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.

In standard contract-theoretic models, the underlying assumption is that agent types differ in their preference or cost parameters, and the principal's objective is to design contracts in order to screen this type. We study a contract-theoretic model in which the heterogeneity among agent types is of a “cognitive” nature. In our model, the agent has dynamically inconsistent preferences. Agent types differ only in their degree of “sophistication”, that is, their ability to forecast the change in their future tastes. We fully characterize the menu of contracts which the principal offers in order to screen the agent's sophistication. The menu does not exclude any type: it provides a perfect commitment device for relatively sophisticated types, and “exploitative” contracts which involve speculation with relatively naive types. More naive types are more heavily exploited and generate a greater profit for the principal. Our results allow us to interpret real-life contractual arrangements in a variety of industries.