One of the reasons why stochastic dynamic games with an underlying dynamic system are challenging is since strategic players have access to enormous amount of information which leads to the use of extremely complex strategies at equilibrium. One approach to resolve this challenge is to simplify players' strategies by identifying appropriate compression of information maps so that the players can make decisions solely based on the compressed version of information, called the information state. For finite dynamic games with asymmetric information, inspired by the notion of information state for single-agent control problems, we propose two notions of information states, namely mutually sufficient information (MSI) and unilaterally sufficient information (USI). Both these information states are obtained with information compression maps independent of the strategy profile. We show that Bayes-Nash Equilibria (BNE) and Sequential Equilibria (SE) exist when all players use MSI-based strategies. We prove that when all players employ USI-based strategies the resulting sets of BNE and SE payoff profiles are the same as the sets of BNE and SE payoff profiles resulting when all players use full information-based strategies. We prove that when all players use USI-based strategies the resulting set of weak Perfect Bayesian Equilibrium (wPBE) payoff profiles can be a proper subset of all wPBE payoff profiles. We identify MSI and USI in specific models of dynamic games in the literature. We end by presenting an open problem: Do there exist strategy-dependent information compression maps that guarantee the existence of at least one equilibrium or maintain all equilibria that exist under perfect recall? We show, by a counterexample, that a well-known strategy-dependent information compression map used in the literature does not possess any of the properties of MSI or USI.

Cooperation in settings where agents have both common and conflicting interests (mixed-motive environments) has recently received considerable attention in multi-agent learning. However, the mixed-motive environments typically studied have a single cooperative outcome on which all agents can agree. Many real-world multi-agent environments are instead bargaining problems (BPs): they have several Pareto-optimal payoff profiles over which agents have conflicting preferences. We argue that typical cooperation-inducing learning algorithms fail to cooperate in BPs when there is room for normative disagreement resulting in the existence of multiple competing cooperative equilibria, and illustrate this problem empirically. To remedy the issue, we introduce the notion of norm-adaptive policies. Norm-adaptive policies are capable of behaving according to different norms in different circumstances, creating opportunities for resolving normative disagreement. We develop a class of norm-adaptive policies and show in experiments that these significantly increase cooperation. However, norm-adaptiveness cannot address residual bargaining failure arising from a fundamental tradeoff between exploitability and cooperative robustness.

This paper presents a technique for approximating, up to any precision, the set of subgame-perfect equilibria (SPE) in repeated games with discounting. The process starts with a single hypercube approximation of the set of SPE payoff profiles. Then the initial hypercube is gradually partitioned on to a set of smaller adjacent hypercubes, while those hypercubes that cannot contain any SPE point are gradually withdrawn. Whether a given hypercube can contain an equilibrium point is verified by an appropriate mixed integer program. A special attention is paid to the question of extracting players' strategies and their representability in form of finite automata.