相关论文: Approximating Nash Equilibria and Dense Subgraphs …

We study the 'no-dimension' analogue of Carath{\'e}odory's theorem in Banach spaces. We prove such a result together with its colorful version for uniformly smooth Banach spaces. It follows that uniform smoothness leads to a greedy…

We give a deterministic nearly-linear time algorithm for approximating any point inside a convex polytope with a sparse convex combination of the polytope's vertices. Our result provides a constructive proof for the Approximate…

We present a new methodology for computing approximate Nash equilibria for two-person non-cooperative games based upon certain extensions and specializations of an existing optimization approach previously used for the derivation of fixed…

The approximate Carath\'eodory problem in general form is as follows: Given two symmetric convex bodies $P,Q \subseteq \mathbb{R}^m$, a parameter $k \in \mathbb{N}$ and $\mathbf{z} \in \textrm{conv}(X)$ with $X \subseteq P$, find…

In Feinstein and Rudloff (2023), it was shown that the set of Nash equilibria for any non-cooperative $N$ player game coincides with the set of Pareto optimal points of a certain vector optimization problem with non-convex ordering cone. To…

We investigate the complexity of computing approximate Nash equilibria in anonymous games. Our main algorithmic result is the following: For any $n$-player anonymous game with a bounded number of strategies and any constant $\delta>0$, an…

The $\varepsilon$-well-supported Nash equilibrium is a strong notion of approximation of a Nash equilibrium, where no player has an incentive greater than $\varepsilon$ to deviate from any of the pure strategies that she uses in her mixed…

Since the seminal PPAD-completeness result for computing a Nash equilibrium even in two-player games, an important line of research has focused on relaxations achievable in polynomial time. In this paper, we consider the notion of…

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…

In recent work of Hazan and Krauthgamer (SICOMP 2011), it was shown that finding an $\eps$-approximate Nash equilibrium with near-optimal value in a two-player game is as hard as finding a hidden clique of size $O(\log n)$ in the random…

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 equilibrium} (NE) can be stated as a formal theorem on a multilinear form, free of game theory terminology. On the other hand, inspired by this formalism, we state and prove a {\it multilinear minimax theorem}, a generalization of von…

The colorful Carath\'eodory theorem, proved by B\'ar\'any in 1982, states that given d+1 sets of points S_1,...,S_{d+1} in R^d, with each S_i containing 0 in its convex hull, there exists a subset T of the union of the S_i's containing 0 in…

In this paper we consider the problem of computing an $\epsilon$-approximate Nash Equilibrium of a zero-sum game in a payoff matrix $A \in \mathbb{R}^{m \times n}$ with $O(1)$-bounded entries given access to a matrix-vector product oracle…

This paper is about computing constrained approximate Nash equilibria in polymatrix games, which are succinctly represented many-player games defined by an interaction graph between the players. In a recent breakthrough, Rubinstein showed…

In this paper, we aim to design a distributed approximate algorithm for seeking Nash equilibria of an aggregative game. Due to the local set constraints of each player, projectionbased algorithms have been widely employed for solving such…

We develop a quasi-polynomial time Las Vegas algorithm for approximating Nash equilibria in polymatrix games over trees, under a mild renormalizing assumption. Our result, in particular, leads to an expected polynomial-time algorithm for…

We study the deterministic and randomized query complexity of finding approximate equilibria in bimatrix games. We show that the deterministic query complexity of finding an $\epsilon$-Nash equilibrium when $\epsilon < \frac{1}{2}$ is…

In an $\epsilon$-Nash equilibrium, a player can gain at most $\epsilon$ by unilaterally changing his behaviour. For two-player (bimatrix) games with payoffs in $[0,1]$, the best-known$\epsilon$ achievable in polynomial time is 0.3393. In…

This work proposes a novel distributed approach for computing a Nash equilibrium in convex games with restricted strongly monotone pseudo-gradients. By leveraging the idea of the centralized operator extrapolation method presented in [4] to…