Related papers: Zero-Sum Games for Continuous-time Markov Decision…
We address payoff-based decentralized learning in infinite-horizon zero-sum Markov games. In this setting, each player makes decisions based solely on received rewards, without observing the opponent's strategy or actions nor sharing…
This paper studies continuous-time Markov decision processes under the risk-sensitive average cost criterion. The state space is a finite set, the action space is a Borel space, the cost and transition rates are bounded, and the…
We study the problem of solving fixed-point equations for seminorm-contractive operators and establish foundational results on the non-asymptotic behavior of iterative algorithms in both deterministic and stochastic settings. Specifically,…
The mathematical characterization of social-distancing games in classical epidemic theory remains an important question, for their applications to both infectious-disease theory and memetic theory. We consider a special case of the dynamic…
This work presents a novel policy iteration algorithm to tackle nonzero-sum stochastic impulse games arising naturally in many applications. Despite the obvious impact of solving such problems, there are no suitable numerical methods…
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…
In this paper, we consider the gradual-impulse control problem of continuous-time Markov decision processes, where the system performance is measured by the expectation of the exponential utility of the total cost. We prove, under very…
We introduce a new non-zero-sum game of optimal stopping with asymmetric exercise opportunities. Given a stochastic process modelling the value of an asset, one player observes and can act on the process continuously, while the other player…
We consider a general type of non-Markovian impulse control problems under adverse non-linear expectation or, more specifically, the zero-sum game problem where the adversary player decides the probability measure. We show that the upper…
We construct a saddle point in a class of zero-sum games between a stopper and a singular-controller. The underlying dynamics is a one-dimensional, time-homogeneous, singularly controlled diffusion taking values either on $\mathbb{R}$ or on…
Mean-payoff zero-sum stochastic games can be studied by means of a nonlinear spectral problem. When the state space is finite, the latter consists in finding an eigenpair $(u,\lambda)$ solution of $T(u)=\lambda e + u$, where $T:\mathbb{R}^n…
This paper investigates properties of Blackwell $\epsilon$-optimal strategies in zero-sum stochastic games when the adversary is restricted to stationary strategies, motivated by applications to robust Markov decision processes. For a class…
In the present work, we consider 2-person zero-sum stochastic differential games with a nonlinear pay-off functional which is defined through a backward stochastic differential equation. Our main objective is to study for such a game the…
In this paper, we focus on the stochastic representation of a system of coupled Hamilton-Jacobi-Bellman-Isaacs (HJB-Isaacs (HJBI), for short) equations which is in fact a system of coupled Isaacs' type integral-partial differential…
In the framework of stochastic zero-sum differential games, we establish a verification theorem, inspired by those existing in stochastic control, to provide sufficient conditions for a pair of feedback controls to form a Nash equilibrium.…
We introduce a modification of Perron's method, where semi-solutions are considered in a carefully defined asymptotic sense. With this definition, we can show, in a rather elementary way, that in a zero-sum game or a control problem (with…
Optimization under uncertainty is a fundamental problem in learning and decision-making, particularly in multi-agent systems. Previously, Feldman, Kalai, and Tennenholtz [2010] demonstrated the ability to efficiently compete in repeated…
This paper considers the theoretical, computational, and econometric properties of continuous time dynamic discrete choice games with stochastically sequential moves, introduced by Arcidiacono, Bayer, Blevins, and Ellickson (2016). We…
Mean field games formalize dynamic games with a continuum of players and explicit interaction where the players can have heterogeneous states. As they additionally yield approximate equilibria of corresponding $N$-player games, they are of…
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…