Related papers: FPTAS for Mixed-Strategy Nash Equilibria in Tree G…

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 it is PPAD-hard to compute a Nash equilibrium in a tree polymatrix game with twenty actions per player. This is the first PPAD hardness result for a game with a constant number of actions per player where the interaction graph…

Nash equilibrium has long been a desired solution concept in multi-player games, especially for those on continuous strategy spaces, which have attracted a rapidly growing amount of interests due to advances in research applications such as…

Finite-horizon probabilistic multiagent concurrent game systems, also known as finite multiplayer stochastic games, are a well-studied model in computer science due to their ability to represent a wide range of real-world scenarios…

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…

Stochastic games generalize Markov decision processes (MDPs) to a multiagent setting by allowing the state transitions to depend jointly on all player actions, and having rewards determined by multiplayer matrix games at each state. We…

Many important real-world settings contain multiple players interacting over an unknown duration with probabilistic state transitions, and are naturally modeled as stochastic games. Prior research on algorithms for stochastic games has…

We present a novel polynomial time approximation scheme for two-strategy anonymous games, in which the players' utility functions, although potentially different, do not differentiate among the identities of the other players. Our algorithm…

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…

Mean field type games (MFTGs) describe Nash equilibria between large coalitions: each coalition consists of a continuum of cooperative agents who maximize the average reward of their coalition while interacting non-cooperatively with a…

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…

We consider the problem of learning sparse polymatrix games from observations of strategic interactions. We show that a polynomial time method based on $\ell_{1,2}$-group regularized logistic regression recovers a game, whose Nash…

We show that the BIMATRIX game does not have a fully polynomial-time approximation scheme, unless PPAD is in P. In other words, no algorithm with time polynomial in n and 1/\epsilon can compute an \epsilon-approximate Nash equilibrium of an…

We present efficient approximation algorithms for finding Nash equilibria in anonymous games, that is, games in which the players utilities, though different, do not differentiate between other players. Our results pertain to such games…

This paper deals with the complexity of the problem of computing a pure Nash equilibrium for discrete preference games and network coordination games beyond $O(\log n)$-treewidth and tree metric spaces. First, we estimate the number of…

We design a distributed algorithm to seek generalized Nash equilibria of a robust game with uncertain coupled constraints. Due to the uncertainty of parameters in set constraints, we aim to find a generalized Nash equilibrium in the worst…

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…

In this article, we consider generalized Nash games where the associated constraint map is not necessarily self. The classical Nash equilibrium may not exist for such games and therefore we introduce the notion of best approximate solution…

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…

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…