Related papers: Zero-Sum Semi-Markov Games with State-Action-Depen…

We consider zero sum stochastic games. For every discount factor $\lambda$, a time normalization allows to represent the game as being played on the interval [0, 1]. We introduce the trajectories of cumulated expected payoff and of…

We study best-response type learning dynamics for zero-sum polymatrix games under two information settings. The two settings are distinguished by the type of information that each player has about the game and their opponents' strategy. The…

Markov games model interactions among multiple players in a stochastic, dynamic environment. Each player in a Markov game maximizes its expected total discounted reward, which depends upon the policies of the other players. We formulate a…

We show that computing approximate stationary Markov coarse correlated equilibria (CCE) in general-sum stochastic games is computationally intractable, even when there are two players, the game is turn-based, the discount factor is an…

In the paper we consider the controlled continuous-time Markov chain describing the interacting particles system with the finite number of types. The system is controlled by two players with the opposite purposes. The limiting game as the…

We study two person nonzero-sum stochastic differential games with risk-sensitive discounted and ergodic cost criteria. Under certain conditions we establish a Nash equilibrium in Markov strategies for the discounted cost criterion and a…

Zero-sum stochastic games have found important applications in a variety of fields, from machine learning to economics. Work on this model has primarily focused on the computation of Nash equilibrium due to its effectiveness in solving…

Originating in evolutionary game theory, the class of "zero-determinant" strategies enables a player to unilaterally enforce linear payoff relationships in simple repeated games. An upshot of this kind of payoff constraint is that it can…

Establishing the existence of exact or near Markov or stationary perfect Nash equilibria in nonzero-sum Markov games over Borel spaces is a challenging problem with limited positive results. Motivated by problems in multi-agent and Bayesian…

This paper examines a trade execution game for two large traders in a generalized price impact model. We incorporate a stochastic and sequentially dependent factor that exogenously affects the market price into financial markets. Our model…

We analyze a zero-sum stochastic differential game between two competing players who can choose unbounded controls. The payoffs of the game are defined through backward stochastic differential equations. We prove that each player's priority…

Policy gradient methods enjoy strong practical performance in numerous tasks in reinforcement learning. Their theoretical understanding in multiagent settings, however, remains limited, especially beyond two-player competitive and potential…

We propose a new framework of Markov $\alpha$-potential games to study Markov games. We show that any Markov game with finite-state and finite-action is a Markov $\alpha$-potential game, and establish the existence of an associated…

In this paper, we study nonzero-sum separable games, which are continuous games whose payoffs take a sum-of-products form. Included in this subclass are all finite games and polynomial games. We investigate the structure of equilibria in…

We study a model of two-player, zero-sum, stopping games with asymmetric information. We assume that the payoff depends on two continuous-time Markov chains (X, Y), where X is only observed by player 1 and Y only by player 2, implying that…

In a mean-payoff parity game, one of the two players aims both to achieve a qualitative parity objective and to minimize a quantitative long-term average of payoffs (aka. mean payoff). The game is zero-sum and hence the aim of the other…

In this paper, we formulate a two-player zero-sum game under dynamic constraints defined by hybrid dynamical equations. The game consists of a min-max problem involving a cost functional that depends on the actions and resulting solutions…

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…

Zero sum games with risk-sensitive cost criterion are considered with underlying dynamics being given by controlled stochastic differential equations. Under the assumption of geometric stability on the dynamics , we completely characterize…

We consider a general nonzero-sum impulse game with two players. The main mathematical contribution of the paper is a verification theorem which provides, under some regularity conditions, a suitable system of quasi-variational inequalities…