【Micro Seminar】Compellingness in Nash Implementation

  • 研討會日期 : 2023-02-07
  • 時間 : 15:00
  • 主講人 : Professor Takashi Kunimoto
  • 地點 : Conference room B110
  • 主持人 : Professor Wei-Torng Juang
  • 演講者簡介 : Professor Kunimoto received his Ph.D. in Economics from Brown University in 2005. He is currently an Associate Professor at Singapore Management University. His research interests are Bargaining, Contract Theory, Game Theory, Implementation Theory, Mechanism Design, and Microeconomic Theory.
  • 演講摘要 : A social choice function (SCF) is said to be Nash implementable if there exists a mechanism in which every Nash equilibrium outcome coincides with that specified by the SCF. The main objective of this paper is to assess the impact of considering mixed strategy equilibria in Nash implementation. To do this, we focus on environments with two agents and restrict attention to finite mechanisms. We call a mixed strategy equilibrium “compelling” if its outcome Pareto dominates any pure strategy equilibrium outcome. We show that if the finite environment and the SCF to be implemented jointly satisfy what we call Condition P+M, we construct a finite mechanism which Nash implements the SCF in pure strategies and possesses no compelling mixed strategy equilibria. This means that the mechanism might possess mixed strategy equilibria which are “not” compelling. Our mechanism has several desirable features: transfers can be completely dispensable; only finite mechanisms are considered; integer games are not invoked; and agents' attitudes toward risk do not matter. These features make our result quite distinct from many other prior attempts to handle mixed strategy equilibria in the theory of implementation. We also illustrate the difficulty of extending our result to the case of more than two agents.