Fault tolerant implementation

In this paper we investigate the implementation problem arising when some of the players are "faulty" in the sense that they fail to act optimally. The planner and the non-faulty players only know that there can be at most k faulty players in the population. However, they know neither the identity of the faulty players, their exact number nor how faulty players behave. We define a solution concept which requires a player to optimally respond to the non-faulty players regardless of the identity and actions of the faulty players. We introduce a notion of fault tolerant implementation, which unlike standard notions of full implementation, also requires robustness to deviations from the equilibrium. The main result of this paper establishes that under symmetric information any choice rule that satisfies two properties-k-monotonicity and no veto power-can be implemented by a strategic game form if there are at least three players and the number of faulty players is less than 1/2n-1. As an application of our result we present examples of simple mechanisms that implement the constrained Walrasian function and a choice rule for the efficient allocation of an indivisible good.