相关论文: Stable and Historic Behavior in Replicator Equatio…

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…

A replicator equation with explicit space and global regulation is considered. This model provides a natural framework to follow frequencies of species that are distributed in the space. For this model, analogues to classical notions of the…

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…

We develop a general game-theoretic framework for reasoning about strategic agents performing possibly costly computation. In this framework, many traditional game-theoretic results (such as the existence of a Nash equilibrium) no longer…

We propose local symplectic surgery, a two-timescale procedure for finding local Nash equilibria in two-player zero-sum games. We first show that previous gradient-based algorithms cannot guarantee convergence to local Nash equilibria due…

We analyze, using a dynamical systems approach, the replicator dynamics for the asymmetric Hawk-Dove game in which there is a set of four pure strategies with arbitrary payoffs. We give a full account of the equilibrium points and their…

TASP (Time Average Shapley Polygon, Bena{\=\i}m, Hofbauer and Hopkins, \emph{Journal of Economic Theory}, 2009), as a novel evolutionary dynamics model, predicts that a game could converge to cycles instead of fix points (Nash equilibria).…

Game theory provides a well-established framework for the analysis of concurrent and multi-agent systems. The basic idea is that concurrent processes (agents) can be understood as corresponding to players in a game; plays represent the…

We analyze the performance of the best-response dynamic across all normal-form games using a random games approach. The playing sequence -- the order in which players update their actions -- is essentially irrelevant in determining whether…

The uniform distribution is an important counterexample in game theory as many of the canonical game dynamics have been shown not to converge to the equilibrium in certain cases. In particular none of the canonical game dynamics converge to…

Dynamical mechanisms that can stabilize the coexistence or diversity in biology are generally of fundamental interest. In contrast to many two-strategy evolutionary games, games with three strategies and cyclic dominance like the…

We consider evolutionary dynamics for population games in which players have a continuum of strategies at their disposal. Models in this setting amount to infinite-dimensional differential equations evolving on the manifold of probability…

Learning in games considers how multiple agents maximize their own rewards through repeated games. Memory, an ability that an agent changes his/her action depending on the history of actions in previous games, is often introduced into…

We investigate whether having a unique equilibrium (or a given number of equilibria) is robust to perturbation of the payoffs, both for Nash equilibrium and correlated equilibrium. We show that the set of n-player finite games with a unique…

In this paper, we examine the robustness of Nash equilibria in continuous games, under both strategic and dynamic uncertainty. Starting with the former, we introduce the notion of a robust equilibrium as those equilibria that remain…

Evolutionary game theory has impacted many fields of research by providing a mathematical framework for studying the evolution and maintenance of social and moral behaviors. This success is owed in large part to the demonstration that the…

In evolutionary game theory an Evolutionarily Stable Strategy (ESS) is a refinement of the Nash equilibrium concept that is sometimes also recognized as evolutionary stability. It is a game-theoretic model, well known to mathematical…

Many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind. Examples include Nash equilibria in games; market equilibria; computing optimal strategies and the values of competitive games…

Zero-sum stochastic games have found important applications in a variety of fields, from machine learning to economics. Work on this model has primarily focused on the computation of Nash equilibrium due to its effectiveness in solving…

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…