Topic
Replicator equation
About: Replicator equation is a research topic. Over the lifetime, 1464 publications have been published within this topic receiving 36875 citations.
Papers published on a yearly basis
Papers
Book•
1 Jan 1998TL;DR: In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behavior, and of the closely related interactions among species in ecological communities.
Abstract: Every form of behavior is shaped by trial and error. Such stepwise adaptation can occur through individual learning or through natural selection, the basis of evolution. Since the work of Maynard Smith and others, it has been realized how game theory can model this process. Evolutionary game theory replaces the static solutions of classical game theory by a dynamical approach centered not on the concept of rational players but on the population dynamics of behavioral programs. In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behavior, and of the closely related interactions among species in ecological communities. Replicator equations describe how successful strategies spread and thereby create new conditions that can alter the basis of their success, i.e., to enable us to understand the strategic and genetic foundations of the endless chronicle of invasions and extinctions that punctuate evolution. In short, evolutionary game theory describes when to escalate a conflict, how to elicit cooperation, why to expect a balance of the sexes, and how to understand natural selection in mathematical terms.
Comprehensive treatment of ecological and game theoretic dynamics
Invasion dynamics and permanence as key concepts
Explanation in terms of games of things like competition between species
5,583 citations
TL;DR: In this article, the authors consider a class of matrix games in which successful strategies are rewarded by high reproductive rates, so become more likely to participate in subsequent playings of the game, thus, over time, the strategy mix should evolve to some type of optimal or stable state.
Abstract: We consider a class of matrix games in which successful strategies are rewarded by high reproductive rates, so become more likely to participate in subsequent playings of the game. Thus, over time, the strategy mix should evolve to some type of optimal or stable state. Maynard Smith and Price (1973) have introduced the concept of ESS (evolutionarily stable strategy) to describe a stable state of the game. We attempt to model the dynamics of the game both in the continuous case, with a system of non-linear first-order differential equations, and in the discrete case, with a system of non-linear difference equations. Using this model, we look at the notions of stability and asymptotic behavior. Our notion of stable equilibrium for the continuous dynamic includes, but is somewhat more general than, the notion of ESS.
3,491 citations
TL;DR: This paper focuses on frequency-dependent selection, and argues that game-theoretic arguments are more appropriate than optimization algorithms for studying frequency- dependent selection.
Abstract: Darwinian dynamics based on mutation and selection form the core of mathematical models for adaptation and coevolution of biological populations. The evolutionary outcome is often not a fitness-maximizing equilibrium but can include oscillations and chaos. For studying frequency-dependent selection, game-theoretic arguments are more appropriate than optimization algorithms. Replicator and adaptive dynamics describe short- and long-term evolution in phenotype space and have found applications ranging from animal behavior and ecology to speciation, macroevolution, and human language. Evolutionary game theory is an essential component of a mathematical and computational approach to biology.
1,197 citations
TL;DR: A version of Bush and Mosteller's stochastic learning theory in the context of games is considered and it is shown that in the continuous time limit the biological model coincides with the deterministic, continuous time replicator process.
836 citations
TL;DR: In this paper, a review of non-mean-field effects in evolutionary game dynamics is presented, focusing on the non-trivial modifications they induce when compared to the outcome of replicator dynamics.
732 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2026 | 2 |
| 2025 | 24 |
| 2024 | 40 |
| 2023 | 58 |
| 2022 | 153 |
| 2021 | 88 |