Papers by Manipushpak Mitra
Suchismita Banerjee,1, ∗ Soumyajyoti Biswas,2, † Bikas K. Chakrabarti,3, 1, 4, ‡ Asim Ghosh,5, § ... more Suchismita Banerjee,1, ∗ Soumyajyoti Biswas,2, † Bikas K. Chakrabarti,3, 1, 4, ‡ Asim Ghosh,5, § Raju Maiti,1, ¶ Manipushpak Mitra,1, ∗∗ and Dachepalli R. S. Ram2, †† 1Economic Research Unit, Indian Statistical Institute, Kolkata 700108, India. 2SRM University-AP, Andhra Pradesh 522502, India. 3Saha Institute of Nuclear Physics, Kolkata 700064, India. 4S. N. Bose National Centre for Basic Sciences, Kolkata 700106, India. 5Raghunathpur College, Raghunathpur, Purulia 723133, India.
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We provide a survey of the Kolkata index of social inequality, focusing in particular on income i... more We provide a survey of the Kolkata index of social inequality, focusing in particular on income inequality. Based on the observation that inequality functions (such as the Lorenz function), giving the measures of income or wealth against that of the population, to be generally nonlinear, we show that the fixed point (like Kolkata index k) of such a nonlinear function (or related, like the complementary Lorenz function) offer better measure of inequality than the average quantities (like Gini index). Indeed the Kolkata index can be viewed as a generalized Hirsch index for a normalized inequality function and gives the fraction k of the total wealth possessed by the rich (1-k) fraction of the population. We analyze the structures of the inequality indices for both continuous and discrete income distributions. We also compare the Kolkata index to some other measures like the Gini coefficient and the Pietra index. Lastly, we provide some empirical studies which illustrate the difference...
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We study the dynamics of a few stochastic learning strategies for the 'Kolkata Paise Restaura... more We study the dynamics of a few stochastic learning strategies for the 'Kolkata Paise Restaurant' problem, where N agents choose among N equally priced but differently ranked restaurants every evening such that each agent tries get to dinner in the best restaurant (each serving only one customer and the rest arriving there going without dinner that evening). We consider the learning strategies to be similar for all the agents and assume that each follow the same probabilistic or stochastic strategy dependent on the information of the past successes in the game. We show that some 'naive' strategies lead to much better utilization of the services than some relatively 'smarter' strategies. We also show that the service utilization fraction as high as 0.80 can result for a stochastic strategy, where each agent sticks to his past choice (independent of success achieved or not; with probability decreasing inversely in the past crowd size). The numerical results for ...
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A popular measure for the success or citation inequalities of individual scientists have been the... more A popular measure for the success or citation inequalities of individual scientists have been the Hirsch index (h). If the number n_c of citations are plotted against the number n_p of papers (having those citations), then h corresponds to the fixed point (where n_c = h = n_p) of the above-mentioned citation function. There have been theoretical as well as numerical studies suggesting h∼√(N_c)∼√(N_p), for any author having N_p = Σ n_p total papers and N_c = Σ n_c total citations. With extensive data analysis here, we show that h ∼√(N)_c /log N_c ∼√(N)_p /log N_p. Our numerical study also shows that the h-index values for size distribution of avalanches in equal load-sharing fiber bundle models (of materials failure), consisting of N fibers, also scale as √(N)/ log N. We however observe a notable discrepancy in the scaling relation of h for the size distribution of clusters near the percolation point of square lattice (indicating that the scaling behavior depends on the dimension). W...
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We provide a survey of the Kolkata index of social inequality, focusing in particular on income i... more We provide a survey of the Kolkata index of social inequality, focusing in particular on income inequality. We look at both continuous and discrete income distributions. We also compare the Kolkata index to some other measures like the Gini coefficient, Hirsch index and the Pietra index. Lastly, we provide some empirical studies which illustrate the differences between the Kolkata index and the Gini coefficient.
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Economic Theory
Agents from a finite population arrive at various discrete times, and exit after they use a serve... more Agents from a finite population arrive at various discrete times, and exit after they use a server for one period each. Each agent has a per-period cost of queueing, which constitutes his private information. Among direct mechanisms that are prior-free, i.e. independent of distributions of arrivals and costs, and online, i.e. charge only those present in the system, we characterize the class of dynamically strategy-proof mechanisms with least total waiting cost. The budget is balanced eventually under a mild condition on the arrival sequence, while a canonical mechanism that achieves budget balance in each period is also characterized under a stronger condition.
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Core Discussion Papers, May 1, 2003
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Games and Economic Behavior, 2015
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New Economic Windows, 2013
ABSTRACT In this paper we revisit the Kolkata Paise Restaurant problem by allowing for a more gen... more ABSTRACT In this paper we revisit the Kolkata Paise Restaurant problem by allowing for a more general (but common) preference of the n customers defined over the set of n restaurants. This generalization allows for the possibility that each pure strategy Nash equilibrium differs from the Pareto efficient allocation. By assuming that n is small and by allowing for mutual interaction across all customers we design strategies to sustain cyclically fair norm as a sub-game perfect equilibrium of the Kolkata Paise Restaurant problem. We have a cyclically fair norm if n strategically different Pareto efficient strategies are sequentially sustained in a way such that each customer gets serviced in all the n restaurants exactly once between periods 1 and n and then again the same process is repeated between periods (n+1) and 2n and so on.
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We study the mathematical and economic structure of the Kolkata (k) index of income inequality. W... more We study the mathematical and economic structure of the Kolkata (k) index of income inequality. We show that the k-index always exists and is a unique fixed point of the complementary Lorenz function, where the Lorenz function itself gives the fraction of cumulative income possessed by the cumulative fraction of population (when arranged from poorer to richer). We show that the k-index generalizes Pareto's 80/20 rule. Although the k and Pietra indices both split the society into two groups, we show that k-index is a more intensive measure for the poor-rich split. We compare the normalized k-index with the Gini coefficient and the Pietra index and discuss when they coincide. We establish that for any income distribution the value of Gini coefficient is no less than that of the Pietra index and the value of the Pietra index is no less than that of the normalized k-index. While the Gini coefficient and the Pietra index are affected by transfers exclusively among the rich or among t...
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Indian Statistical Institute Series
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In an earlier work on Kolkata paise restaurant problem, Banerjee et al. 2013, we analyzed the cyc... more In an earlier work on Kolkata paise restaurant problem, Banerjee et al. 2013, we analyzed the cyclically fair norm. We identified conditions under which such a fair societal norm can be sustained as an equilibrium. In this chapter we suggest how the Kolkata restaurant problem can be extended in several directions from purely an economics based modeling perspective.
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This paper provides a microeconomic analysis of subsistence consumption in the consumer theory fr... more This paper provides a microeconomic analysis of subsistence consumption in the consumer theory framework. Our key concepts are 'irrelevance' of a good in certain consumption bundles (increasing its amount does not make the consumer better off) and an 'unhappy set' (any bundle outside such a set is preferred to all bundles inside). Using these concepts we axiomatize subsistence and saturation induced irrelevance (SSI) preferences. We also axiomatize a generalized version of Leontief (GL) preferences, for which irrelevance is solely driven by complementarity. Irrelevance in SSI preferences results from the presence of unhappy sets; for GL preferences irrelevance is driven by their absence.
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We address the issue of coalition formation in single and multi-unit Vickrey auctions with unit d... more We address the issue of coalition formation in single and multi-unit Vickrey auctions with unit demand. We address this issue in a bargaining game set up under the assumption of complete information where valuation of participants is commonly known amongst themselves while the seller is unaware of these valuations. In the single goods case, we provide the necessary and sufficient conditions for formation of any bidding ring when the highest valuation agent proposes first. In the multiple goods case, we specify sufficient conditions for formation of an interesting class of coalition structures where exactly one winner colludes with all the losers and, depending on the protocol, the remaining winners either stay alone or collude in pairs.
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Asim Ghosh, ∗ Bikas K. Chakrabarti, 3, 4, † Dachepalli R. S. Ram, ‡ Manipushpak Mitra, § Raju Mai... more Asim Ghosh, ∗ Bikas K. Chakrabarti, 3, 4, † Dachepalli R. S. Ram, ‡ Manipushpak Mitra, § Raju Maiti, ¶ Soumyajyoti Biswas, ∗∗ and Suchismita Banerjee †† Raghunathpur College, Raghunathpur, Purulia 723133, India. Saha Institute of Nuclear Physics, Kolkata 700064, India. Economic Research Unit, Indian Statistical Institute, Kolkata 700108, India. S. N. Bose National Centre for Basic Sciences, Kolkata 700106, India. SRM University-AP, Andhra Pradesh 522502, India.
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We consider the problem of regulating a monopolist with unknown costs when the regulator has limi... more We consider the problem of regulating a monopolist with unknown costs when the regulator has limited funds. The optimal regulatory mechanism satisfies four properties. The first property is bunching at the top, that is the more efficient types produce the same quantity irrespective of their costs. The second property is separability of less efficient types. The third property is full bunching of types when the available fund is small enough. The fourth property of the mechanism is that it is a third best one, that is, the output under this regulatory mechanism is strictly lower than the second best output for any given type.
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We propose an index of electoral competition based on the vote shares of parties competing in the... more We propose an index of electoral competition based on the vote shares of parties competing in the election. This index is the ratio between the probabilities that the two voters drawn at random with (without) replacement have voted for different parties under actual vote shares across the competing parties and under equal vote shares across them. The measure is characterized using two simple axioms, consistency in aggregation and competitive indifference. The former expresses the index as a weighted sum of competitiveness in two party elections. The latter is concerned with redistribution of vote shares across parties.
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Decision Analysis
This paper characterizes lexicographic preferences over alternatives that are identified by a fin... more This paper characterizes lexicographic preferences over alternatives that are identified by a finite number of attributes. Our characterization is based on two key concepts: a weaker notion of continuity called “mild continuity” (strict preference order between any two alternatives that are different with respect to every attribute is preserved around their small neighborhoods) and an “unhappy set” (any alternative outside such a set is preferred to all alternatives inside). Three key aspects of our characterization are as follows: (i) we use continuity arguments; (ii) we use the stepwise approach of looking at two attributes at a time; and (iii) in contrast with the previous literature, we do not impose noncompensation on the preference and consider an alternative weaker condition.
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Papers by Manipushpak Mitra