Outcome-robust mechanisms for Nash implementation

Abstract

Mechanisms for Nash implementation in the literature are fragile in the sense that they fail if just one or two players do not follow their equilibrium strategy. A mechanism is outcome-robust if its equilibrium outcome is not affected by any deviating minority of players. Is Nash implementation possible with outcome-robust mechanisms? I first show that in the standard environment, it is impossible to Nash-implement any nonconstant social choice rule with outcome-robust mechanisms even if a small number of players are partially honest. If simple transfers are used and if at least one player is partially honest, however, any social choice rule is Nash implementable using an outcome-robust mechanism. The mechanism presented in this paper makes no assumptions about how transfers enter players’ preferences except that transfers are valuable. Moreover, it has: no transfers in equilibrium, arbitrarily small off-equilibrium transfers, and no integer or modulo games.