The revelation principle does not always hold when strategies of agents are costly

Wu, Haoyang (2018): The revelation principle does not always hold when strategies of agents are costly.

Abstract

The revelation principle asserts that for any indirect mechanism and equilibrium, there is a corresponding direct mechanism with truth as an equilibrium. Although the revelation principle has been a fundamental theorem in the theory of mechanism design for a long time, so far the costs related to strategic actions of agents spent in a mechanism have not been fully discussed. In this paper, we investigate the correctness of the revelation principle when strategies of agents are costly. We point out two key results: (1) The strategic action of each agent in a direct mechanism is just to report a type. Each agent does not need to take any other action to prove himself that his reported type is truthful, and should not play any strategic action as chosen in an indirect mechanism. Hence in a direct mechanism, each agent should not spend strategic costs occurred in an indirect mechanism (see Proposition 1); (2) When strategic costs cannot be neglected in the indirect mechanism, the proof of revelation principle given in Proposition 23.D.1 of the book ``A. Mas-Colell, M.D. Whinston and J.R. Green, Microeconomic Theory, Oxford University Press, 1995'' is wrong (see Proposition 2). We construct a simple labor model to show that a Bayesian implementable social choice function is not truthfully implementable (see Proposition 4), which contradicts the revelation principle.

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

References

\bibitem{Myerson1979} R. Myerson, Incentive compatibility and the bargaining problem, Econometrica, vol.47, 61-73, 1979.

\bibitem{Myerson1982} R. Myerson, Optimal coordination mechanisms in generalized principal-agent problems, Journal of Mathematical Economics, vol.10, 67-81, 1982.

\bibitem{MWG1995} A. Mas-Colell, M.D. Whinston and J.R. Green, Microeconomic Theory, Oxford University Press, 1995.

\bibitem{Narahari2009} Y. Narahari et al, Game Theoretic Problems in Network Economics and Mechanism Design Solutions, Springer, 2009.

\bibitem{Spence1973} M. Spence, Job Market Signaling. Quarterly Journal of Economics, vol.87, 355-374, 1973.

\bibitem{Kephart2016} 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.

\bibitem{Green1986} J. Green and J.J. Laffont, Partially verifiable information and mechanism design. Review of Economic Studies, vol.53, 447-456, 1986.

\bibitem{Yu2011} L. Yu, Mechanism design with partial verification and revelation principle. Autonomous Agents and Multi-Agent Systems, vol.22, 217-223, 2011.