Related papers: Nash, Conley, and Computation: Impossibility and I…
Motivated by Cournot models, this paper proposes novel models of the noncooperative and cooperative differential games with density constraints in infinite dimensions, where markets consist of infinite firms and demand dynamics are governed…
Economists were content with the concept of the Nash equilibrium as game theory's solution concept until Daskalakis, Goldberg, and Papadimitriou showed that finding a Nash equilibrium is most likely a computationally hard problem, a result…
A fundamental shortcoming of the concept of Nash equilibrium is its computational intractability: approximating Nash equilibria in normal-form games is PPAD-hard. In this paper, inspired by the ideas of smoothed analysis, we introduce a…
This paper introduces two fundamentally new concepts to game theory: multilateral Nash equilibria and families of games. Starting with non-cooperative games, we show how these notions together seamlessly integrate into and naturally extend…
Imitating successful behavior is a natural and frequently applied approach to trust in when facing scenarios for which we have little or no experience upon which we can base our decision. In this paper, we consider such behavior in atomic…
Computing Nash equilibrium policies is a central problem in multi-agent reinforcement learning that has received extensive attention both in theory and in practice. However, provable guarantees have been thus far either limited to fully…
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…
Motivated by the scarcity of accurate payoff feedback in practical applications of game theory, we examine a class of learning dynamics where players adjust their choices based on past payoff observations that are subject to noise and…
We consider a class of two-player dynamic stochastic nonzero-sum games where the state transition and observation equations are linear, and the primitive random variables are Gaussian. Each controller acquires possibly different dynamic…
The overall aim of our research is to develop techniques to reason about the equilibrium properties of multi-agent systems. We model multi-agent systems as concurrent games, in which each player is a process that is assumed to act…
Dynamic games are powerful tools to model multi-agent decision-making, yet computing Nash (generalized Nash) equilibria remains a central challenge in such settings. Complexity arises from tightly coupled optimality conditions, nested…
We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…
In this paper, we consider a Nash equilibrium seeking problem for a class of high-order multi-agent systems with unknown dynamics. Different from existing results for single integrators, we aim to steer the outputs of this class of…
We present a framework for computing approximate mixed-strategy Nash equilibria of continuous-action games. It is a modification of the traditional double oracle algorithm, extended to multiple players and continuous action spaces. Unlike…
We propose a new dynamics for equilibrium selection of finite player discrete strategy games. The dynamics is motivated by optimal transportation, and models individual players' myopicity, greedy and uncertainty when making decisions. The…
We consider the problem of approximating Nash equilibria of $N$ functions $f_1,\dots, f_N$ of $N$ variables. In particular, we deduce conditions under which systems of the form $$ \dot u_j(t)=-\nabla_{x_j}f_j(u(t)) $$ $(j=1,\dots, N)$ are…
Game-theoretic approaches and Nash equilibrium have been widely applied across various engineering domains. However, practical challenges such as disturbances, delays, and actuator limitations can hinder the precise execution of Nash…
We consider the problem of computing Nash equilibria in potential games where each player's strategy set is subject to private uncoupled constraints. This scenario is frequently encountered in real-world applications like road network…
We study the amount of entropy players asymptotically need to play a repeated normal-form game in a Nash equilibrium. Hub\'a\v{c}ek, Naor, and Ullman (SAGT'15, TCSys'16) gave sufficient conditions on a game for the minimal amount of…
We analyse the computational complexity of finding Nash equilibria in turn-based stochastic multiplayer games with omega-regular objectives. We show that restricting the search space to equilibria whose payoffs fall into a certain interval…