fact, there was an indication that the Northwest – KLM alliance did end up attracting increasingly more traffic on the transatlantic market, directing it through their major hubs. This fact did play some role in granting antitrust immunity to further alliances on the market (US Department of Transportation, 2000). 16 Of course, nothing precludes the alliance to set the fares at the level of 5c + 2π − ε , but the actual level of fares is not crucial for our analysis here. 27 j j Π NonAllied = 2(π + c)[q~SD H D + q~S D H O ] < Π No Alliance (23) Furthermore: j j j Π NonAllied < Π Alliance < Π Allied (24) Once we have these relationships set up, we can easily see that ‘Enter Alliance’ strategy strictly dominates the ‘Stay Away’ strategy. Note that here ‘Enter Alliance’ strategy involves alliance with immunity, and a member of alliance with immunity obtains higher profit than does a carrier within the alliance without immunity, no matter what the other player does. Moreover, the larger the carriers involved, the larger their payoffs from entering the alliances, conditional on other airlines remaining non-allied. Therefore, it is individually rational for each of the airlines to form alliances with the respective overseas j j , airline, and to seek antitrust immunity for their partnership. When Π Alliance < Π NoAlliance this game is structurally equivalent to the prisoners’ dilemma. 2 Implications for Future Research and Antitrust Policy This subsection considers implications of our model for future research and antitrust policy. In fact, a lot of work remains to be done before artificial barriers, still governing most international airline markets are relaxed to allow market forces to govern behavior of firms. As deregulation of international aviation continues, importance of the relevant research will increase. The model presented in this paper is one of the first steps towards analyzing one of the phenomena that resulted from relaxing some of the barriers. Our model is simple, and a number of extensions can be suggested. One line of research could consider the possible extensions of the analysis presented in this paper, which will involve relaxing the basic assumptions of the model. The first obvious ramification would be to consider capacity constraints and other entry barriers. Yet, relaxing this assumption will immediately lead to the Bertrand – Edgeworth type of competition and is very likely to render the model intractable. Another way to consider the entry barriers is 28 to take a closer look at airport congestion. Some work has already been done in this area (Brueckner, 2001 b, 2002, Borenstein, 1989). In fact, the number of take-offs and landings that a runway can service within a given time period is limited, which is a substantial entry barrier, especially in congested airports during peak hours. Another possible direction of theoretical and empirical research would be identification and incorporation of other parameters, by which the airline services can be differentiated. One could try to identify what other possible premiums consumers are willing to pay for better service; also, one can determine what characteristics of the airline service do not play any important role, thus defining services on which some airlines possibly only waste money, and for which consumers are not really willing to pay more, or those, which would be more likely to deter an average consumer from using services of an airline (e.g., allowing smoking on board17). Some premiums could be associated with the frequent flier programs, but the question of importance of those premiums in strengthening the possible market power of alliances is open. Other implication of our model for the future research concerns the treatment of competition. Different competitors may have different impact on fares, depending on the number of stops they offer relative to the number of stops offered by a given carrier. Of course, for a time-sensitive customer duration of the journey is more important than the number of connecting flights, but more connecting flights usually implies longer trip. Finally, we briefly examine implications of our results for competition policy. The most important issue here is whether international alliances should be given (or in some cases, whether they should have been given) antitrust immunity. Our analysis (as well as previous research) shows that antitrust immunity can be welfare-decreasing on the hub-to-hub routes, but increases welfare (by lowering fares and increasing traffic) on the interline spoke-to-spoke routes. Generally, this model will predict that alliances without antitrust immunity produce higher overall welfare gains than do those, which enjoy such immunity, if the latter produce overall welfare gains at all. Thus, one would suggest that giving antitrust immunity to airlines is not going to produce any benefits to interline passengers beyond those obtained when airlines connect their network through code- 17 When Aeroflot Russian International Airlines prohibited smoking on its transatlantic flights in 2002, this move increased the number of airline’s passengers on those routes by about one third. 29 sharing. Yet, our analysis also shows that airlines might not be willing to enter into alliances without antitrust immunity, since such are more likely to decrease their profits. Hence, even though antitrust immunity is not the first-best policy here, it may nevertheless have been (and remain) necessary, as otherwise carriers could have been discouraged from forming partnerships they did. Yet, if antitrust immunity should be granted in the future, it should be done for those partnerships between carriers, which involve thin hub-to-hub markets. Also, as indicated above, antitrust immunity can be justified where it prompts alliance members to create non-stop services between their hubs. It is possible, for example, that the recently granted immunity to American Airlines and Finnair would create non-stop flights between Helsinki and one of American Airlines’ hub airports18, if the carriers are successful in channeling their traffic through these hubs. Other issues to consider when deciding on antitrust immunity are presence of other competitors on the same route, possibility of one-stop competition (or in the more general sense, competition with more connections), and market share of the proposed alliance partners. Take the case of the proposed alliance between British Airways and American Airlines. This prospective partnership raised concerns over the possible dominant position of the carriers on London – New York route. On one hand, one-stop competition on this route is not very likely, since it will involve significant increases in flight duration, and the current share of British Airways and American Airlines on that market is rather high. On the other hand, there are other non-stop competitors on that market. The general conclusion from the above paragraphs is that proposed alliances must be considered on a case by case basis, taking into account the specific network structure of the partner airlines, as well as the actual and potential competition on the routes involved. With this respect it may be interesting to theoretically examine the effects of the possible alliances between the US carriers (note that this model allows us to extend the logic of our analysis to networks with different structures, as noted above). Another issue that warrants further investigation is the one of differences in effects between the 18 In fact, Finnair opened non-stop service between Helsinki and Miami, after this paragraph was originally written. 30 code-sharing agreements with and without the antitrust immunity. At this stage we can say that there are considerable possible welfare gains from consolidation of airlines, but welfare losses can follow if we do not consider each proposed case carefully, taking into account specifics of the networks involved. V. Concluding Comments This paper develops a new model of competition between the international airline alliances, expanding the network structure first proposed by Brueckner and departing from Cournot to a differentiated Bertrand setting. In the model there are two international alliances, each comprised of two airlines with hub-and-spoke networks, engaged in price competition with the product being vertically differentiated by one parameter. Other things equal, all consumers prefer flights with less stops to flights with more stops. Three different scenarios are considered: competition between alliances with antitrust immunity, competition between alliances without antitrust immunity, as well as the case with no alliances. Results of the analysis show that establishment of and competition between two alliances without antitrust immunity leads to lower fares for interline passengers, due to removal of double marginalization, which existed prior to establishment of alliances, since networks of the individual carriers were not connected and carriers were assumed unable to distinguish between passengers traveling within their networks, and the interline passengers. Granting the antitrust immunity to both alliances increases fares for non-stop trips between the hub airports of alliance partners, not producing any additional benefits to interline passengers, beyond those already offered by alliances without immunity. The last result is different from what was previously suggested by Cournot – type models: those models claim that to completely remove double marginalization on interline trips, antitrust immunity was necessary. We were also able to offer a convincing explanation for formation of alliances even in cases this leads to decreased profits for individual alliance members. In fact, given the network and assumptions of the model, each airline’s dominant strategy is to enter into alliance and to seek antitrust immunity for the partnership. 31 The main implication of our model for antitrust policy is that each proposed alliance (especially the issue of granting the antitrust immunity to the partner carriers) must be considered on the case by case basis, taking into account the current network structure of the prospective alliance partners. Alliances with antitrust immunity produce benefits for the interline passengers, and not granting immunity may discourage airlines from consolidation. That is, losses to passengers traveling between hub airports of the alliance members can be considered the price of possibly wider gains to interline passengers. It is in the interest of regulatory authorities to seek solutions that minimize such price. Possibly an ideal variant would be the partnership, which by itself creates the non-stop service between the hub airports of the partner airlines (such as the KLM – Northwest alliance), in which case possible losses due to higher fares on the route (in case antitrust immunity is granted) are to some extent offset by gains, accruing to passengers, who now benefit from shorter duration of the trip. 32 Works Cited Bamberger, Gustavo E, D. W. Carlton and L. R. 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(Harper Collins Academic) ____________, 2001, The Airline Business in the 21st Century, Routledge Economist, The, 2001, A Survey of Air Travel, March 10-16, 2001 Hendricks, Ken, M. Piccione and G. Tan, 1999, Equilibria in Networks, Econometrica, Vol. 67, No. 6, November 1999 Neven, Damien J, Roeller, Lars-Hendrik and Zhentang Zhang, 1998, Union Power and Product Market Competition: Evidence from the Airline Industry, Centre for Economic Policy Research Discussion Paper No. 1912, June 1998 33 Pels, Eric, Peter Nijkamp and Piet Rietveld, 2000, A Note on the Optimality of Airline Networks, Economics Letters 69, p.p. 429-434 Porter, M., 1990, The Competitive Advantage of Nations, Free Press: New York Tirole, Jean, 1988, The Theory of Industrial Organization (MIT Press, London) Transportation Research Board, 1999, Entry and Competition in the U.S. Airline Industry: Issues and Opportunities (Special Report 225) (National Academy Press, Washington D.C.) US Department of Transportation, 2000, Transatlantic Deregulation: Alliance Network Effects, Report Winston, Clifford, 1985, Conceptual Developments in the Economics of Transportation: An Interpretive Survey, Journal of Economic Literature, Vol. 23, No. 1. (Mar., 1985), 57-94 34 Appendix Proofs of Propositions Proof of Proposition 1: Suppose nijJ < nijK and let cijJ and cijK denote average cost of alliance J and K, respectively. The proof is trivial where cijJ ≤ cijK (which includes the model’s cost symmetry assumption as a special case19). Here travel with alliance J is both preferred by customers and less expensive. So, alliance J in this case can take away the entire market by setting the price at a level, which is slightly below the one where the pijK ( pijJ ) = cijK . This can be rearranged as pijJ = cijK + π ij ( pijJ ) , following equality holds: ~ where π ij ( pijJ ) is as defined above20. This will also imply that pijJ > cijK ≥ cijJ , which suggests that alliance J will have positive mark-ups on those routes which it can serve with fewer connections, when cijJ ≤ cijK . Proof of Proposition 2: Proof in this case is trivial, once one recognizes that the above cost symmetry assumptions make the cost of travel on the routes concerned equal for both alliances, and given that travel will involve the same number of flight segments irrespective of the alliance chosen. Also note that (8) in this case collapses to the textbook Bertrand case, so the classical Bertrand equilibrium applies, given cost symmetry. Proof of Proposition 3: Parts (a) and (b) follow directly from Proposition 2. On each of those markets we have two competitors offering service with the same number of stops. Cost symmetries do not allow for successful competition by carriers offering services with more connecting flights. An important result that follows from (a) is that fares on non-stop overseas hub-to-hub routes will be lower under no alliance competition than when alliances are present. Part (c) follows from Propositions 1 and 2. Fares on those markets will be equal to D + π ( p Si H i ) , which implies that the operating carrier will make economic p Si H i = C SH D D D D profit. Also note that this is the same fare as would be observed in case alliances are present. To see that what we state in Part (d) is true it is important to consider options the travelers face on such markets when there are no alliances. Consider a passenger wishing to travel from spoke 1 to hub 2. He can either choose airline 1 for the entire journey or use airline Note that this proposition can be generalized to the case of asymmetric costs. This result will be true in case of asymmetric costs as long as ~ pijK (cijJ ) < cijJ is pijK (cijJ ) < cijK . In case the inequality cijK ≤ ~ 19 satisfied, it can be shown that alliance K has cost advantage over alliance J, sufficient to capture the market, even though alliance K offers travel with more stops. 20 Strictly speaking, the price charged by alliance J will be pij − ε but this does affect our results much, J be pij = min{cij + π ij ( pij ), pij } , where pm is the monopoly price. However, there is no reason to yet reduces the notational burden. Another presumably more correct way of writing the above result would J K J m believe that premiums for travel with less stops are high enough for the monopoly price to be charged in a naturally occurring situation 35 1 to travel to hub 1 and then fly with airline 2 to the final destination21. The fare if the first option is taken will be p1S1H 2 . If the second option is selected, then the fare will be D + π ( p1S1H1 ) . Further, part (a) of this Proposition equal to: p H2 1H 2 + p1S1H1 = p H2 1H 2 + C SH O D + C SH + π ( p 1S1H1 ) , which is strictly greater than the cost suggests that p H2 1H 2 + p1S1H1 = C HH of providing the service for airline 1, given cost symmetry. That is, airline 1 can capture O D O D + C SH + C SH + π ( p1S1H1 )) , which , C HH all the traffic on this market by setting p 1S1H 2 ∈ (C HH means that the fare charged by airline 1 will be slightly less than the upper bound of this interval. In fact, there is no qualitative difference between this result and the one for the same market under the alliance equilibrium. This logic applies to all similar markets. Proving result in part (e) of the proposition will be similar to proving the previous result. Let us take a passenger traveling from spoke 1 to spoke 3. Assume away airlines 3 and 4 for a moment22. The passenger will buy two tickets, and he can select one of the following: either use airline 1 to hub 2 and airline 2 thereafter; or, use airline 1 to hub 1 and airline 2 thereafter. Obviously, in the equilibrium the total price has to be the same, no matter which option is selected. Yet, in either case he will pay more than in the alliance competition equilibrium, since he will have to buy one ticket for domestic spoke to domestic hub segment, and one ticket for domestic spoke to overseas hub route; both tickets will be priced above cost, according to parts (c) and (d). To be more specific, the fares on such spoke-to-spoke routes will be equal to: D O p S D SO = p S D H O + p H O SO = p S D H D + p H D SO = 2C SH + C HH + 2π ( p S D H D ) (A.1) which is higher than would have been observed under the alliance equilibrium by twice the amount of the premium (note also that half of this premium will go to each of the operating airlines). We can state that passengers on the routes under consideration will be equally divided by all four airlines in a sense that each airline will obtain the premium from each of the passengers flying on this route, but serve only one half of the traffic. That is, each passenger will be a source of positive profits for two airlines. As for Part (f) of the Proposition, Part (a) clearly suggests that fares offered on the onestop hub-to-hub markets will be equal to the respective marginal costs. As for unclear distribution of traffic, consider market for travel between hub 1 and hub 4. Here any passenger faces four options, two involving change of carrier and two not involving such a change, but in each case the passenger will face equal fares. Yet, what is important for our analysis is that there will be no positive profits earned by either carrier on these markets. 21 Ruling out other options, involving more stops. If we consider other two airlines we will see that they are able to offer rather similar alternatives to the passenger wishing to travel on the route under consideration. So, in the end traffic will be divided not by two, but by four airlines, but analysis is logically more tractable if we only consider two options available to the passenger. 22 36