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Imitation dynamics for population games are studied and their asymptotic properties analyzed. In the considered class of imitation dynamics - that encompass the replicator equation as well as other models previously considered in…

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…

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 study evolutionary games with a continuous trait space in which replicator dynamics are restricted to the manifold of multidimensional Gaussian distributions. We demonstrate that the replicator equations are natural gradient flow for…

We study a dynamic game with a large population of players who choose actions from a finite set in continuous time. Each player has a state in a finite state space that evolves stochastically with their actions. A player's reward depends…

We consider the problem of learning discriminative representations for data in a high-dimensional space with distribution supported on or around multiple low-dimensional linear subspaces. That is, we wish to compute a linear injective map…

We analyze the problem of distributed power allocation for orthogonal multiple access channels by considering a continuous non-cooperative game whose strategy space represents the users' distribution of transmission power over the network's…

We study an atomic signaling game under stochastic evolutionary dynamics. There is a finite number of players who repeatedly update from a finite number of available languages/signaling strategies. Players imitate the most fit agents with…

Evolutionary games are a developing sub-field of game theory. This branch of game theory is used in the study of the adaptation of large, but finite, populations of agents to changes in the environment. It assumes that each agent has no…

We study the evolutionary dynamics of games under environmental feedback using replicator equations for two interacting populations. One key feature is to consider jointly the co-evolution of the dynamic payoff matrices and the state of the…

When a prediction algorithm serves a collection of users, disparities in prediction quality are likely to emerge. If users respond to accurate predictions by increasing engagement, inviting friends, or adopting trends, repeated learning…

In recent years, there has been growing interest in studying evolutionary games with environmental feedback. Previous studies exclusively focus on two-player games. However, extension to multi-player game is needed to study problems such as…

A new mathematical model for evolutionary games on graphs is proposed to extend the classical replicator equation to finite populations of players organized on a network with generic topology. Classical results from game theory,…

Game dynamics in which three or more strategies are cyclically competitive, as represented by the rock-scissors-paper game, have attracted practical and theoretical interests. In evolutionary dynamics, cyclic competition results in…

We study a class of evolutionary game dynamics defined by balancing a gain determined by the game's payoffs against a cost of motion that captures the difficulty with which the population moves between states. Costs of motion are…

We use analytical techniques based on an expansion in the inverse system size to study the stochastic evolutionary dynamics of finite populations of players interacting in a repeated prisoner's dilemma game. We show that a mechanism of…

Game-theoretic solution concepts, such as the Nash equilibrium, have been key to finding stable joint actions in multi-player games. However, it has been shown that the dynamics of agents' interactions, even in simple two-player games with…

Applying the concepts and formalisms from Evolutionary Game Theory to the data regime, the fundamental paradigms of Evolutionary Data Theory are introduced. Interpreting data in matrix form as evolutionary entities, input data is mapped to…

Equilibrium solution concepts of normal-form games, such as Nash equilibria, correlated equilibria, and coarse correlated equilibria, describe the joint strategy profiles from which no player has incentive to unilaterally deviate. They are…

In this work, we study the social learning problem, in which agents of a networked system collaborate to detect the state of the nature based on their private signals. A novel distributed graphical evolutionary game theoretic learning…