Implementation with a Bounded Action Space

Liad Blumrosen () and Michal Feldman ()

Discussion Paper Series from The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem

Abstract: While traditional mechanism design typically assumes isomorphism between the agents' type- and action spaces, in many situations the agents face strict restrictions on their action space due to, e.g., technical, behavioral or regulatory reasons. We devise a general framework for the study of mechanism design in single-parameter environments with restricted action spaces. Our contribution is threefold. First, we characterize sufficient conditions under which the information-theoretically optimal social-choice rule can be implemented in dominant strategies, and prove that any multilinear social-choice rule is dominant-strategy implementable with no additional cost. Second, we identify necessary conditions for the optimality of action-bounded mechanisms, and fully characterize the optimal mechanisms and strategies in games with two players and two alternatives. Finally, we prove that for any multilinear social-choice rule, the optimal mechanism with k actions incurs an expected loss of O(1/k^2) compared to the optimal mechanisms with unrestricted action spaces. Our results apply to various economic and computational settings, and we demonstrate their applicability to signaling games, public-good models and routing in networks.

Pages: 25 pages
Date: 2005-12
New Economics Papers: this item is included in nep-cmp and nep-mic
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Citations: View citations in EconPapers (1)

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