相关论文: Tarski's Theorem, Supermodular Games, and the Comp…

A central challenge in game theory and learning systems such as GANs is understanding which algorithms can efficiently compute equilibria across the heterogeneous landscape of games. Equilibrium computation is typically studied solver by…

In repeated-game applications where both the collusive and non-collusive outcomes can be supported as equilibria, researchers must resolve underlying selection questions if theory will be used to understand counterfactual policies. One…

We extend the construction of equilibria for linear-quadratic and mean-variance portfolio problems available in the literature to a large class of mean-field time-inconsistent stochastic control problems in continuous time. Our approach…

This paper studies the relation between equilibria in single-period, discrete-time and continuous-time mean field game models. First, for single-period mean field games, we establish the existence of equilibria and then prove the…

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…

Meirowitz [17] showed existence of continuous behavioural function equilibria for Bayesian games with non-finite type and action spaces. A key condition for the proof of the existence result is equi-continuity of behavioural functions…

The works of (Daskalakis et al., 2009, 2022; Jin et al., 2022; Deng et al., 2023) indicate that computing Nash equilibria in multi-player Markov games is a computationally hard task. This fact raises the question of whether or not…

This paper introduces a notion of weak solution for the coupled system of master equations in mean field games with a major player. It extends the previously introduced notion of Lipschitz solutions in mean field games. By relying on a…

In this work, we study the distributed Nash equilibrium seeking problem for monotone generalized noncooperative games with set constraints and shared affine inequality constraints. A distributed regularized penalty method is proposed. The…

Polynomial optimization problems often arise in sequences indexed by dimension, and it is of interest to compute bounds on the optimal values of all problems in the sequence. Examples include certifying inequalities between symmetric…

This paper studies a system security problem in the context of observability based on a two-person noncooperative infinitely repeated game. Both the attacker and the defender have means to modify the dimension of the unobservable subspace,…

Consider a strongly monotone game where the players' utility functions include a reward function and a linear term for each dimension, with coefficients that are controlled by the manager. Gradient play converges to a unique Nash…

We consider two-player non zero-sum infinite duration games played on weighted graphs. We extend the notion of secure equilibrium introduced by Chatterjee et al., from the Boolean setting to this quantitative setting. As for the Boolean…

The paper is concerned with two-person dynamic zero-sum games. We investigate the limit of value functions of finite horizon games with long run average cost as the time horizon tends to infinity, and the limit of value functions of…

We investigate the connection between the complexity of nonlocal games and the arithmetical hierarchy, a classification of languages according to the complexity of arithmetical formulas defining them. It was recently shown by Ji, Natarajan,…

We investigate the complexity of bounding the uncertainty of graphical games, and we provide new insight into the intrinsic difficulty of computing Nash equilibria. In particular, we show that, if one adds very simple and natural additional…

We analyse the computational complexity of finding Nash equilibria in stochastic multiplayer games with $\omega$-regular objectives. While the existence of an equilibrium whose payoff falls into a certain interval may be undecidable, we…

In this paper, we resolve the computational complexity of a number of outstanding open problems with practical applications. Here is the list of problems we show to be PPAD-complete, along with the domains of practical significance:…

Adversarial multiplayer games are an important object of study in multiagent learning. In particular, polymatrix zero-sum games are a multiplayer setting where Nash equilibria are known to be efficiently computable. Towards understanding…

Stackelberg games originate where there are market leaders and followers, and the actions of leaders influence the behavior of the followers. Mathematical modelling of such games results in what's called a Bilevel Optimization problem.…