Publication Type
Working Paper
Version
publishedVersion
Publication Date
2-2024
Abstract
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 fi-nite mechanisms are considered; integer games are not invoked; and players’ attitudes toward risk do not matter.
Keywords
implementation, compelling equilibria, ordinality, mixed strate-gies, Nash equilibrium.
Discipline
Economic Theory
Research Areas
Economic Theory
First Page
1
Last Page
61
Publisher
SMU Economics and Statistics Working Paper Series Paper No. 02-2024
City or Country
Singapore
Citation
CHATTERJI, Shurojit; KUNIMOTO, Takashi; and RAMOS, Paulo Daniel Salles.
Compellingness in Nash implementation. (2024). 1-61.
Available at: https://ink.library.smu.edu.sg/soe_research/2626
Copyright Owner and License
Authors
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.