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 nge 3 individuals, a social choice rule that can be Nash implemented is termed partially-honestly 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.
Highlights
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
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, widely referred to as Maskin monotonicity
In the coalitional game environment, we show that the core solution is not Nash implementable with partially-honest individuals when the mechanism designer knows the coalitional function of the games, who, does not know the prevailing state
Summary
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. Theorem 2 shows that every unanimous SCR is implementable when all agents are partially-honest and the mechanism designer knows this. By means of Condition μ∗(ii), we can check what SCR is implementable within the domain of unanimous SCRs. For instance, in the coalitional game environment, we show that the core solution is not Nash implementable with partially-honest individuals when the mechanism designer knows the coalitional function of the games, who, does not know the prevailing state. We show that every unanimous SCR is Nash implementable in a society in which all individuals are partially-honest and the designer knows it.
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