Recent working papers

[1.] Self-implementation of social choice correspondences in Nash equilibrium (2021)

Saptarshi Mukherjee, Hans Peters

 Abstract A social choice correspondence is Nash self-implementable if it can be implemented in Nash equilibrium by a social choice function that selects from it as the game form. We provide a fairly complete characterization of all unanimous and anonymous social choice correspondences that can be Nash implemented by an anonymous selection. In particular, such social choice correspondences include the top correspondence and are included in the Pareto correspondence.

[2.] Strategic transfers between cooperative games (2021)

Caroline Berden, Hans Peters, Laura Robles, Dries Vermeulen 

Abstract  We consider a model where the same group of players is involved in more than one cooperative (transferable utility) game.  A rule determines the payoffs per game, and for each player a utility function evaluates the resulting vector of payoffs. We assume that each player, independently, can make transfers of worth between different games, thereby affecting its payoff vector and, thus, utility. Two transfer systems are considered, resulting in two distinct noncooperative games, and the focus of the paper is on establishing existence and a characterization of Nash equilibria in these games.

[3.] Group strategy-proof rules in multidimensional binary domains (2020)

Aditya Aradhye, Hans Peters 

Abstract  We consider a setting in which the alternatives are binary vectors and the preferences of the agents are determined by the Hamming distance from their most preferred alternatives. We consider social choice functions that are unanimous, anonymous, and neutral, and focus on strategy-proofness, weak group strategy-proofness, and strong group strategy-proofness. Our results range from possibility results concerning strategy-proofness and weak group strategy-proofness, to impossibility of strong group strategy-proof social choice functions. Related work includes work on judgment aggregation and on classification.

[4.] Sequential claim games (2021)

Qianqian Kong, Hans Peters

Abstract  We consider the estate division or bankruptcy problem, and assume that players sequentially put claims on the estate. Each part of the estate is then divided proportionally with respect to the number of claims on it. We focus on myopic play: players first claim the hitherto least claimed parts, and on subgame perfect equilibria. Our main result is that myopic play is a subgame perfect equilibrium if punishments for deviators are included.

[5.] Power indices for networks, with applications to matching markets (2021)

Qianqian Kong, Hans Peters

Abstract We study situations where agents can form or sever links in a network: what agents can do exactly is described by effectivity functions. A power index assigns to such an effectivity function a number for each agent, measuring the opportunities of that agent. We characterize a class of power indices by four axioms: the Transfer Property, the Dummy Property, Symmetry, and Network Neutrality. As a corollary, we obtain power indices for the case where effectivity functions are induced by preferences of agents about the other agents.  Applications include one-to-one, one-to-many, and many-to-many matching markets, as well as roommate problems.