Robust Equilibria in General Competing Mechanism Games

This paper proposes the notion of robust PBE in a general competing mechanism game of incomplete information where a mechanism allows its designer to send a message to himself at the same time agents send messages. It identifies the utility environments where the notion of robust PBE coincides with that of strongly robust PBE (Epstein and Peters (1999), Han (2007)) and with that of robust PBE respectively. If each agent's utility function is additively separable with respect to principals' actions, it is possible to provide the full characterization of equilibrium allocations under the notion of robust PBE and its variations, in terms of Bayesian incentive compatible (BIC) direct mechanisms, without reference to the set of arbitrary general mechanisms allowed in the game. However, in the standard competing mechanism agme, the adoption of robust PBE as the solution concept does not lead to the full characterization of equilibrium allocations in terms of BIC direct mechanisms even with agents' separable utility functions.