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3 results

Evolutionary Games and the Replicator Dynamics

Evolutionary Games and the Replicator Dynamics
  • Saul Mendoza-Palacios, Onésimo Hernández-Lerma
  • Published online:
    13 May 2024
    Print publication:
    06 June 2024
  • 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.

  • 3 - Artificial Games

  • from Part I - Artificial Economics and Mainstream Economics
  • Ruben Mercado
  • Book:
    Artificial Economics
    Published online:
    28 October 2021
    Print publication:
    04 November 2021, pp 50-59

  • Summary

    Chapter 3 presents models in which artificial agents interact through games. It first introduces a typical mainstream economics model known as the prisoner’s dilemma, in which agents interact through a classic game theory game, and then contrast it with an artificial evolutionary game based on the same dilemma. In this evolutionary game, the dynamic evolution of a population of boundedly rational agents is represented and simulated using a genetic algorithm. It finally contrasts the assumptions of artificial economics against those of mainstream economics when modeling games.

  • 7 - Artificial Complexity

  • from Part II - Complementary Topics and Discussions
  • Ruben Mercado
  • Book:
    Artificial Economics
    Published online:
    28 October 2021
    Print publication:
    04 November 2021, pp 103-127

  • Summary

    Chapter 7 introduces the subject matter of artificial complexity. First, it presents examples of artificial complexity by means of cellular automata. It presents one-dimensional cellular automata following Wolfram’s rules, and a two-dimensional cellular automaton in the form of a spatial evolutionary game.Then it introduces the concepts of complexity and emergence, as used in the science of complexity, and discusses some issues related to their definition and measurement. Finally, it discusses the scope and controversies around the application of the concepts and models of the science of complexity in economics.