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 disclose 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. Further, extending previous work on program equilibrium, we develop an implementation of conditional information disclosure. We show that this implementation forms program ε-Bayesian Nash equilibria corresponding to the Bayesian Nash equilibria of these commitment games.

We study the problem of adaptability in repeated games: simultaneously guaranteeing low regret for several classes of opponents. We add the constraint that our algorithm is non-exploitable, in that the opponent lacks an incentive to use an algorithm against which we cannot achieve rewards exceeding some “fair” value. Our solution is an expert algorithm (LAFF), which searches within a set of sub-algorithms that are optimal for each opponent class, and punishes evidence of exploitation by switching to a policy that enforces a fair solution. With benchmarks that depend on the opponent class, we first show that LAFF has sublinear regret uniformly over these classes. Second, we show that LAFF discourages exploitation, because exploitative opponents have linear regret. To our knowledge, this work is the first to provide guarantees for both regret and non-exploitability in multi-agent learning.

Reinforcement learning problems with multiple agents pose the challenge of efficiently adapting to nonstationary dynamics arising from other agents’ strategic behavior. Although several algorithms exist for these problems with promising empirical results, regret analysis and efficient use of other-agent models in general-sum games is very limited. We propose an algorithm (TSMG) for general-sum Markov games against agents that switch between several stationary policies, combining change detection with Thompson sampling to learn parametric models of these policies. Under standard assumptions for parametric Markov decision process (MDP) learning, the expected regret of TSMG in the worst case over policy parameters and switch schedules is near-optimal in time and number of switches, up to logarithmic factors. Our experiments on simulated games show that TSMG can outperform standard Thompson sampling and a version of Thompson sampling with a static reset schedule, despite the violation of an assumption that the MDPs induced by the other player are ergodic.