Related papers: Playing against a stationary opponent

We consider a zero-sum stochastic game for continuous-time Markov chain with countable state space and unbounded transition and pay-off rates. The additional feature of the game is that the controllers together with taking actions are also…

In this paper, we consider both finite and infinite horizon discounted dynamic mean-field games where there is a large population of homogeneous players sequentially making strategic decisions and each player is affected by other players…

Computing Nash equilibrium policies is a central problem in multi-agent reinforcement learning that has received extensive attention both in theory and in practice. However, provable guarantees have been thus far either limited to fully…

We are interested in the convergence of the value of n-stage games as n goes to infinity and the existence of the uniform value in stochastic games with a general set of states and finite sets of actions where the transition is commutative.…

We study countably infinite stochastic 2-player games with reachability objectives. Our results provide a complete picture of the memory requirements of $\varepsilon$-optimal (resp. optimal) strategies. These results depend on the size of…

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…

Policy-based methods with function approximation are widely used for solving two-player zero-sum games with large state and/or action spaces. However, it remains elusive how to obtain optimization and statistical guarantees for such…

This paper considers the discounted criterion of nonzero-sum decentralized stochastic games with prospect players. The state and action spaces are finite. The state transition probability is nonstationary. Each player independently controls…

We consider discrete-time Markov decision processes in which the decision maker is interested in long but finite horizons. First we consider reachability objective: the decision maker's goal is to reach a specific target state with the…

We consider games played on finite graphs, whose goal is to obtain a trace belonging to a given set of winning traces. We focus on those states from which Player 1 cannot force a win. We explore and compare several criteria for establishing…

This paper studies the optimization of strategies in the context of possibly randomized two players zero-sum games with incomplete information. We compare 5 algorithms for tuning the parameters of strategies over a benchmark of 12 games. A…

We study nonzero-sum stochastic differential games with risk-sensitive ergodic cost criterion. Under certain conditions, using multi-parameter eigenvalue approach, we establish the existence of a Nash equilibrium in the space of stationary…

We study some ergodicity property of zero-sum stochastic games with a finite state space and possibly unbounded payoffs. We formulate this property in operator-theoretical terms, involving the solvability of an optimality equation for the…

We study a two-player discounted zero-sum stochastic game model for dynamic operational planning in military campaigns. At each stage, the players manage multiple commanders who order military actions on objectives that have an open line of…

One of the most classical games for stochastic processes is the zero-sum Dynkin (stopping) game. We present a complete equilibrium solution to a general formulation of this game with an underlying one-dimensional diffusion. A key result is…

This paper provides necessary and sufficient conditions for a pair of randomised stopping times to form a saddle point of a zero-sum Dynkin game with partial and/or asymmetric information across players. The framework is non-Markovian and…

We investigate the increasingly important and common game-solving setting where we do not have an explicit description of the game but only oracle access to it through gameplay, such as in financial or military simulations and computer…

A satisfactory multiagent learning algorithm should, {\em at a minimum}, learn to play optimally against stationary opponents and converge to a Nash equilibrium in self-play. The algorithm that has come closest, WoLF-IGA, has been proven to…

We apply Blackwell optimality to repeated games. An equilibrium whose strategy profile is sequentially rational for all high enough discount factors simultaneously is a Blackwell (subgame-perfect, perfect public, etc.) equilibrium. The bite…

This paper studies a multi-player, general-sum stochastic game characterized by a dual-stage temporal structure per period. The agents face uncertainty regarding the time-evolving state that is realized at the beginning of each period.…