Arunava Sen

The implementation theory is widely regarded as the reverse engineering of game theory.[4] It is concerned with the design of a game (or game-form) such that every equilibrium outcome of the game produces the desired outcome (modeled as a social choice rule) of the designer. The notion of equilibrium or the solution concept allows flexibility in designing games. In his Nobel prize winning work, Eric Maskin investigates implementation using Nash equilibrium as the solution concept.[5] Maskin shows that any Nash implementable social choice rule must satisfy a monotonicity property, which is now called Maskin monotonicity. Conversely, every social choice rule which is Maskin monotone and satisfies a mild property, called no veto power, can be implemented in Nash equilibrium.[5] This started a large literature in implementation theory. Arunava Sen, along with his coauthors, has contributed to this literature by extending Maskin's results in various directions.

Maskin's result [5] requires that there are at least three agents who will play the designed game. In his work [6] with Bhaskar Dutta, Arunava Sen extends Maskin's result when there are only two agents. In his work [7] with Dilip Abreu, they introduce a new implementation framework. In their model, a social choice rule produces a lottery over a finite set of outcomes at every profile of preferences. The equilibrium outcome lottery of the designed game need not coincide with the social choice rule outcome, but they have to be arbitrarily close. They call this virtual implementation [7] and show that virtual implementation using Nash equilibrium as the solution concept is quite permissive. In another joint work [8] with Dilip Abreu, Arunava Sen investigates implementation where a designer can design extensive form games. They describe the social choice rules that can be implemented in subgame perfect equilibrium. Their result extends the work of Moore and Repullo.[9]

In his work [10] with Bhaskar Dutta, Arunava Sen studies a new model of implementation, where agents (playing the game) can be partially honest. In their model, an agent is partially honest if she strictly prefers telling the truth whenever she is indifferent between telling the truth and lying. This paper revisits Maskin's seminal paper [5] in this new model and presents several new insights. They show that if there is at least one partially honest agent (out of at least three agents), then every social choice rule satisfying no veto power can be implemented in Nash equilibrium. Thus, Maskin monotonicity is no longer a necessary condition in this model.

In his work [11] with Saptarshi Mukherjee (one of his Ph.D. students), Nozumo Muto, and Eve Raemakers, Arunava Sen studies implementation in undominated strategies using bounded mechanisms. They show that the Pareto correspondence is implementable in undominated strategies using bounded mechanisms.[11] This answers an open question in the literature posed by Tilman Borgers.[12] The work is also important because implementation in undominated strategies has been criticised for using unbounded mechanisms to establish various results,[13] and their work provides a general positive result on implementation using bounded mechanisms and undominated strategies.

Arunava Sen has done fundamental contributions to the theory of strategic voting. The starting point of this theory is an impossibility result due to Gibbard and Satterthwaite: the Gibbard-Satterthwaite (GS) impossibility theorem and Gibbard's theorem. Roughly, it states that there is no voting rule which is unanimous, non-dictatorial, and non-manipulable (strategyproof) if the preferences of voters are unrestricted. Arunava Sen's work in this area identifies environments where such theorems hold or well-behaved voting rules exist. In his work[14] with his coauthors Navin Aswal and Shurojit Chatterji, he provides a comprehensive description of environments where GS theorem holds. In his works[15] and [16] with coauthors Shurojit Chatterji, Huaxia Zeng, and Remzi Sanver, he identifies environments where GS theorem does not hold, i.e., well-behaved voting rules exist. In his work[17] with coauthors Shurojit Chatterji and Huaxia Zeng, he has identified environments where the GS theorem type result continues to hold even if the voting rule allows for randomization (which generalizes Gibbard's theorem).

In his work [18] with his coauthor (and Ph.D. student) Dipjyoti Majumdar, he weakens the notion of non-manipulability in the GS theorem to Ordinal Bayesian Incentive Compatibility, first studied in an important paper by Claude d'Aspremont and Gerard Varet.[19] Arunava's work[18] with Dipjyoti Majumdar shows that whether well-behaved voting rules exist with this weakening of non-manipulability depends on the beliefs of the voters on other voters' preferences. If beliefs are uniformly distributed, then many well-behaved voting rules exist and they provide a comprehensive description of such voting rules. However, if voters have generic beliefs (which are independent), a GS theorem type impossibility reappears. In a follow up work[20] with Mohit Bhargava and Dipjyoti Majumdar, he shows that if voters beliefs are correlated, then it is possible to escape the impossibility of the GS theorem using this weaker notion of incentive compatibility.

In his work[21] with his coauthor Michel Le Breton, he studies a voting environment where voters vote on various dimensions but preferences of voters are separable across dimensions. Their work identifies conditions on environments such that every unanimous and non-manipulable (strategyproof) voting rule can be decomposed along each dimension. He has pursued this line of research in some of his other work.[22] In his work[23] with Bhaskar Dutta and Hans Peters, he shows that considering cardinal voting schemes does not allow one to escape the consequences of GS impossibility theorem.

Arunava Sen has done fundamental contributions to the theory of mechanism design where transfers are used for incentives, e.g., auction design. In mechanism design, incentive compatibility is often characterized by (equivalent to) some form of monotonicity condition. In his seminal work on revenue-maximizing single object auctions, Roger Myerson provides such a monotonicity condition. In his work[24] with Sushil Bikhchandani, Shurojit Chatterji, Ron Lavi, Ahuva Mualem, and Noam Nisan, Arunava Sen provides an analogue of this monotonicity condition which works in a variety of problems, including multi-object auctions and provision of multiple public goods. This work [24] is regarded as a fundamental contribution to the multidimensional mechanism design literature, where private information of agents have multiple dimensions. In his works [25] and [26] with Debasis Mishra and Swaprava Nath, he has described the set of all strategyproof mechanisms in mechanism design settings which permit transfers. These contributions extend a seminal characterization of strategyproof mechanisms in these settings due to Kevin W. S. Roberts.

Arunava Sen has provided simple proofs of three important theorems in mechanism design. In his work,[27] he uses induction on the number of agents to provide a simple proof of the Gibbard-Satterthwaite (GS) theorem. The induction technique in proving the GS theorem is quite easily extendible to other settings where such theorems hold. For instance, in his work[18] with Dipjyoti Majumdar, he uses similar induction techniques to prove an analogue of the GS theorem using a weaker notion of incentive compatibility. He uses the induction technique to prove a simpler version of Gibbard's theorem in his work.[28] In his work [25] with Debasis Mishra, he provides a simpler proof of an important theorem, due to Kevin W. S. Roberts, which characterizes the set of strategyproof mechanisms in mechanism design problems with transfers. This proof uses ideas from social choice theory, particularly in.[19]

In general, Arunava Sen's works tend to connect different branches of mechanism design theory and social choice theory to establish elegant results in different areas of economic theory. A prime example of such a work is [29] with Mridul Prabal Goswami. In this work,[29] they use ideas from Myerson's single object auction design to prove a dictatorship result in an exchange economy setting, a problem which was first studied by Leonid Hurwicz.

His contributions have been published in journals like Econometrica, Review of Economic Studies, Theoretical Economics, Journal of Economic Theory, Games and Economic Behavior and Social Choice and Welfare among others.[1]