Commitment games with conditional information revelation

The conditional commitment abilities of mutually transparent computer agents have been studied in previous work on commitment games and program equilibrium. This literature has shown how these abilities can help resolve Prisoner's Dilemmas and other failures of cooperation in complete information settings. But inefficiencies due to private information have been neglected thus far in this literature, despite the fact that these problems are pervasive and might also be addressed by greater mutual transparency. In this work, we introduce a framework for commitment games with a new kind of conditional commitment device, which agents can use to conditionally reveal private information. We prove a folk theorem for this setting that provides sufficient conditions for ex post efficiency, and thus represents a model of ideal cooperation between agents without a third-party mediator. Connecting our framework with the literature on strategic information revelation, we explore cases where conditional revelation can be used to achieve full cooperation while unconditional revelation cannot. Finally, extending previous work on program equilibrium, we develop an implementation of conditional information revelation. We show that this implementation forms program $\epsilon$-Bayesian Nash equilibria corresponding to the Bayesian Nash equilibria of these commitment games.