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Correlated equilibrium is an established solution concept in game theory describing a situation when players condition their strategies on external signals produced by a correlation device. In recent years, the concept has begun gaining traction also in general artificial intelligence because of its suitability for studying coordinated multi-agent systems. Yet the original formulation of correlated equilibrium assumes entirely rational players and hence fails to capture the subrational behavior of human decision-makers. We investigate the analogue of quantal response for correlated equilibrium, which is among the most commonly used models of bounded rationality. We coin the solution concept the quantal correlated equilibrium and study its relation to quantal response and correlated equilibria. The definition corroborates with prior conception as every quantal response equilibrium is a quantal correlated equilibrium, and correlated equilibrium is its limit as quantal responses approach the best response. We prove the concept remains PPAD-hard but searching for an optimal correlation device is beneficial for the signaler. To this end, we introduce a homotopic algorithm that simultaneously traces the equilibrium and optimizes the signaling distribution. Empirical results on one structured and one random domain show that our approach is sufficiently precise and several orders of magnitude faster than a state-of-the-art non-convex optimization solver. [ABSTRACT FROM AUTHOR]

Finite state machines are a well-known representation of strategies in (in)finitely repeated or stochastic games. Actions of players correspond to states in the machine and the transition between machine-states are caused by observations in the game. For extensive-form games (EFGs), machines can act as a formal grounding for abstraction methods used for solving large EFGs and as a domain-independent approach for generating sufficiently compact abstractions. We show that using machines of a restricted size in EFGs can both (i) reduce the theoretical complexity of computing some solution concepts, including Strong Stackelberg Equilibrium (SSE), (ii) as well as bring new practical algorithms that compute near-optimal equilibria considering only a fraction of strategy space. Our contributions include (1) formal definition and theoretical characterization of machine strategies in EFGs, (2) formal definitions and complexity analysis for solution concepts and their computation when restricted to small classes of machines, (3) new algorithms for computing SSE in general-sum games and Nash Equilibrium in zero-sum games that both directly use the concept of machines. Experimental results on two different domains show that the algorithms compute near-optimal strategies and achieve significantly better scalability compared to previous state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Dynamic interaction appears in many real-world scenarios where players are able to observe (perhaps imperfectly) the actions of another player and react accordingly. We consider the baseline representation of dynamic games - the extensive form - and focus on computing Stackelberg equilibrium (SE), where the leader commits to a strategy to which the follower plays a best response. For one-shot games (e.g., security games), strategy-generation (SG) algorithms offer dramatic speed-up by incrementally expanding the strategy spaces. However, a direct application of SG to extensive-form games (EFGs) does not bring a similar speed-up since it typically results in a nearly-complete strategy space. Our contributions are twofold: (1) for the first time we introduce an algorithm that allows us to incrementally expand the strategy space to find a SE in EFGs; (2) we introduce a heuristic variant of the algorithm that is theoretically incomplete, but in practice allows us to find exact (or close-to optimal) Stackelberg equilibrium by constructing a significantly smaller strategy space. Our experimental evaluation confirms that we are able to compute SE by considering only a fraction of the strategy space that often leads to a significant speed-up in computation times. [ABSTRACT FROM AUTHOR]