Evolutionary Games And The Replicator Dynamics
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Evolutionary Games and the Replicator Dynamics
Author: Saul Mendoza-Palacios
language: en
Publisher: Cambridge University Press
Release Date: 2024-06-06
This Element introduces the replicator dynamics for symmetric and asymmetric games where the strategy sets are metric spaces. Under this hypothesis the replicator dynamics evolves in a Banach space of finite signed measures. The authors provide a general framework to study the stability of the replicator dynamics for evolutionary games in this Banach space. This allows them to establish a relation between Nash equilibria and the stability of the replicator for normal a form games applicable to oligopoly models, theory of international trade, public good models, the tragedy of commons, and War of attrition game among others. They also provide conditions to approximate the replicator dynamics on a space of measures by means of a finite-dimensional dynamical system and a sequence of measure-valued Markov processes.
Evolutionary Games in Natural, Social, and Virtual Worlds
Authors Daniel Friedman and Barry Sinervo show how to use theoretical developments in evolutionary game theory to build useful models describing parts of the worlds we live in --- the natural world of biology, the social world of politics and economics, and the virtual world that is emerging from our connected electronic devices.
Evolutionary Games and Population Dynamics
Author: Josef Hofbauer
language: en
Publisher: Cambridge University Press
Release Date: 1998-05-28
Every form of behaviour 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 realised how game theory can model this process. Evolutionary game theory replaces the static solutions of classical game theory by a dynamical approach centred not on the concept of rational players but on the population dynamics of behavioural programmes. In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behaviour, and of the closely related interactions between species in ecological communities. Replicator equations describe how successful strategies spread and thereby create new conditions which 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 which 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.