Related papers: Replicator dynamics for the game theoretic selecti…

This work introduces a novel modified Replicator Dynamics model, which includes external influences on the population. This framework models a realistic market into which companies, the external dynamic influences, invest resources in order…

The finitely repeated Prisoners' Dilemma is a good illustration of the discrepancy between the strategic behaviour suggested by a game-theoretic analysis and the behaviour often observed among human players, where cooperation is maintained…

We consider three distinct discrete-time models of learning and evolution in games: a biological model based on intra-species selective pressure, the dynamics induced by pairwise proportional imitation, and the exponential / multiplicative…

Population dynamics are often subject to random independent changes in the environment. For the two strategy stochastic replicator dynamic, we assume that stochastic changes in the environment replace the payoffs and variance. This is…

In this paper, we study a special case of the invasion fitness matrix in a replicator equation: the invader-driven case. In this replicator, each species is defined by its unique active invasiveness potential (initial growth rate when…

The replicator equation is one of the fundamental tools to study evolutionary dynamics in well-mixed populations. This paper contributes to the literature on evolutionary graph theory, providing a version of the replicator equation for a…

We construct two models of discrete-time replicator dynamics with time delay. In the social-type model, players imitate opponents taking into account average payoffs of games played some units of time ago. In the biological-type model, new…

Evolutionary games provide the theoretical backbone for many aspects of our social life: from cooperation to crime, from climate inaction to imperfect vaccination and epidemic spreading, from antibiotics overuse to biodiversity…

We present a microscopic model of replicator dynamics with strategy-dependent time delays. In such a model, new players are born from parents who interacted and received payoffs in the past. In the case of small delays, we use Taylor…

This chapter is an overview of foundational results in the mathematical theory of replicator systems. Its primary aim is to provide a unified framework for the mathematical formalisation of evolutionary processes in the spirit of…

We consider a multiagent system consisting of selfish and heterogeneous agents. Its behavior is modeled by multipopulation replicator dynamics, where payoff functions of populations are different from each other. In general, there exist…

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…

Using a new dynamical network model of society in which pairwise interactions are weighted according to mutual satisfaction, we show that cooperation is the norm in the Hawks-Doves game when individuals are allowed to break ties 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…

A replicator dynamic for non-exchangeable agents in a continuous action space is formulated and its well-posedness is proven in a space of probability measures. The non-exchangeability allows for the analysis of evolutionary games involving…

This paper is concerned with the death-birth updating process. This model is an example of a spatial game in which players located on the~$d$-dimensional integer lattice are characterized by one of two possible strategies and update their…

In the optional prisoner's dilemma (OPD), players can choose to cooperate and defect as usual, but can also abstain as a third possible strategy. This strategy models the players' participation in the game and is a relevant aspect in many…

We introduce and study a mean-field model for a system of spatially distributed players interacting through an evolutionary game driven by a replicator dynamics. Strategies evolve by a replicator dynamics influenced by the position and the…

The environment has a strong influence on a population's evolutionary dynamics. Driven by both intrinsic and external factors, the environment is subject to continual change in nature. To capture an ever-changing environment, we consider a…

Starting with a group of reinforcement-learning agents we derive coupled replicator equations that describe the dynamics of collective learning in multiagent systems. We show that, although agents model their environment in a…