Mechanism design with a restricted action space

Liad Blumrosen; Michal Feldman

doi:10.1016/j.geb.2013.03.005

Mechanism design with a restricted action space

Liad Blumrosen^*, Michal Feldman

^*Corresponding author for this work

Business Administration

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

While traditional mechanism design typically assumes isomorphism between the type space of the players and their action space, behavioral, technical or regulatory factors can severely restrict the set of actions that are actually available to players. We study single-parameter mechanism-design problems in environments with restricted action spaces. In our first main result, we provide sufficient conditions under which the information-theoretically optimal solution can be implemented in equilibrium. Our second main result shows that for a wide family of social-choice rules the optimal mechanisms with k actions incur an expected loss of O(1k2) compared to the optimal mechanisms with unrestricted action space. We also fully characterize the optimal mechanisms in some simple environments and, finally, we apply our general results to signaling games, public-good models and project planning.

Original language	English
Pages (from-to)	424-443
Number of pages	20
Journal	Games and Economic Behavior
Volume	82
DOIs	https://doi.org/10.1016/j.geb.2013.03.005
State	Published - 2013

Bibliographical note

Funding Information:
✩ The authors are grateful to Itzhak Gilboa, Zvika Neeman, Noam Nisan, Ady Pauzner, Yuval Salant and Ilya Segal for valuable discussions, and to anonymous referees for their thoughtful comments and suggestions. We also thank the participants of the SITE workshop on Market Design at Stanford, and of other seminars at Berkeley, Harvard, Cornell and the Hebrew University, for helpful comments. An extended abstract of this paper with preliminary results appeared in the Proceedings of the ACM Conference on Electronic Commerce, Ann Arbor, MI, 2006. The first author was supported by the Israel Science Foundation grant number 230/10, by the Google Inter-university center for Electronic Markets and Auctions, and by the Maurice Falk Institute for Economic Research in Israel. * Corresponding author at: Department of Economics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem, 91905, Israel. E-mail addresses: [email protected] (L. Blumrosen), [email protected] (M. Feldman). 1 Current address: School of Business Administration, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem, 91905, Israel.

Keywords

Communication complexity
D82
D83
Expressiveness
Implementation
Mechanism design
Message space

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10.1016/j.geb.2013.03.005

Cite this

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abstract = "While traditional mechanism design typically assumes isomorphism between the type space of the players and their action space, behavioral, technical or regulatory factors can severely restrict the set of actions that are actually available to players. We study single-parameter mechanism-design problems in environments with restricted action spaces. In our first main result, we provide sufficient conditions under which the information-theoretically optimal solution can be implemented in equilibrium. Our second main result shows that for a wide family of social-choice rules the optimal mechanisms with k actions incur an expected loss of O(1k2) compared to the optimal mechanisms with unrestricted action space. We also fully characterize the optimal mechanisms in some simple environments and, finally, we apply our general results to signaling games, public-good models and project planning.",

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Mechanism design with a restricted action space

Abstract

Bibliographical note

Keywords

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