A note on the definition of Bayesian Nash equilibrium of a mechanism when strategies of agents are costly actions

Wu, Haoyang (2019): A note on the definition of Bayesian Nash equilibrium of a mechanism when strategies of agents are costly actions.

Abstract

In the framework of mechanism design theory, in order to implement a desired social choice function in Bayesian Nash equilibrium, a designer constructs a mechanism which specifies her favorite outcome for each possible profile of agents' types. Generally speaking, each agent's strategy has two possible formats: an action, or a message. In this paper, we focus on the former case and claim that the definitions of Bayesian Nash equilibrium of a mechanism and Bayesian incentive compatibility should all be based on a profit function instead of a utility function. Next, we derive the main result: Given a social choice function which can be implemented by an indirect mechanism in Bayesian Nash equilibrium, if all strategies of agents are costly actions, then it cannot be inferred that there exists a direct mechanism that can truthfully implement the social choice function in Bayesian Nash equilibrium.

• Item Type: MPRA Paper
• Language: English
• Keywords: Bayesian Nash Equilibrium; Mechanism design; Revelation Principle.
• Subjects: D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; Associations; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty

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