Related papers: Tropical complementarity problems and Nash equilib…

We observe that a significant class of Nash equilibrium problems in non-potential games can be associated with monotone inclusion problems. We propose splitting techniques to solve such problems and establish their convergence. Applications…

The complexity of computing equilibrium refinements has been at the forefront of algorithmic game theory research, but it has remained open in the seminal class of potential games; we close this fundamental gap in this paper. We first show…

We conjecture that PPAD has a PCP-like complete problem, seeking a near equilibrium in which all but very few players have very little incentive to deviate. We show that, if one assumes that this problem requires exponential time, several…

In general, Nash equilibria in normal-form games may require players to play (probabilistically) mixed strategies. We define a measure of the complexity of finite probability distributions and study the complexity required to play Nash…

We provide the first fully polynomial time approximation scheme (FPTAS) for computing an approximate mixed-strategy Nash equilibrium in tree-structured graphical multi-hypermatrix games (GMhGs). GMhGs are generalizations of normal-form…

With increasing game size, a problem of computational complexity arises. This is especially true in real world problems such as in social systems, where there is a significant population of players involved in the game, and the complexity…

The rank of a bimatrix game (A,B) is defined as rank(A+B). Computing a Nash equilibrium (NE) of a rank-$0$, i.e., zero-sum game is equivalent to linear programming (von Neumann'28, Dantzig'51). In 2005, Kannan and Theobald gave an FPTAS for…

Leadership games provide a powerful paradigm to model many real-world settings. Most literature focuses on games with a single follower who acts optimistically, breaking ties in favour of the leader. Unfortunately, for real-world…

This paper identifies a manifold in the space of bimatrix games which contains games that are strategically equivalent to rank-1 games through a positive affine transformation. It also presents an algorithm that can compute, in polynomial…

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,…

A polynomial complexity algorithm is designed which tests whether a point belongs to a given tropical linear variety.

In this paper, we study the dynamic behavior of Hedge, a well-known algorithm in theoretical machine learning and algorithmic game theory. The empirical average (arithmetic mean) of the iterates Hedge generates is known to converge to a…

In this brief note, we prove that the existence of Nash equilibria on integer programming games is $\Sigma^p_2$-complete.

McLennan and Tourky (2010) showed that "imitation games" provide a new view of the computation of Nash equilibria of bimatrix games with the Lemke-Howson algorithm. In an imitation game, the payoff matrix of one of the players is the…

Signaling game problems investigate communication scenarios where encoder(s) and decoder(s) have misaligned objectives due to the fact that they either employ different cost functions or have inconsistent priors. This problem has been…

We consider a project that consists of a set of activities performed in parallel under constraints on their start and finish times, including start-finish precedence relationships, release start times, release end times, and deadlines. The…

We study the problem of checking for the existence of constrained pure Nash equilibria in a subclass of polymatrix games defined on weighted directed graphs. The payoff of a player is defined as the sum of nonnegative rational weights on…

We consider decision problems of rating alternatives based on their pairwise comparisons according to two criteria. Given pairwise comparison matrices for each criterion, the problem is to find the overall scores of the alternatives. We…

We study the global convergence of policy optimization for finding the Nash equilibria (NE) in zero-sum linear quadratic (LQ) games. To this end, we first investigate the landscape of LQ games, viewing it as a nonconvex-nonconcave…

We consider structural and algorithmic questions related to the Nash dynamics of weighted congestion games. In weighted congestion games with linear latency functions, the existence of (pure Nash) equilibria is guaranteed by potential…