Informational cascades: A mirage?

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/4972737 Informational Cascades: A Mirage? Article in Journal of Economic Behavior & Organization · July 2008 DOI: 10.1016/j.jebo.2007.06.005 · Source: RePEc CITATIONS READS 15 69 3 authors, including: Markus Spiwoks Kilian Bizer 31 PUBLICATIONS 90 CITATIONS 86 PUBLICATIONS 267 CITATIONS Ostfalia University of Applied Sciences SEE PROFILE Georg-August-Universität Göttingen SEE PROFILE All content following this page was uploaded by Markus Spiwoks on 04 July 2014. The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately. Author manuscript, published in "Journal of Economic Behavior & Organization 67, 1 (2008) 193" DOI : 10.1016/j.jebo.2007.06.005 Accepted Manuscript Title: Informational Cascades: A Mirage? peer-00598265, version 1 - 6 Jun 2011 Authors: Markus Spiwoks, Kilian Bizer, Oliver Hein PII: DOI: Reference: S0167-2681(07)00142-4 doi:10.1016/j.jebo.2007.06.005 JEBO 2123 To appear in: Journal Received date: Revised date: Accepted date: 5-5-2006 20-6-2007 20-6-2007 of Economic Behavior & Organization Please cite this article as: Spiwoks, M., Bizer, K., Hein, O., Informational Cascades: A Mirage? Journal of Economic Behavior and Organization (2007), doi:10.1016/j.jebo.2007.06.005 This is a PDF file of an unedited manuscript that has been accepted for publication. 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Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. * Title Page (with Full Author Details) Informational Cascades: A Mirage? us an pte dM ce Prof. Dr. Kilian Bizer Göttingen University Faculty of Economics Chair in Economic Policy Platz der Göttinger Sieben 3 D-37073 Göttingen Germany bizer@wiwi.uni-goettingen.de Ac peer-00598265, version 1 - 6 Jun 2011 cri Corresponding Author: Prof. Dr. Markus Spiwoks Wolfsburg University of Applied Sciences Faculty of Business Administration Chair in Finance Robert-Koch-Platz 10-14 D-38440 Wolfsburg Germany Phone: +49-5361-83-1511 Fax: +49-5361-83-1502 Mobil: +49-173-65 15 835 m.spiwoks@fh-wolfsburg.de pt Markus Spiwoks, Kilian Bizer, and Oliver Hein Ph.D. candidate Oliver Hein Frankfurt University Faculty of Business Administration Chair in Information Systems D-60054 Frankfurt Germany ohein@is-frankfurt.de Page 1 of 21 Blinded Manuscript (NO Author Details) pt Informational Cascades: A Mirage? cri Abstract us cascades. Whereas Anderson and Holt (1997) confirmed the model of Banerjee (1992), and an Bikhchandani et al. (1992) through lab tests, Huck and Oechssler (2000) came to contradictory results on crucial issues. This article presents experimental evidence supporting pte dM further doubts concerning “Bayesian” informational cascades: Just under two thirds of all decisions are characterized by an excessive orientation towards the private signal, and only a small number of the subjects (<6%) make rational decisions systematically and consistently. ce JEL classification: C91; D82 Keywords: Informational cascades; Experiments; Bayes’ rule Ac peer-00598265, version 1 - 6 Jun 2011 Experimental research found contradictory results regarding the occurrence of informational Page 2 of 21 Rational herding and the precise circumstances under which it can arise have been studied by economists for around 70 years. 1 The theory of informational cascades put forward by Banerjee (1992) and Bikhchandani et al. (1992) has enlivened this debate considerably. Particular attention has been paid in this context to herds that occur because subjects draw pt conclusions about the private signals of their predecessors on the basis of their actions and then take into account the reliability of their own and their predecessors’ private signals and cri the a priori probability before finally making a rational decision by correctly using Bayes’ rule. 2 This combination of circumstances will be referred to here as “Bayesian” informational us The first to present experimental evidence were Anderson and Holt (1997). According to an them, “Bayesian” informational cascades occur regularly. 4 Huck and Oechssler (2000), pte dM however, come to a different result. According to their understanding, the correct use of Bayes’ rule is annulled by a systematic overrating of the respective private signals. This study investigates this contradiction. 1. Experimental Design Each subject has to solve three tasks (Table 1).5 Let A and B denote the possible decisions, a ce and b be possible signals, and α and β possible states of the world. The subjects have to decide between two alternative actions A and B. α has an a priori probability of 0.49 and β of Ac peer-00598265, version 1 - 6 Jun 2011 cascades. 3 0.51. They are informed which private signal (a or b) they have, how good the reliability of their private signal (q) is, and how good the reliability of their predecessors’ private signal is 1 The two approaches of reputational herding and investigative herding date back to Keynes (1936). As in the famous restaurant example used by Banerjee. 3 This specification is necessary, as the concept of informational cascades put forward by Banerjee and by Bikhchandani et al. was initially used as a generic term for various explanatory approaches (e.g. sanctions on deviants, positive pay-off externalities, conformity preference). 4 Hung and Plott (2001), Sgroi (2003) and Celen and Kariv (2004) analyze various model extensions. Partly explicitly, partly at least with regard to various marginal aspects, these studies support the results of Anderson and Holt. 5 The tasks are similar to the study of Huck and Oechssler. See Appendix A for the text of the tasks. Appendix C for detailed solution methods. Appendices are available on the JEBO website. 2 1 Page 3 of 21 (p). Finally they get to know which decisions their predecessors made. They are also told that all predecessors have exactly one private signal and have made rational decisions. Then they p Signal q 0.80 0.65 0.60 a a b 0.80 0.65 0.65 us an These three decision-making situations have the clear advantage that they allow a distinct differentiation as to whether the subjects act according to Anderson and Holt, or according to pte dM Huck and Oechssler’s interpretation. The subjects either make a rational decision in the sense of “Bayesian” informational cascades, or they trust their own private signal. This clear distinction, which for the first time allows a clear discrimination between the two stated explanation patterns, is an important advance. To a considerable degree, both the analyses of Anderson and Holt and the study of Huck and Oechssler present decision-making ce situations in which the strict orientation towards one’s own private signal leads to the same decision as an inference of the private signals of the predecessors and, based on this, a rational use of Bayes’ rule. Ac peer-00598265, version 1 - 6 Jun 2011 With an a priori probability for β = 0.51 and for α = 0.49. Rational action B B A cri Table 1 The three decision tasks Previous decisions Task 1 B Task 2 ABB Task 3 AA pt have to decide between actions A and B. Table 2 The distinction between the two explanatory patterns Solution that obtains by rational decision-making Task 1 B Task 2 B Task 3 A Solution that obtains by strong overweighting of the private signal A A B 2 Page 4 of 21 227 subjects took part in six sessions with respective totals of 55, 50, 46, 37, 24 and 15 persons. In each of the six sessions the subjects were divided into three groups. These groups varied with regard to the order in which the tasks had to be solved. All subjects were students at the Wolfsburg University of Applied Sciences who study business administration. None of pt them had any experience of experimental research, and all had a thorough education in the calculus of probability. The use of a pocket calculator was allowed. There was no payment for cri participation in this experiment. Those subjects who correctly solve tasks received bonus us an 2. Results Table 3 summarizes the results of the six sessions. “R” (for “Right”) marks those decisions pte dM that can be called correct in the sense of a rational decision given the deduction of the private signals of the predecessors and the correct use of Bayes’ rule. Thus “R” marks all those decisions that confirm the approach of Anderson and Holt. “W” (for “Wrong”) marks those decisions which are not based on rationale but rather follow the person’s own private signal. Thus “W” highlights all those decisions which confirm Huck and Oechssler’s approach. ce In total, the subjects made 681 decisions (see Table 3). Only 248 of them, or 36%, were answered correctly in the rational sense. 433 decisions were wrong, so in 64% of all decisions the subjects either failed to draw conclusions from their predecessors’ decisions about their Ac peer-00598265, version 1 - 6 Jun 2011 points for a later exam. 6 private signals, did not correctly use Bayes’ rule, and/or based their decisions on completely different aspects. 6 For the effect of such incentives see Selten et al. (2003, p. 22). Those subjects who correctly solve all tasks receive 15 bonus points for a later exam (five bonus points for each correctly solved task). Other students were asked how much 15 bonus points for a later exam were worth to them, were they able to buy the 15 bonus points. The 42 students asked gave numbers between € 25 and € 200. The average was € 72.45. 3 Page 5 of 21 Table 3 Summary of the results of the whole study r o W 46 2 R 33 R Task 2 3 R 11 R 33 W 140 60% R 88 40% W 64 Task 3 W 41 R 27 W 134 60% R 66 29% Task 2 R 82 36% R 79 35% R 87 38% R 248 36% W 48 Task 1 W 159 71% W 145 64% W 148 65% W 140 62% W 433 64% an R = Right (in the sense of a rational decision with correct use of Bayes’ rule); W = Wrong (the decision follows a private signal). pte dM What further aggravates the situation is that of the 248 right decisions, only a minority are accompanied by a correct reason for the decision. Table 4 summarizes the methods of solution given by those subjects who made “right” decisions. It becomes obvious that less than a quarter of the right decisions are based on the right rationale. For about 40% of the right decisions either faulty, nonsensical or no methods were given. Approximately every ce tenth person stated that they only guessed. About a quarter of the correct decisions are based on simplifying thumb rules: around 10% of the subjects are oriented towards the a priori probability, and 15% just decide as the majority of their predecessors did. Ac peer-00598265, version 1 - 6 Jun 2011 ∑ W 41 W 51 W 47 Task 2 Task 1 Task 3 R 94 40% R 28 Task 3 W 43 R 27 W 52 us R 35 ∑ 3 R 22 Task 1 n u 2 R 32 1 p cri 1 u pt G 4 Page 6 of 21 Table 4 Explanations given by subjects for the 248 “right” decisions Percentage 58 23.4% 88 12 26 38 26 35.5% 4.8% 10.5% 15.3% 10.5% cri Right method (inferring the private signals of the predecessors and correct use of Bayes’ rule) Faulty use of Bayes’ rule / nonsensical or incomprehensible methods No method given as to how the stated solution was arrived at Guessed Decision according to the majority decision of the predecessors Decision according to the a priori probability Number pt Methods given to arrive at the “right” decisions us informational cascades. Of these 36% about three quarters of the decisions are made for the an wrong reasons and are therefore only accidentally correct. Regarding the whole population pte dM this means that not even every tenth decision is a correct one based on the correct reasons. As 64% of all decisions correspond to the person’s own private signals, and although this could in no case lead to the right decision (and thus to a reward), it must be presumed that a large part of the decision making was excessively influenced by own private signals. The present study results confirm the explanatory approach of Huck and Oechssler. Examination of the number of correct decisions per participant permits further insights ce (Figure 1). 41% of the subjects followed their own private signal in all three situations. Around 45% of the subjects gave both right and wrong answers. Only around 13% of the participants solved all three tasks correctly. Median results (one or two right decisions) were Ac peer-00598265, version 1 - 6 Jun 2011 Only about 36% of the decisions are made according to the postulate of “Bayesian” only obtained by persons who neither systematically followed their own private signal nor made consistently rational decisions. These are the persons who guessed or who followed irrational thumb rules that purely coincidentally lead to success or failure. However, it is also possible to obtain three correct or three incorrect answers with random decisions. In the case of three decisions with two alternative answers each, only three-fourths of the subjects who simply guess or make random decisions attain a median result (one or two right decisions). If 5 Page 7 of 21 this is taken into account, it is revealed that around 60% (7.6% + 23.1% + 22.3% + 7.6%) of subjects tend towards decisions made at random, about a third always follow their own private signal, and only around 6% make systematic rational decisions. 45 Strategy "Bayes Rule" (5.9%) pt 30 Strategy "Private Signal" (33.4%) 15 1 right decision (23.1%) 2 right decisions (22.3%) 3 right decisions (13.5%) us no right decision (41.0%) an Fig. 1. Classification of the subjects into four groups according to their level of success manner: pte dM Further results stress that it cannot be assumed that subjects act in a consistently rational 1. A review of the three groups that had to solve the tasks in varying orders shows significantly varying success rates (see Table 3). While the results of group 1 (order: Task 1, Task 2, Task 3) and group 2 (order: Task 3, Task 1, Task 2) are almost exactly alike (success ce rate 40%), group 3 (order: Task 2, Task 3, Task 1) achieved a success rate of only 29%. Such considerable variations of the success rate, which solely result from varying task orders, are no indication of rational decision making behavior by the subjects. Ac peer-00598265, version 1 - 6 Jun 2011 0 cri Random Decisions (60.6%) 2. The three tasks do not have corresponding success rates. As can be seen in Table 5, Task 3 is solved in only 26% of all cases, while Task 1 and 2 are solved correctly in more than 40%. This clear difference between the success rates does not indicate that the subjects are willing and able to apply Bayes’ rule appropriately to concrete decision-making situations (in potential “Bayesian” informational cascades), although they fundamentally manage the necessary procedures of probability calculation. 6 Page 8 of 21 Task 2 R W 35 43 33 41 28 47 96 131 42% 58% Task 3 R W 27 51 22 52 11 64 60 167 26% 74% pt Table 5 Different success rates of the three tasks Task 1 Group R W 1 32 46 2 33 41 3 27 48 92 135 ∑ 41% 59% cri R = Right (in the sense of a rational decision with correct use of Bayes’ rule); W = Wrong (the decision follows a private signal). us are presently completing postgraduate business administration studies comparable to an an MBA), the ban on communication is lifted. The students receive the three tasks and have to hand in the solutions to the experimenter 36 hours later. Interchange is explicitly allowed, and pte dM the consultation of textbooks or expert opinions is not forbidden. When some of the participants are not intellectually up to the task but still strive for the best possible rational decision, it can be expected that they will use the time to gather information and to make the correct decisions. As can be seen from Table 6 the success rates are surprisingly similar to those of the rest of the study: 38% of all tasks were answered correctly, and for 62% of all tasks wrong answers were given. Obviously the decisions are based on different decision- ce making preferences than the “Bayesian” informational cascades suggest. The majority of the subjects do not seem to look for rational, best possible decisions by applying Bayes’ rule. Ac peer-00598265, version 1 - 6 Jun 2011 3. In the sixth and last session with 15 students (who already have an engineering degree and 7 Page 9 of 21 Table 6 The results of the six sessions Session Number of correct answers Number of false answers Percentage of correct answers Percentage of false answers I 57 108 35% 65% II 60 90 40% 60% III 51 87 38% 62% IV 35 76 32% 68% V 28 44 39% 61% VI 17 28 38% 62% pt Session I: 55 undergraduate students; session II: 50 graduate students; session III: 46 undergraduate students; session IV: 37 graduate students; session V: 24 undergraduate and graduate students; session VI: 15 postgraduate students (corresponds to MBA). cri A certain amount of variation in the six sessions can be clearly seen (Table 6). The percentage us of correct answers varies between 32% in session IV and 40% in session II, but no session biasing peculiarities of the subject populations. an Anderson and Holt’s and Huck and Oechssler’s results can be explained by accidental, pte dM Therefore, the present results in no way support the estimation that “Bayesian” informational cascades can occur in reality. In the end, the model of “Bayesian” informational cascades only works when the successors can be sure that their predecessors have made rational decisions. However, the results of the study show that one certainly can not assume that all predecessors have made rational decisions. Kübler and Weizsäcker (2004) reveal that the successors do not ce really rely on their predecessors. In their study, the subjects (in contrast to this study) are left in the dark as to whether their predecessors made rational decisions or not. It turns out that the subjects always believe their predecessors to be less capable of rational decisions than Ac peer-00598265, version 1 - 6 Jun 2011 provides a majority of correct solutions. There is no indication that the contradiction between themselves. 7 7 More recent studies have shown that noisy behavior of the other subjects can frequently lead to considerable deviations from rational decision-making; see Goeree and Holt (1999, 2004). However, this does not explain the results presented here, as all the subjects were very clearly informed that all predecessors had made perfectly rational decisions. These newer studies do, however, emphasise existing doubts about whether informational cascades can genuinely occur in reality. Real decision-making situations are namely characterized by noisy behavior of the other subjects. 8 Page 10 of 21 3. Conclusion The contradictory results of the experimental studies of Anderson and Holt and of Huck and Oechssler were the point of departure for this study. A total of 227 subjects were confronted with decision-making situations that permit a clear differentiation between orientation pt towards rationale and orientation towards the person’s own private signal. Of the total number of 681 decisions, only 248 (36%) were based on rationale. Of these 248 cri decisions only 58 were made for the right reasons. For the other 190 correct decisions it us became obvious that the subjects had either decided by simplifying irrational thumb rules, had an 433 decision-making situations (64%) the participants made decisions that were contrary to the rational solution and in favor of their private signal. pte dM Further results indicate that subjects are rarely willing to calculate the probabilities and then make a rational decision: 1. the order in which the tasks are presented influences the results, 2. the degree to which the subjects successfully deal with the three decision-making situations varies considerably, and 3. the success rates are not increased by the lifting of the communication ban and the possibility to refer to text books and expert opinions. ce The urge to decide by simplifying thumb rules is obviously very strong, at least for these kinds of decision-making situations. Only a small number (< 6%) of the subjects systematically made a rational decision, considered all probabilities, and correctly applied Ac peer-00598265, version 1 - 6 Jun 2011 only guessed, or were not able to sketch a comprehensible way to the solution. Similarly, in Bayes’ rule. In some decision-making situations, one can obtain very good results by simplifying thumb rules or just by guessing. 8 This type of behavior can therefore sometimes even be meaningful, if one considers that finding the right solution can be rather strenuous. In this experiment, 8 Huck et al. (2003, 2004), for example, show that in a sequence of decision-making situations, subjects can come very close to the optimal solution with simple trial and error strategies without having recognized the background to the decision-making situation and thus the systematic way to reach a solution. 9 Page 11 of 21 however, the subjects face considerable disadvantages. Those who simply guess lose an average of half of their “fee” (7.5 bonus points ≈ € 36.23). Those who always follow their private signal actually lose their whole compensation (15 bonus points ≈ € 72.45). On average for all subjects, just under two thirds of their possible bonus is lost (9.58 bonus points ≈ € pt 46.30). The use of simplifying thumb rules or pure guesswork therefore involves significant losses. The fact that the subjects accept these losses indicates that their preference for the use cri of simplifying thumb rules is highly developed. This study confirms the results of Huck and Oechssler. The results of Anderson and Holt, us decisions against the background of one private signal and their observation of the decisions an of their predecessors, undoubtedly decision sequences emerge that look like “Bayesian” pte dM informational cascades. Then, however, one needs to examine whether the subjects have consistently made rational decisions or not. 2 a B 3 a B 4 a B 5 a B 6 a B 7 a B ce Table 7 Banerjee’s restaurant example Subject 1 Private signal b Decision B With an a priori probability for β = 0.51 and for α = 0.49. When a laboratory experiment leads to a situation such as the one given in Table 7 one may Ac peer-00598265, version 1 - 6 Jun 2011 however, will presumably have to be reinterpreted: if a number of subjects have to make not simply infer the existence of a “Bayesian” informational cascade. Maybe subjects 2 and 3 decide merely upon the a priori probability, subjects 4 and 5 only according to the majority of their predecessors, and subjects 6 and 7 possibly only guess and hope to luck out and make a favorable decision. What then looks like a sequence of rational decisions derived by observing the actions of the predecessors, by drawing conclusions about their private signals, 10 Page 12 of 21 and correctly using Bayes’ rule is in reality nothing more than an ostensible “Bayesian” us an pte dM ce Ac peer-00598265, version 1 - 6 Jun 2011 cri pt informational cascade. 11 Page 13 of 21 Appendix A. Text of the Tasks Task 3: You must decide between alternative actions A and B. When you make the right decision you will get 5 bonus points for the exam. pt To begin with, action A is right in 49% of all cases, and action B is right in 51% of all cases. Before you have to make your decision you will receive a hint (either “a” or “b”) towards the cri right action. This hint reveals the correct action to you in 65 out of 100 cases. 9 This means: us should you receive the hint “b”, in 65 out of 100 cases action B is the right one. an to make his decision first, then person 2, and so forth. Each person could see the decision their predecessors made, but not the hints these persons received. You know that the reliability of pte dM the hints for the persons before you was only 60%. 10 This means: should one of these persons for example receive hint “b”, in only 60 out of 100 cases is action B correct. All participants receive exactly one hint. The hints are independent of each other. All persons who already made their decision made a rational decision. You are the third person to decide. The two predecessors decided thus: A A You receive hint “b”. 11 ce Which action should you now choose? A B Please briefly explain upon which rationale you based your decision, or which way, if at all, Ac peer-00598265, version 1 - 6 Jun 2011 Other persons before you were confronted with this decision making situation. Person 1 had you went about resolving this problem. These explanations have no influence on the granting of bonus points for the exam, therefore you should give an open and honest answer here! 9 Task 1: 80 out of 100 cases; Task 2: 65 out of 100 cases. Task 1: also 80%; Task 2: also 65%. 11 Task 1: You are the second person to decide. The person before you chose action B. You receive hint “a”; Task 2: You are the 4th person to decide. The three predecessors decided thus: A B B. You receive hint “a”. 10 12 Page 14 of 21 Appendix B. Detailed results of the six sessions Table 8 Session I: 55 undergraduate students r o R 5 W 9 R 7 Task 1 n u W 13 R R 7 ∑ W 12 R 23 40% R 5 W 11 R 0 R 10 W 8 R 22 41% W 18 Task 3 R 7 Task 2 W 34 60% W 13 Task 2 Task 1 Task 3 W 11 Task 1 W 32 59% R 16 29% R 17 31% R 24 44% R 57 35% R 12 22% W 42 78% W 39 71% W 38 69% W 31 56% W 108 65% pte dM R = Right (in the sense of a rational decision made by correctly applying Bayes’ Rule); W = Wrong (that means that the decision follows the person’s private signal). Table 9 Session II: 50 graduate students G R 3 R 9 R 6 W 6 2 Ac Task 1 n u o W 7 R 8 R 27 56% W 14 W 8 R 8 W 21 44% R 5 W 12 Task 3 W 11 Task 2 R 15 29% W 9 Task 2 W 11 R 6 ∑ 3 Task 1 Task 3 ∑ p Task 3 Task 2 3 u 2 R 10 1 r ce 1 R peer-00598265, version 1 - 6 Jun 2011 3 W 13 Task 3 Task 2 ∑ 3 us 2 R 10 2 an 1 R 6 p cri 1 u pt G W 36 71% R 5 W 12 Task 1 R 18 35% W 33 65% R 21 42% R 20 40% R 19 38% R 60 40% W 29 58% W 30 60% W 31 62% W 90 60% R = Right (in the sense of a rational decision made by correctly applying Bayes’ Rule); W = Wrong (that means that the decision follows the person’s private signal). 13 Page 15 of 21 Table 10 Session III: 46 undergraduate students r o W 10 R 7 Task 2 R 3 R 2 Task 3 W 9 R 8 Task 2 W 31 65% R 20 44% W 13 W 7 Task 1 W 25 56% R 14 31% R 17 37% R 16 35% R 18 39% R 51 38% W 31 69% W 29 63% W 30 65% W 28 61% W 87 62% pte dM an R = Right (in the sense of a rational decision made by correctly applying Bayes’ Rule); W = Wrong (that means that the decision follows the person’s private signal). Table 11 Session IV: 37 graduate students G 1 R 3 o W 9 R 4 2 W 8 Ac R 3 W 9 Task 3 ∑ R 10 28% p W 26 72% W 9 R 7 R 6 R 1 Task 1 W 12 Task 3 W 7 Task 2 R 15 42% W 7 Task 2 W 5 R 5 ∑ 3 Task 3 Task 2 3 u R 3 Task 1 n u r 2 ce 1 R peer-00598265, version 1 - 6 Jun 2011 Task 3 ∑ W 8 R 6 W 11 Task 2 Task 1 W 12 R 17 35% R 4 Task 3 W 9 R 4 W 8 us R 7 2 ∑ 3 R 7 Task 1 n u 2 R 6 1 p cri 1 u pt G W 21 58% R 3 W 10 Task 1 R 10 26% W 29 74% R 12 32% R 12 32% R 11 30% R 35 32% W 25 68% W 25 68% W 26 70% W 76 68% R = Right (in the sense of a rational decision made by correctly applying Bayes’ Rule); W = Wrong (that means that the decision follows the person’s private signal). 14 Page 16 of 21 Table 12 Session V: 24 undergraduate and graduate students r o W 5 R 4 Task 2 R 3 R 2 Task 3 W 3 R 2 Task 2 W 20 67% R 11 52% W 5 W 5 Task 1 W 10 48% R 7 33% R 11 46% R 9 37% R 8 33% R 28 39% W 14 67% W 13 54% W 15 63% W 16 67% W 44 61% pte dM an R = Right (in the sense of a rational decision made by correctly applying Bayes’ Rule); W = Wrong (that means that the decision follows the person’s private signal). Table 13 Session VI: 15 postgraduate students (corresponds to an MBA) with no order of the tasks, with the possibility to communicate among the subjects, and handing in after 36 hours maximum to work on it. G 1 R 2 o W 3 R 2 2 W 3 Ac R 3 W 2 Task 3 ∑ R 7 47% p W 8 53% W 4 R 2 R 2 R 1 Task 1 W 4 Task 3 W 3 Task 2 R 5 33% W 3 Task 2 W 3 R 2 ∑ 3 Task 3 Task 2 3 u R 1 Task 1 n u r 2 ce 1 R peer-00598265, version 1 - 6 Jun 2011 Task 3 ∑ W 3 R 4 W 4 Task 2 Task 1 W 8 R 10 33% R 3 Task 3 W 7 R 2 W 4 us R 3 2 ∑ 3 R 3 Task 1 n u 2 R 5 1 p cri 1 u pt G W 10 67% R 2 W 3 Task 1 R 5 33% W 10 67% R 5 33% R 5 33% R 7 47% R 17 38% W 10 67% W 10 67% W 8 53% W 28 62% R = Right (in the sense of a rational decision made by correctly applying Bayes’ Rule); W = Wrong (that means that the decision follows the person’s private signal). 15 Page 17 of 21 Appendix C. Detailed ways of solution of the three tasks Task 1: The only predecessor chose B; thus the conclusion is that his private signal was b. The subject receives the private signal a. The two private signals neutralize each other, so the decision must be based on the a priori probability. Therefore action B is the right one. pt Task 2: The first predecessor chose A, from which it follows that his private signal is a. The second predecessor chose B, which hints at b as his private signal. The third predecessor has cri obviously also received signal b because had he received a, A would have been the rational us decision (two a’s would have exceeded b with a reliability of the signals of 0.65, even when an private signals of his predecessors and his own private signal exactly neutralize each other (two a’s and two b’s). Therefore the subject again has to orient himself towards the a priori pte dM probability, which speaks for action B. Task 3: It is necessary to calculate the more probable of the two alternative actions. α,β = States of the world prob ( α | a ) = 0.60 prob ( α ) = 0.49 prob ( β | a ) = 0.40 prob ( β ) = 0.51 a, b = Signals prob (a) prob ( α a ) prob ( α ) prob ( a ) = prob ( α | a ) * prob ( α ) + prob ( β | a ) * prob ( β ) = 0.60 * 0.49 + 0.40 * 0.51 = 0.498 prob ( a | α ) = prob (b | α) = prob (b) prob ( β | b ) = 0.65 ce prob ( a | α ) = prob ( α | b ) = 0.35 Ac peer-00598265, version 1 - 6 Jun 2011 the a priori probability speaks for B). Now the student receives signal a. He must note that the 0.6*0.49 0.294 = = 0.590361445 0.498 0.498 prob ( α b ) prob ( α ) prob ( b ) = prob ( α | b ) * prob ( α ) + prob ( β | b ) * prob ( β ) = 0.35 * 0.49 + 0.65 * 0.51 = 0.503 16 Page 18 of 21 prob ( b | α ) = 0.35*0.49 0.1715 = = 0.340954274 0.503 0.503 prob ( a | β ) = 0.4*0.51 0.204 = = 0.409638554 0.498 0.498 prob ( b | β ) = 0.65*0.51 0.3315 = = 0.659045725 0.503 0.503 ) prob ( α ) prob ( aab α ) prob ( α ) + prob ( aab β ) prob ( β ) 2 cri ( 0.590361445) = ( 0.590361445) = 0.058227506 = 0.507966743 0.058227506 + 0.056401073 *0.340954274*0.49 + ( 0.409638554 ) *0.659045725*0.51 *0.340954274*0.49 us 2 an 2 pt prob ( aab α ce pte dM The decision for alternative A is the rational one, because it is more probable. Ac peer-00598265, version 1 - 6 Jun 2011 prob ( α | aab ) = 17 Page 19 of 21 References Anderson, L.R., Holt, C.A., 1997. Information cascades in the laboratory. The American Economic Review 87, 847-862. pt Banerjee, A.V., 1992. A simple model of herd behavior. The Quarterly Journal of Economics 107, 797-817. cri Bikhchandani, S., Hishleifer, D., Welch, I., 1992. A theory of fads, fashion, custom, and cultural change as informational cascades. Journal of Political Economy 100, 992-1026. us laboratory. The American Economic Review 94, 484-498. an Goeree, J. K., Holt, C. A., 1999. Stochastic game theory: for playing games, not just for doing theory. Proceedings of the National Academy of Sciences 96, 10564-10567. pte dM Goeree, J. K., Holt, C. A., 2004. A model of noisy introspection. Games and Economic Behavior 46, 365-382. Huck, S., Oechssler, J., 2000. Informational cascades in the laboratory: do they occur for the right reasons? Journal of Economic Psychology 21, 661-671. Huck, S., Normann, H.-T., Oechssler, J., 2003. Zero-knowledge cooperation in dilemma ce games. Journal of Theoretical Biology 220, 47-54. Huck, S., Normann, H.-T., Oechssler, J., 2004. Through trial and error to collusion. International Economic Review 45, 205-224. Ac peer-00598265, version 1 - 6 Jun 2011 Celen, B., Kariv, S., 2004. Distinguishing information cascades from herd behavior in the Hung, A.A., Plott, C.R., 2001. Information cascades: replication and an extension to majority rule and conformity-rewarding institutions. The American Economic Review 91, 15081520. Keynes, J.M., 1936. The General Theory of Employment, Interest, and Money. London: Macmillan. 18 Page 20 of 21 Kübler, D., Weizsäcker, G., 2004. Limited depth of reasoning and failure of cascade formation in the laboratory. Review of Economic Studies 71, 425-441. Selten, R., Abbink, K., Buchta, J., Sadrieh, A., 2003. How to play (3 x 3)-games. A strategy method experiment. Games and Economic Behavior 45, 19-37. pt Sgroi, D., 2003. The right choice at the right time: a herding experiment in endogenous time. Ac ce pte dM an peer-00598265, version 1 - 6 Jun 2011 us cri Experimental Economics 6, 159-180. 19 View publication stats Page 21 of 21