Related papers: Solving a class of zero-sum stopping game with reg…

This paper deals with N-person nonzero-sum discrete-time Markov games under a probability criterion, in which the transition probabilities and reward functions are allowed to vary with time. Differing from the existing works on the expected…

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…

We derive the rate of convergence to the strongly variationally stable Nash equilibrium in a convex game, for a zeroth-order learning algorithm. Though we do not assume strong monotonicity of the game, our rates for the one-point feedback…

We consider the problem of finding Nash equilibrium for two-player turn-based zero-sum games. Inspired by the AlphaGo Zero (AGZ) algorithm, we develop a Reinforcement Learning based approach. Specifically, we propose…

This paper is concerned with a non-zero sum differential game problem of an anticipated forward-backward stochastic differential delayed equation under partial information. We establish a necessary maximum principle and sufficient…

On a filtered probability space $(\Omega ,\mathcal{F}, (\mathcal{F}_t)_{t\in[0,\infty]}, \mathbb{P})$, we consider the two-player non-zero-sum stopping game $u^i := \mathbb{E}[U^i(\rho,\tau)],\ i=1,2$, where the first player choose a…

We study a nonzero-sum stochastic differential game with both players adopting impulse controls, on a finite time horizon. The objective of each player is to maximize her total expected discounted profits. The resolution methodology relies…

In game theory, the concept of Nash equilibrium reflects the collective stability of some individual strategies chosen by selfish agents. The concept pertains to different classes of games, e.g. the sequential games, where the agents play…

We consider a general-sum N-player linear-quadratic game with stochastic dynamics over a finite horizon and prove the global convergence of the natural policy gradient method to the Nash equilibrium. In order to prove the convergence of the…

In this article we consider zero and non-zero sum risk-sensitive average criterion games for semi-Markov processes with a finite state space. For the zero-sum case, under suitable assumptions we show that the game has a value. We also…

This paper studies game-type credit default swaps that allow the protection buyer and seller to raise or reduce their respective positions once prior to default. This leads to the study of an optimal stopping game subject to early default…

We consider a general class of nonzero-sum $N$-player stochastic games with impulse controls, where players control the underlying dynamics with discrete interventions. We adopt a verification approach and provide sufficient conditions for…

Zero-sum games are a fundamental setting for adversarial training and decision-making in multi-agent learning (MAL). Existing methods often ensure convergence to (approximate) Nash equilibria by introducing a form of regularization. Yet,…

In this paper we study a zero-sum switching game and its verification theorems expressed in terms of either a system of Reflected Backward Stochastic Differential Equations (RBSDEs in short) with bilateral interconnected obstacles or a…

We consider two-player non-zero-sum stopping games in discrete time. Unlike Dynkin games, in our games the payoff of each player is revealed after both players stop. Moreover, each player can adjust her own stopping strategy according to…

We study a new kind of non-zero-sum stochastic differential game with mixed impulse/switching controls, motivated by strategic competition in commodity markets. A representative upstream firm produces a commodity that is used by a…

In this paper, we investigate a competitive market involving two agents who consider both their own wealth and the wealth gap with their opponent. Both agents can invest in a financial market consisting of a risk-free asset and a risky…

We study two natural problems about rational behaviors in multiplayer non-zero-sum sequential infinite duration games played on graphs: checking problems, that consist in deciding whether a strategy profile, defined by a Mealy machine, is…

We are interested in the study of stochastic games for which each player faces an optimal stopping problem. In our setting, the players may interact through the criterion to optimise as well as through their dynamics. After briefly…

In this paper, we consider a differential stochastic zero-sum game in which two players intervene by adopting impulse controls in a finite time horizon. We provide a numerical solution as an approximation of the value function, which turns…