相关论文: The Computational Complexity of Variational Inequa…
This paper is concerned with complexity theoretic aspects of a general formulation of quantum game theory that models strategic interactions among rational agents that process and exchange quantum information. In particular, we prove that…
PPAD refers to a class of computational problems for which solutions are guaranteed to exist due to a specific combinatorial principle. The most well-known such problem is that of computing a Nash equilibrium of a game. Other examples…
We study the problem of computing stationary Nash equilibria in discounted perfect information stochastic games from the viewpoint of computational complexity. For two-player games we prove the problem to be in PPAD, which together with a…
Variational inequality problems allow for capturing an expansive class of problems, including convex optimization problems, convex Nash games and economic equilibrium problems, amongst others. Yet in most practical settings, such problems…
The framework outlined in [arXiv:2010.13024] provides an approximation algorithm for computing Nash equilibria of normal form games. Since NASH is a well-known PPAD-complete problem, this framework has potential applications to other $PPAD$…
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…
We prove that finding an epsilon-Nash equilibrium in a succinctly representable game with many players is PPAD-hard for constant epsilon. Our proof uses succinct games, i.e. games whose payoff function is represented by a circuit. Our…
Equilibria of realistic multiplayer games constitute a key solution concept both in practical applications, such as online advertising auctions and electricity markets, and in analytical frameworks used to study strategic voting in…
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…
Performative prediction captures the phenomenon where deploying a predictive model shifts the underlying data distribution. While simple retraining dynamics are known to converge linearly when the performative effects are weak ($\rho < 1$),…
Computational aspects of solution notions such as Nash equilibrium have been extensively studied, including settings where the ultimate goal is to find an equilibrium that possesses some additional properties. Furthermore, in order to…
Strategic interactions can be represented more concisely, and analyzed and solved more efficiently, if we are aware of the symmetries within the multiagent system. Symmetries also have conceptual implications, for example for equilibrium…
We prove that finding an $\epsilon$-approximate Nash equilibrium is PPAD-complete for constant $\epsilon$ and a particularly simple class of games: polymatrix, degree 3 graphical games, in which each player has only two actions. As…
We provide a complete characterization for the computational complexity of finding approximate equilibria in two-action graphical games. We consider the two most well-studied approximation notions: $\varepsilon$-Nash equilibria…
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,…
We study generalized games defined over Banach spaces using variational analysis. To reformulate generalized games as quasi-variational inequality problems, we will first form a suitable principal operator and study some significant…
In this paper, we study a theoretical math problem of game theory and calculus of variations in which we minimize a functional involving two players. A general relationship between the optimal strategies for both players is presented,…
We present a unifying representation of computation as a two-player game between an \emph{Algorithm} and \emph{Nature}, grounded in domain theory and game theory. The Algorithm produces progressively refined approximations within a Scott…
The quasi-variational inequalities play a significant role in analyzing a wide range of real-world problems. However, these problems are more complicated to solve than variational inequalities as the constraint set is based on the current…