Related papers: An algorithmic solution to the Blotto game using m…
We investigate the problem of equilibrium computation for "large" $n$-player games. Large games have a Lipschitz-type property that no single player's utility is greatly affected by any other individual player's actions. In this paper, we…
In general, Nash equilibria in normal-form games may require players to play (probabilistically) mixed strategies. We define a measure of the complexity of finite probability distributions and study the complexity required to play Nash…
This paper is concerned with two-person mean-field linear-quadratic non-zero sum stochastic differential games in an infinite horizon. Both open-loop and closed-loop Nash equilibria are introduced. Existence of an open-loop Nash equilibrium…
Recently, the paper [12] introduces a derivative-free consensus-based particle method that finds the Nash equilibrium of non-convex multiplayer games, where it proves the global exponential convergence in the sense of mean-field law. This…
A central task of artificial intelligence is the design of artificial agents that act towards specified goals in partially observed environments. Since such environments frequently include interaction over time with other agents with their…
We propose an implementable, neural network-based structure preserving probabilistic numerical approximation for a generalized obstacle problem describing the value of a zero-sum differential game of optimal stopping with asymmetric…
We address learning Nash equilibria in convex games under the payoff information setting. We consider the case in which the game pseudo-gradient is monotone but not necessarily strictly monotone. This relaxation of strict monotonicity…
We investigate a two-player zero-sum stochastic differential game in which the players have an asymmetric information on the random payoff. We prove that the game has a value and characterize this value in terms of dual solutions of some…
Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…
A new solution concept for two-player zero-sum matrix games with multi-dimensional payoff is introduced. It is based on extensions of vector orders in K-dimensional spaces to order relations in their power sets, so-called set relations, and…
We consider a stochastic tournament game in which each player is rewarded based on her rank in terms of the completion time of her own task and is subject to cost of effort. When players are homogeneous and the rewards are purely rank…
This work addresses competitive resource allocation in a sequential setting, where two players allocate resources across objects or locations of shared interest. Departing from the simultaneous Colonel Blotto game, our framework introduces…
This paper aims to design a distributed coordination algorithm for solving a multi-agent decision problem with a hierarchical structure. The primary goal is to search the Nash equilibrium of a noncooperative game such that each player has…
We study a class of nonzero-sum stochastic differential games between two teams with agents in each team interacting through graphon aggregates. On the one hand, in each large population group, agents act together to optimize a common…
Today's multiagent systems have grown too complex to rely on centralized controllers, prompting increasing interest in the design of distributed algorithms. In this respect, game theory has emerged as a valuable tool to complement more…
We observe that a significant class of Nash equilibrium problems in non-potential games can be associated with monotone inclusion problems. We propose splitting techniques to solve such problems and establish their convergence. Applications…
We study the subclass of singleton congestion games with identical and increasing cost functions, i.e., each agent tries to utilize from the least crowded resource in her accessible subset of resources. Our main contribution is a novel…
We study a distributed approach for seeking a Nash equilibrium in $n$-cluster games with strictly monotone mappings. Each player within each cluster has access to the current value of her own smooth local cost function estimated by a…
Computing Nash equilibria for strategic multi-agent systems is challenging for expensive black box systems. Motivated by the ubiquity of games involving exploitation of common resources, this paper considers the above problem for potential…
In this paper, we first devise two algorithms to determine whether or not a bimatrix game has a strategically equivalent zero-sum game. If so, we propose an algorithm that computes the strategically equivalent zero-sum game. If a given…