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This work studies an independent natural policy gradient (NPG) algorithm for the multi-agent reinforcement learning problem in Markov potential games. It is shown that, under mild technical assumptions and the introduction of the…
Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…
We consider two-player games with imperfect information and the synthesis of a randomized strategy for one player that ensures the objective is satisfied almost-surely (i.e., with probability 1), regardless of the strategy of the other…
For a two-player imperfect-information extensive-form game (IIEFG) with $K$ time steps and a player action space of size $U$, the game tree complexity is $U^{2K}$, causing existing IIEFG solvers to struggle with large or infinite $(U,K)$,…
This paper considers a zero-sum two-player asymmetric information stochastic game where only one player knows the system state, and the transition law is controlled by the informed player only. For the informed player, it has been shown…
We address two-player general-sum stochastic Stackelberg games (SSGs), where the leader's policy is optimized considering the best-response follower whose policy is optimal for its reward under the leader. Existing policy gradient and value…
This paper extends Berge's maximum theorem for possibly noncompact action sets and unbounded cost functions to minimax problems and studies applications of these extensions to two-player zero-sum games with possibly noncompact action sets…
In this paper, we investigate the seeking of Nash equilibrium (NE) in a non-cooperative quadratic game where all agents exchange their delayed strategy information with their neighbors. To extend best-response algorithms to the delayed…
Zero-determinant strategies are a class of strategies in repeated games which unilaterally control payoffs. Zero-determinant strategies have attracted much attention in studies of social dilemma, particularly in the context of evolution of…
We consider zero-sum repeated games in which the players are restricted to strategies that require only a limited amount of randomness. Let $v_n$ be the max-min value of the $n$ stage game; previous works have characterized…
We study reinforcement learning for two-player zero-sum Markov games with simultaneous moves in the finite-horizon setting, where the transition kernel of the underlying Markov games can be parameterized by a linear function over the…
We study zero-sum stochastic differential games with player dynamics governed by a nondegenerate controlled diffusion process. Under the assumption of uniform stability, we establish the existence of a solution to the Isaac's equation for…
We develop value iteration-based algorithms to solve in a unified manner different classes of combinatorial zero-sum games with mean-payoff type rewards. These algorithms rely on an oracle, evaluating the dynamic programming operator up to…
Desensitization addresses safe optimal planning under parametric uncertainties by providing sensitivity function-based risk estimates. This paper expands upon the existing work on desensitization in optimal control to address safe planning…
We motivate and propose a new model for non-cooperative Markov game which considers the interactions of risk-aware players. This model characterizes the time-consistent dynamic "risk" from both stochastic state transitions (inherent to the…
A checkers-like model game with a simplified set of rules is studied through extensive simulations of agents with different expertise and strategies. The introduction of complementary strategies, in a quite general way, provides a tool to…
It is well-known that for infinitely repeated games, there are computable strategies that have best responses, but no computable best responses. These results were originally proved for either specific games (e.g., Prisoner's dilemma), or…
We propose a new dynamics for equilibrium selection of finite player discrete strategy games. The dynamics is motivated by optimal transportation, and models individual players' myopicity, greedy and uncertainty when making decisions. The…
This paper studies multiplayer turn-based games on graphs in which player preferences are modeled as $\omega$-automatic relations given by deterministic parity automata. This contrasts with most existing work, which focuses on specific…
Secure equilibrium is a refinement of Nash equilibrium, which provides some security to the players against deviations when a player changes his strategy to another best response strategy. The concept of secure equilibrium is specifically…