Coordination Failure in Repeated Games with Private Monitoring

Abstract

Players coordinate continuation play in repeated games with public monitoring. This paper asks the robustness of such equilibrium play with respect to private monitoring perturbations that are ex-ante close to the public-monitoring structure. We show that, in two-player games with full support of public signals, no perfect public equilibrium is robust to private-monitoring perturbations under a regularity condition. This non-robustness result does not apply to belief-free equilibria, which violate the regularity condition. Indeed, we show that, in two-player games with an individual rank condition on public signals, every interior belief-free equilibrium is robust to private-monitoring perturbations. We also argue by means of an example that the non-robustness result is sensitive to the assumption that every private signal must be interpreted as some public signal with probability 1, and not with probability close to 1.