Manipushpak Mitra

Mechanism design in queueing problems

Summary. A well-known result in incentive theory is that for a very broad class of decision problems, there is no mechanism which achieves truth-telling in dominant strategies, efficiency and budget balancedness (or first best implementability). On the contrary, Mitra and Sen (1998), prove that linear cost queueing problems are first best implementable. This paper is an attempt at identification of cost structures for which queueing problems are first best implementable. The broad conclusion is that, this is a fairly large class. Some of these first best implementable problems can be implemented by mechanisms that satisfy individual rationality.

The Kolkata Paise Restaurant problem and resource utilization

We study the dynamics of the “Kolkata Paise Restaurant problem”. The problem is the following: In each period, N agents have to choose between N restaurants. Agents have a common ranking of the restaurants. Restaurants can only serve one customer. When more than one customer arrives at the same restaurant, one customer is chosen at random and is served; the others do not get the service. We first introduce the one-shot versions of the Kolkata Paise Restaurant problem which we call one-shot KPR games. We then study the dynamics of the Kolkata Paise Restaurant problem (which is a repeated game version of any given one shot KPR game) for large N. For statistical analysis, we explore the long time steady state behavior. In many such models with myopic agents we get under-utilization of resources, that is, we get a lower aggregate payoff compared to the social optimum. We study a number of myopic strategies, focusing on the average occupation fraction of restaurants.

Group Strategyproofness in Queueing Models

We identify and characterize a natural and intuitive class of mechanisms called the k-pivotal mechanisms. The axioms used are efficiency, pairwise strategyproofness, equal treatment of equals and weak linearity. We also identify the subclass of these mechanisms which do not run a budget deficit at all profiles and the mechanism which runs the least budget surplus. We also show that while k-pivotal mechanisms are also weak group strategyproof, strong group strategyproofness and efficiency are incompatible.

On the coincidence of the prenucleolus and the Shapley value

We identify a sufficient class of coalitional form games with transferable utility for which prenucleolus coincides with the Shapley value. We then apply our result to simple games and to generalized queueing games

Strategy proofness and Pareto efficiency in quasilinear exchange economies

In this paper, we revisit a long-standing question on the structure of strategy-proof and Pareto-efficient social choice functions (SCFs) in classical exchange economies (Hurwicz (1972)). Using techniques developed by Myerson in the context of auction-design, we show that in a specific quasi-linear domain, every Pareto-efficient and strategy-proof SCF satisfying non-bossiness and a mild continuity property is dictatorial. The result holds for an arbitrary number of agents but the two-person version does not require either the non-bossiness or continuity assumptions. It also follows that the dictatorship conclusion holds on any superset of this domain. We also provide a minimum consumption guarantee result in the spirit of Serizawa and Weymark (2003).

Incomplete information and multiple machine queueing problems

In mechanism design problems under incomplete information, it is generally difficult to find decision problems that are first best implementable. A decision problem under incomplete information is first best implementable if there exists a mechanism that extracts the private information and achieves efficiency with a transfer scheme that adds up to zero in every state. One such problem is the queueing problem with one machine. In this paper we identify the conditions on cost structure for which queueing problems with multiple machines are first best implementable.

Privatization, Underpricing, and Welfare in the Presence of Foreign Competition

We analyze privatization in a differentiated oligopoly setting with a domestic public firm and foreign profit-maximizing firms. In particular, we examine pricing below marginal cost by public firm, the optimal degree of privatization and, the relationship between privatization and foreign ownership restrictions. When market structure is exogenous, partial privatization of the public firm improves welfare by reducing public sector losses. Surprisingly, even at the optimal level of privatization, the public firms price lies strictly below marginal cost, resulting in losses. Our analysis also reveals a potential conflict between privatization and investment liberalization (i.e., relaxing restrictions on foreign ownership) in the short run. With endogenous market structure (i.e., free entry of foreign firms), partial privatization improves welfare through an additional channel: more foreign varieties. Furthermore, at the optimal level of privatization, the public firms price lies strictly above marginal cost and it earns positive profits.

Regulation of an open access essential facility

In this paper we consider the problem of regulating an open access essential facility. A vertically integrated firm owns an essential input and operates on the downstream market under the roof of a regulatory mechanism. There is a potential entrant in the downstream market. Both competitors use the same essential input to provide the final services to the consumers. The regulator designs a mechanism that guarantees financing of the essential input and adequate competition in the downstream market. We consider a regulatory mechanism that grants non-discriminatory access of the essential facility to a competitor. We show that this mechanism is welfare improving but it generates inefficient entry. That is a more efficient competitor may stay out of the market or a less efficient competitor may enter the market.

Reversal of Bertrand-Cournot Rankings in the Presence of Welfare Concerns

We revisit the comparison between Bertrand and Cournot competition in a symmetric differentiated oligopoly where each firm maximizes a weighted average of its own profit and welfare. Under very general specifications, Bertrand competition yields higher prices and profits, and lower quantities, consumer surplus, and welfare than Cournot when the weight on profit is lower than a threshold value. The threshold weight on profit (welfare) can be arbitrarily close to unity (zero) for both quadratic and CES utilities. Particularly striking is the following asymptotic result for CES: irrespective of the degree of substitutability, the threshold weight on profit tends to unity as the number of firms approaches infinity.

A course on cooperative game theory

Cooperative game theory deals with situations where objectives of participants of the game are partially cooperative and partially conflicting. It is in the interest of participants to cooperate in the sense of making binding agreements to achieve the maximum possible benefit. When it comes to distribution of benefit/payoffs, participants have conflicting interests. Such situations are usually modelled as cooperative games. While the book mainly discusses transferable utility games, there is also a brief analysis of non-transferable utility games. Alternative solution concepts to cooperative game theoretic problems are presented in chapters 1-9 and the next four chapters present issues related to computations of solutions discussed in the earlier chapters. The proofs of all results presented in the book are quite explicit. Additionally the mathematical techniques employed in demonstrating the results will be helpful to those who wish to learn application of mathematics for solving problems in game theory.