Related papers: Multiplicative weights, equalizers, and P=PPAD
We present a computational formulation for the approximate version of several variational inequality problems, investigating their computational complexity and establishing PPAD-completeness. Examining applications in computational game…
Parity games are abstract infinite-round games that take an important role in formal verification. In the basic setting, these games are two-player, turn-based, and played under perfect information on directed graphs, whose nodes are…
While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the properties that optimal solutions need to have, and devised a…
We study equilibrium finding in polymatrix games under differential privacy constraints. Prior work in this area fails to achieve both high-accuracy equilibria and a low privacy budget. To better understand the fundamental limitations of…
Multi-dimensional mean-payoff and energy games provide the mathematical foundation for the quantitative study of reactive systems, and play a central role in the emerging quantitative theory of verification and synthesis. In this work, we…
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…
Motivated by the sequence form formulation of Koller et al. (GEB'96), this paper defines {\em bilinear games}, and proposes efficient algorithms for its rank based subclasses. Bilinear games are two-player non-cooperative single-shot games…
We study the problem of finding robust equilibria in multiplayer concurrent games with mean payoff objectives. A $(k,t)$-robust equilibrium is a strategy profile such that no coalition of size $k$ can improve the payoff of one its member by…
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…
We use techniques from the statistical mechanics of disordered systems to analyse the properties of Nash equilibria of bimatrix games with large random payoff matrices. By means of an annealed bound, we calculate their number and analyse…
This paper provides a new version of matrix semi-tensor product method based on adjacent transpositions to test symmetric games. The advantage of using adjacent transpositions lies in the great simplification of analysis of symmetric games.…
The Nash equilibrium is an important benchmark for behaviour in systems of strategic autonomous agents. Polymatrix games are a succinct and expressive representation of multiplayer games that model pairwise interactions between players. The…
Energy games belong to a class of turn-based two-player infinite-duration games}played on a weighted directed graph. It is one of the rare and intriguing combinatorial problems that lie in ${\sf NP} \cap {\sf co\mbox{-}NP}$, but are not…
Self-play is a technique for machine learning in multi-agent systems where a learning algorithm learns by interacting with copies of itself. Self-play is useful for generating large quantities of data for learning, but has the drawback that…
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…
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…
In mean-payoff games, the objective of the protagonist is to ensure that the limit average of an infinite sequence of numeric weights is nonnegative. In energy games, the objective is to ensure that the running sum of weights is always…
In a multi-objective game, each individual's payoff is a \emph{vector-valued} function of everyone's actions. Under such vectorial payoffs, Pareto-efficiency is used to formulate each individual's best-response condition, inducing…
We provide a unifying, black-box tool for establishing existence of approximate equilibria in weighted congestion games and, at the same time, bounding their Price of Stability. Our framework can handle resources with general…
A recent body of experimental literature has studied empirical game-theoretical analysis, in which we have partial knowledge of a game, consisting of observations of a subset of the pure-strategy profiles and their associated payoffs to…