Related papers: Algorithm for Computing Approximate Nash Equilibri…
Structured game representations have recently attracted interest as models for multi-agent artificial intelligence scenarios, with rational behavior most commonly characterized by Nash equilibria. This paper presents efficient, exact…
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…
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…
The Nash equilibrium problem is a widely used tool to model non-cooperative games. Many solution methods have been proposed in the literature to compute solutions of Nash equilibrium problems with continuous strategy sets, but, besides some…
Extensive-form games with imperfect recall are an important game-theoretic model that allows a compact representation of strategies in dynamic strategic interactions. Practical use of imperfect recall games is limited due to negative…
Learning and equilibrium computation in games are fundamental problems across computer science and economics, with applications ranging from politics to machine learning. Much of the work in this area revolves around a simple algorithm…
We present a simple primal-dual algorithm for computing approximate Nash-equilibria in two-person zero-sum sequential games with incomplete information and perfect recall (like Texas Hold'em Poker). Our algorithm is numerically stable,…
Consider a two-player zero-sum stochastic game where the transition function can be embedded in a given feature space. We propose a two-player Q-learning algorithm for approximating the Nash equilibrium strategy via sampling. The algorithm…
We consider the following Colonel Blotto game between parties $P_1$ and $P_A.$ $P_1$ deploys a non negative number of troops across $J$ battlefields, while $P_A$ chooses $K,$ $K < J,$ battlefields to remove all of $P_1$'s troops from the…
Subgame solving is a technique for scaling algorithms to large games by locally refining a precomputed blueprint strategy during gameplay. While straightforward in perfect-information games where search starts from the current state,…
We introduce a new variation of the m-player asymmetric Colonel Blotto game, where the n battles occur as sequential stages of the game, and the winner of each stage needs to spend resources for maintaining his win. The limited resources of…
Nash equilibria provide a principled framework for modeling interactions in multi-agent decision-making and control. However, many equilibrium-seeking methods implicitly assume that each agent has access to the other agents' objectives and…
In this paper, we study the problem of learning the set of pure strategy Nash equilibria and the exact structure of a continuous-action graphical game with quadratic payoffs by observing a small set of perturbed equilibria. A…
We characterize Nash equilibrium by postulating coherent behavior across varying games. Nash equilibrium is the only solution concept that satisfies the following axioms: (i) strictly dominant actions are played with positive probability,…
We develop a probabilistic approach to continuous-time finite state mean field games. Based on an alternative description of continuous-time Markov chain by means of semimartingale and the weak formulation of stochastic optimal control, our…
We derive sublinear-time quantum algorithms for computing the Nash equilibrium of two-player zero-sum games, based on efficient Gibbs sampling methods. We are able to achieve speed-ups for both dense and sparse payoff matrices at the cost…
Nash equilibrium is perhaps the best-known solution concept in game theory. Such a solution assigns a strategy to each player which offers no incentive to unilaterally deviate. While a Nash equilibrium is guaranteed to always exist, the…
In the context of large population symmetric games, approximate Nash equilibria are introduced through equilibrium solutions of the corresponding mean field game in the sense that the individual gain from optimal unilateral deviation under…
Generalized Nash equilibrium problems with mixed-integer variables constitute an important class of games in which each player solves a mixed-integer optimization problem, where both the objective and the feasible set is parameterized by…
We study the problem of repeated play in a zero-sum game in which the payoff matrix may change, in a possibly adversarial fashion, on each round; we call these Online Matrix Games. Finding the Nash Equilibrium (NE) of a two player zero-sum…