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 mechanism design theory, a designer would like to implement a desired social choice function which specifies her favorite outcome for each possible profile of agents' types. To do so, the designer constructs a mechanism which describes each agent's feasible strategy set and the outcome function. 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 notion of Bayesian Nash equilibrium of a mechanism should be based on a three-parameter profit function instead of the conventional two-parameter utility function when strategies of agents are costly actions. 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

References

1. A. Mas-Colell, M.D. Whinston and J.R. Green, Microeconomic Theory, Oxford University Press, 1995.

2. R. Myerson, Incentive compatibility and the bargaining problem, Econometrica, vol.47, 61-73, 1979.

3. R. Myerson, Optimal coordination mechanisms in generalized principal-agent problems, Journal of Mathematical Economics, vol.10, 67-81, 1982.

4. Y. Narahari et al, Game Theoretic Problems in Network Economics and Mechanism Design Solutions, Springer, 2009.

5. N. Kartik, Strategic Communication with Lying Costs. The Review of Economic Studies, vol.76, 1359-1395, 2009.

6. A. Kephart and V. Conitzer, The revelation principle for mechanism design with reporting cost, In Proceedings of the ACM Conference on Electronic Commerce (EC), Maastricht, The Netherlands, 2016.

7. H. Bester and R. Strausz, Contracting with imperfect commitment and the revelation principle: The single agent case. Econometrica, Vol.69, No.4, 1077-1098, 2001.

8. D. Martimort and L. Stole, The revelation and delegation principles in common agency games. Econometrica, Vol.70, No.4, 1659-1673, 2002.