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We revisit the complexity of deciding, given a {\it bimatrix game,} whether it has a {\it Nash equilibrium} with certain natural properties; such decision problems were early known to be ${\mathcal{NP}}$-hard~\cite{GZ89}. We show that…
Many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind. Examples include Nash equilibria in games; market equilibria; computing optimal strategies and the values of competitive games…
In real-world multi-agent reinforcement learning (MARL) applications, agents may not have perfect state information (e.g., due to inaccurate measurement or malicious attacks), which challenges the robustness of agents' policies. Though…
We consider the existence and computational complexity of coalitional stability concepts based on social networks. Our concepts represent a natural and rich combinatorial generalization of a recent approach termed partition equilibrium. We…
Adversarial training is a standard technique for training adversarially robust models. In this paper, we study adversarial training as an alternating best-response strategy in a 2-player zero-sum game. We prove that even in a simple…
Recently, invariant risk minimization (IRM) (Arjovsky et al.) was proposed as a promising solution to address out-of-distribution (OOD) generalization. In Ahuja et al., it was shown that solving for the Nash equilibria of a new class of…
We analyse the computational complexity of finding Nash equilibria in simple stochastic multiplayer games. We show that restricting the search space to equilibria whose payoffs fall into a certain interval may lead to undecidability. In…
In practical multi-agent systems, agents often have diverse objectives, which makes the system more complex, as each agent's performance across multiple criteria depends on the joint actions of all agents, creating intricate strategic…
Motivated by the fact that in many game-theoretic settings, the game analyzed is only an approximation to the game being played, in this work we analyze equilibrium computation for the broad and natural class of bimatrix games that are…
Nash equilibria are crucial for understanding game behavior and systems in economics, physics, biology, and computer science. A significant application arises from the connection between Nash equilibria and optimization problems . However,…
In noncooperative Nash games, equilibria are often inefficient. This is exemplified by the Prisoner's Dilemma and was first provably shown in the 1980s. Since then, understanding the quality of Nash equilibrium (NE) received considerable…
Concurrent multi-player games with $\omega$-regular objectives are a standard model for systems that consist of several interacting components, each with its own objective. The standard solution concept for such games is Nash Equilibrium,…
We study the computational complexity of decision problems about Nash equilibria in $m$-player games. Several such problems have recently been shown to be computationally equivalent to the decision problem for the existential theory of the…
Many efficient algorithms have been designed to recover Nash equilibria of various classes of finite games. Special classes of continuous games with infinite strategy spaces, such as polynomial games, can be solved by semidefinite…
We study the problem of learning Nash equilibria in offline two-player zero-sum Markov games. While existing approaches often rely on explicit pessimism to address distribution shift, we show that KL regularization alone suffices to…
Model-based algorithms -- algorithms that explore the environment through building and utilizing an estimated model -- are widely used in reinforcement learning practice and theoretically shown to achieve optimal sample efficiency for…
In this paper a distribution-free methodology is presented for providing robustness guarantees for Nash equilibria (NE) of multi-agent games. Leveraging recent a posteriori developments of the so called scenario approach (Campi et al.,…
We explore the computational complexity of computing pure Nash equilibria for a new class of strategic games called integer programming games with difference of piecewise linear convex payoffs. Integer programming games are games where…
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…
This paper investigates a distributed robust Nash Equilibrium (NE) seeking problem for second-order players subject to external disturbances and uncertain dynamics while communicating via semi-Markov switching topologies. To accommodate the…