Partially-honest Nash implementation: a full characterization
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Partially-honest Nash implementation: a full characterization Michele Lombardi1,2 · Naoki Yoshihara3,4,5 Received: 28 January 2019 / Accepted: 22 October 2019 © The Author(s) 2019
Abstract A partially-honest individual is a person who follows the maxim, “Do not lie if you do not have to”, to serve your material interest. By assuming that the mechanism designer knows that there is at least one partially-honest individual in a society of n ≥ 3 individuals, a social choice rule that can be Nash implemented is termed partiallyhonestly Nash implementable. The paper offers a complete characterization of the (unanimous) social choice rules that are partially-honestly Nash implementable. When all individuals are partially-honest, then any (unanimous) rule is partially-honestly Nash implementable. An account of the welfare implications of partially-honest Nash implementation is provided in a variety of environments. Keywords Nash implementation · Pure strategy Nash equilibrium · Partial honesty · Condition μ∗ (ii) JEL Classification C72 · D71
We are grateful to Nicholas Yannelis and two referees of this journal for their thoughtful comments and suggestions. The usual caveat applies.
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Michele Lombardi [email protected] Naoki Yoshihara [email protected]
1
Adam Smith Business School, University of Glasgow, Glasgow G12 8QQ, UK
2
Department of Economics and Statistics, University of Naples Federico II, Naples, Italy
3
Department of Economics, University of Massachusetts Amherst, 412 North Pleasant Street, Amherst, MA 01002, USA
4
The Institute of Economic Research, Hitotsubashi University, Kunitachi, Tokyo 186-0004, Japan
5
School of Management, Kochi University of Technology, Kochi 782-8502, Japan
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M. Lombardi, N. Yoshihara
1 Introduction The implementation problem is the problem of designing a mechanism or game form with the property that, for each state of the world, the equilibrium outcomes of the mechanism played in that state coincide with the recommendations that a given social choice rule (SCR) F would prescribe for that state. If that mechanism design exercise can be accomplished, the SCR is said to be implementable. The fundamental paper on implementation in Nash equilibrium is thanks to Maskin (1999; circulated since 1977), who proves that any SCR that can be Nash implemented satisfies a remarkably strong invariance condition, now widely referred to as Maskin monotonicity. Moreover, he shows that when the mechanism designer faces n ≥ 3 individuals, a SCR is Nash implementable if it is Maskin monotonic and satisfies the condition of no veto-power, subsequently, Maskin’s theorem.1 Since the introduction of Maskin’s theorem, economists have been interested in understanding how to circumvent the limitations imposed by Maskin monotonicity by exploring the possibilities offered by approximate (as opposed to exact) implementation (Matsushima 1988; Abreu and Sen 1991), as well as by implementation in refinements of Nash equilibrium (Moore and Repullo 1988; Abreu and Sen 1990; Palfre
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