n 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 exact number and identity of the faulty players is unknown to the planner and to the nonfaulty players, but it is common knowledge that there are at most k faulty players. We define a solution concept which requires a player to optimally respond to the nonfaulty 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+1 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. For exchange economies we show that the Walrasian correspondence and the core correspondence are implementable. 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.
