Related papers: $\epsilon$-Optimally Solving Zero-Sum POSGs

While value iteration (VI) is a standard solution approach to simple stochastic games (SSGs), it suffered from the lack of a stopping criterion. Recently, several solutions have appeared, among them also "optimistic" VI (OVI). However, OVI…

Quantitative games are two-player zero-sum games played on directed weighted graphs. Total-payoff games (that can be seen as a refinement of the well-studied mean-payoff games) are the variant where the payoff of a play is computed as the…

Constrained Markov games offer a formal mathematical framework for modeling multi-agent reinforcement learning problems where the behavior of the agents is subject to constraints. In this work, we focus on the recently introduced class of…

Mean-payoff games (MPGs) are infinite duration two-player zero-sum games played on weighted graphs. Under the hypothesis of perfect information, they admit memoryless optimal strategies for both players and can be solved in…

In cooperative game theory, the primary focus is the equitable allocation of payoffs or costs among agents. However, in the practical applications of cooperative games, accurately representing games is challenging. In such cases, using an…

In this paper, zero-sum mean-field type games (ZSMFTG) with linear dynamics and quadratic utility are studied under infinite-horizon discounted utility function. ZSMFTG are a class of games in which two decision makers whose utilities sum…

We study nonzero-sum stochastic games for continuous time Markov decision processes on a denumerable state space with risk-sensitive ergodic cost criterion. Transition rates and cost rates are allowed to be unbounded. Under a Lyapunov type…

One-counter MDPs (OC-MDPs) and one-counter simple stochastic games (OC-SSGs) are 1-player, and 2-player turn-based zero-sum, stochastic games played on the transition graph of classic one-counter automata (equivalently, pushdown automata…

Game theory serves as a powerful tool for distributed optimization in multi-agent systems in different applications. In this paper we consider multi-agent systems that can be modeled by means of potential games whose potential function…

Many economic games and machine learning approaches can be cast as competitive optimization problems where multiple agents are minimizing their respective objective function, which depends on all agents' actions. While gradient descent is a…

Policy iteration and value iteration are at the core of many (approximate) dynamic programming methods. For Markov Decision Processes with finite state and action spaces, we show that they are instances of semismooth Newton-type methods to…

We study episodic two-player zero-sum Markov games (MGs) in the offline setting, where the goal is to find an approximate Nash equilibrium (NE) policy pair based on a dataset collected a priori. When the dataset does not have uniform…

In order to address the imprecision often introduced by widening operators in static analysis, policy iteration based on min-computations amounts to considering the characterization of reachable value set of a program as an iterative…

In this paper we consider two-person zero-sum risk-sensitive stochastic dynamic games with Borel state and action spaces and bounded reward. The term risk-sensitive refers to the fact that instead of the usual risk neutral optimization…

Many processes, such as discrete event systems in engineering or population dynamics in biology, evolve in discrete space and continuous time. We consider the problem of optimal decision making in such discrete state and action space…

Multi-agent learning is a challenging problem in machine learning that has applications in different domains such as distributed control, robotics, and economics. We develop a prescriptive model of multi-agent behavior using Markov games.…

We investigate a time-inconsistent, non-Markovian finite-player game in continuous time, where each player's objective functional depends non-linearly on the expected value of the state process. As a result, the classical Bellman optimality…

While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the properties that optimal solutions need to have, and devised a…

Stochastic games are a well established model for multi-agent sequential decision making under uncertainty. In practical applications, though, agents often have only partial observability of their environment. Furthermore, agents…

We propose a continuous version of the classical Gale--Berlekamp switching game. We also study a weighted version of this new continuous game. The main results of this paper concern growth estimates for the corresponding optimization…