The revelation principle fails when the format of each agent's strategy is an action

Wu, Haoyang (2020): The revelation principle fails when the format of each agent's strategy is an action.

Abstract

In mechanism design theory, a designer would like to implement a social choice function which specifies her favorite outcome for each possible profile of agents' private types. The revelation principle asserts that if a social choice function can be implemented by a mechanism in equilibrium, then there exists a direct mechanism that can truthfully implement it.

This paper aims to propose a failure of the revelation principle. At first we point out that in any game the format of each agent's strategy is either an abstract message or a real action. For any given social choice function, if the mechanism which implements it in Bayesian Nash equilibrium has action-format strategies, then ``honest and obedient'' will not be an equilibrium strategy in the corresponding direct mechanism. Consequently, the revelation principle fails.

• Item Type: MPRA Paper
• Language: English
• Keywords: Mechanism design; Revelation principle.
• Subjects: D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; Associations

References

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

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

3. R. Serrano, The theory of implementation of social choice rules. SIAM Review 46 (2004) 377-414.

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

5. 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.

6. Epstein and Peters, A revelation principle for competing mechanisms. Journal of Economic Theory, 88, 119-160 (1999).

7. 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.