Fault Tolerant Bayesian Implementation in Exchange Economies

In this work, we extend the concept of Fault Tolerant Implementation of Eliaz (2002) to the concept of Fault Tolerant Implementation in incomplete information environments. In particular, we work in a domain where information is non-exclusive by choosing a model of pure exchange economy. As in Eliaz (2002), we suppose the existence of at most k faulty players who do not act in an optimal way, either because they do not understand the rules of the game or they make mistakes. We develop a new concept of equilibrium, called k-Fault Tolerant Bayesian Equilibrium (k-FTBE) and a new concept of implementation, called fault tolerant Bayesian implementation. In a model of pure exchange economy, we show that weak k- Bayesian monotonicity is a necessary condition for the implementation of social choice correspondences in k-FTBE. We also introduce the no-exclusiveness information condition (k-NEI), and we show that k-Bayesian monotonicity and k-NEI are sufficient conditions for implementation when there are at least three players and the number of the faulty players is less then (n/2)-1.