English
Related papers

Related papers: Replicator dynamics with mutations for games with …

200 papers

The game dynamical equations are derived from Boltzmann-like equations for individual pair interactions by assuming a certain kind of imitation behavior, the so-called proportional imitation rule. They can be extended to a stochastic…

Statistical Mechanics · Physics 2007-05-23 Dirk Helbing

In the original Evolutionary Minority Game, a segregation into two populations with opposing preferences is observed under many circumstances. We show that this segregation becomes more pronounced and more robust if the dynamics are changed…

Disordered Systems and Neural Networks · Physics 2009-11-07 Richard Metzler , Christian Horn

Recent studies in the spatial prisoner's dilemma games with reinforcement learning have shown that static agents can learn to cooperate through a diverse sort of mechanisms, including noise injection, different types of learning algorithms…

Artificial Intelligence · Computer Science 2025-07-08 Gustavo C. Mangold , Heitor C. M. Fernandes , Mendeli H. Vainstein

A discrete-time version of the replicator equation for two-strategy games is studied. The stationary properties differ from that of continuous time for sufficiently large values of the parameters, where periodic and chaotic behavior replace…

Adaptation and Self-Organizing Systems · Physics 2011-07-14 Daniele Vilone , Alberto Robledo , Angel Sánchez

We consider the general properties of the replicator dynamical system from the standpoint of its evolution and stability. Vector field analysis as well as spectral properties of such system has been studied. Lyaponuv function for…

Disordered Systems and Neural Networks · Physics 2007-05-23 A. A. Prykarpatsky , V. V. Gafiychuk

We investigate the win-lose relations between strategies of iterated prisoner's dilemma games by using a directed network concept to display the replicator dynamics results. In the giant strongly-connected component of the win/lose network,…

Physics and Society · Physics 2015-01-16 Young Jin Kim , Myungkyoon Roh , Seon-Young Jeong , Seung-Woo Son

Dynamic environments shape diverse dynamics in evolutionary game systems. We introduce spatial heterogeneity of resources into the prisoner's dilemma game model to explore coevolutionary game dynamics with environmental feedback. The…

Populations and Evolution · Quantitative Biology 2025-02-17 Yi-Duo Chen , Jian-Yue Guan , Zhi-Xi Wu

We present a detailed study of prisoner's dilemma game with stochastic modifications on a two-dimensional lattice, in presence of evolutionary dynamics. By very nature of the rules, the cooperators have incentive to cheat and the fear to…

Statistical Mechanics · Physics 2015-05-14 M. Ali Saif , Prashant M. Gade

In this paper, we consider finite-strategy approximations of infinite-strategy evolutionary games. We prove that such approximations converge to the true dynamics over finite-time intervals, under mild regularity conditions which are…

Theoretical Economics · Economics 2025-11-18 Brendon G. Anderson

The replicator equations are a family of ordinary differential equations that arise in evolutionary game theory, and are closely related to Lotka-Volterra. We produce an infinite family of replicator equations which are Liouville-Arnold…

Dynamical Systems · Mathematics 2023-06-07 Josh Paik , Christopher Griffin

We provide results of a deterministic approximation for non-Markovian stochastic processes modeling finite populations of individuals who recurrently play symmetric finite games and imitate each other according to payoffs. We show that a…

Dynamical Systems · Mathematics 2023-06-05 Ozgur Aydogmus , Yun Kang

We investigate a class of reinforcement learning dynamics where players adjust their strategies based on their actions' cumulative payoffs over time - specifically, by playing mixed strategies that maximize their expected cumulative payoff…

Optimization and Control · Mathematics 2016-02-10 Panayotis Mertikopoulos , William H. Sandholm

For the iterated Prisoner's Dilemma, there exist Markov strategies which solve the problem when we restrict attention to the long term average payoff. When used by both players these assure the cooperative payoff for each of them. Neither…

Dynamical Systems · Mathematics 2017-04-27 Ethan Akin

We present detailed numerical results for a modified form of the so-called Minority Game, which provides a simplified model of a competitive market. Each agent has a limited set of strategies, and competes to be in a minority. An…

Condensed Matter · Physics 2009-10-31 T. S. Lo , S. W. Lim , P. M. Hui , N. F. Johnson

In this paper, I model and study the process of natural selection between all possible mixed strategies in classical two-player two-strategy games. I derive and solve an equation that is a natural generalization of the Taylor-Jonker…

Populations and Evolution · Quantitative Biology 2018-02-21 Georgy Karev

Continuous-time game dynamics are typically first order systems where payoffs determine the growth rate of the players' strategy shares. In this paper, we investigate what happens beyond first order by viewing payoffs as higher order forces…

Optimization and Control · Mathematics 2013-08-01 Rida Laraki , Panayotis Mertikopoulos

Although learning has found wide application in multi-agent systems, its effects on the temporal evolution of a system are far from understood. This paper focuses on the dynamics of Q-learning in large-scale multi-agent systems modeled as…

Multiagent Systems · Computer Science 2022-03-04 Shuyue Hu , Chin-Wing Leung , Ho-fung Leung , Harold Soh

An alternate Lagrangian scheme at discrete times is proposed for the approximation of a nonlinear continuity equation arising as a mean-field limit of spatially inhomogeneous evolutionary games, describing the evolution of a system of…

Analysis of PDEs · Mathematics 2020-05-25 Stefano Almi , Marco Morandotti , Francesco Solombrino

We study linear quadratic dynamic games where players are uncertain about each other's control policies or goals and consequently seek to be strategically robust. Building on recent work on strategically robust and risk-averse game theory,…

Optimization and Control · Mathematics 2026-04-27 Boris Velasevic , Nicolas Lanzetti , Eric Mazumdar

Human decision behaviour is quite diverse. In many games humans on average do not achieve maximal payoff and the behaviour of individual players remains inhomogeneous even after playing many rounds. For instance, in repeated prisoner…

Physics and Society · Physics 2015-11-11 Martin Spanknebel , Klaus Pawelzik