Related papers: Playing repeated games with sublinear randomness
The central result of classical game theory states that every finite normal form game has a Nash equilibrium, provided that players are allowed to use randomized (mixed) strategies. However, in practice, humans are known to be bad at…
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 consider a repeated Matching Pennies game in which players have limited access to randomness. Playing the (unique) Nash equilibrium in this n-stage game requires n random bits. Can there be Nash equilibria that use less than n random…
We prove that in a normal form n-player game with m actions for each player, there exists an approximate Nash equilibrium where each player randomizes uniformly among a set of O(log(m) + log(n)) pure strategies. This result induces an…
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…
A fundamental problem with the Nash equilibrium concept is the existence of certain "structurally deficient" equilibria that (i) lack fundamental robustness properties, and (ii) are difficult to analyze. The notion of a "regular" Nash…
Under what conditions do the behaviors of players, who play a game repeatedly, converge to a Nash equilibrium? If one assumes that the players' behavior is a discrete-time or continuous-time rule whereby the current mixed strategy profile…
We study the problem of computing an $\epsilon$-Nash equilibrium in repeated games. Earlier work by Borgs et al. [2010] suggests that this problem is intractable. We show that if we make a slight change to their model---modeling the players…
Generating payoff matrices of normal-form games at random, we calculate the frequency of games with a unique pure strategy Nash equilibrium in the ensemble of $n$-player, $m$-strategy games. These are perfectly predictable as they must…
We consider finite $n$-person deterministic graphical games and study the existence of pure stationary Nash-equilibrium in such games. We assume that all infinite plays are equivalent and form a unique outcome, while each terminal position…
We study the problem of computing approximate Nash equilibria (epsilon-Nash equilibria) in normal form games, where the number of players is a small constant. We consider the approach of looking for solutions with constant support size. It…
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…
In competitive multi-player interactions, simultaneous optimality is a key requirement for establishing strategic equilibria. This property is explicit when the game-theoretic equilibrium is the simultaneously optimal solution of coupled…
We consider zero-sum repeated games in which the players are restricted to strategies that require only a limited amount of randomness. Let $v_n$ be the max-min value of the $n$ stage game; previous works have characterized…
We investigate the existence of certain types of equilibria (Nash, $\varepsilon$-Nash, subgame perfect, $\varepsilon$-subgame perfect, Pareto-optimal) in multi-player multi-outcome infinite sequential games. We use two fundamental…
We prove that there exists a constant $\epsilon>0$ such that, assuming the Exponential Time Hypothesis for PPAD, computing an $\epsilon$-approximate Nash equilibrium in a two-player (nXn) game requires quasi-polynomial time,…
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 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…
We study the computation of equilibria of anonymous games, via algorithms that may proceed via a sequence of adaptive queries to the game's payoff function, assumed to be unknown initially. The general topic we consider is \emph{query…
We consider a 3-player game in the normal form, in which each player has two actions. We assume that the game is symmetric and repeated infinitely many times. At each stage players make their choices knowing only the average payoffs from…