Robust Equilibria in General Competing Mechanism Games

TL;DR

This paper introduces the concept of robust PBE in competing mechanism games with incomplete information, characterizes equilibrium allocations under certain utility conditions, and discusses limitations in standard settings.

Contribution

It defines robust PBE for competing mechanism games and provides full characterizations under additive utility separability, highlighting differences from standard models.

Findings

Robust PBE coincides with strongly robust PBE under certain utility environments.

Full characterization of equilibrium allocations is possible with additive separable utilities.

Standard competing mechanism games do not allow full characterization of equilibrium allocations with robust PBE.

Abstract

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.