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Social Learning Algorithms Reaching Nash Equilibrium in Symmetric Cournot Games

  • Mattheos K. Protopapas
  • Francesco Battaglia
  • Elias B. Kosmatopoulos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6024)

Abstract

The series of studies about the convergence or not of the evolutionary strategies of players that use co-evolutionary genetic algorithms in Cournot games has not addressed the issue of individual players’ strategies convergence, but only of the convergence of the aggregate indices (total quantity and price) to the levels that correspond either to the Nash or Walrash Equilibrium. Here we discover that while some algorithms lead to convergence of the aggregates to Nash Equilibrium values, this is not the case for the individual players’ strategies (i.e. no NE is reached). Co-evolutionary programming social learning, as well as a social learning algorithm we introduce here, achieve this goal (in a stochastic sense); this is displayed by statistical tests, as well as “NE stages” evaluation, based on ergodic Markov chains.

Keywords

Genetic Algorithm Nash Equilibrium Individual Player Inverse Demand Function Ergodic Markov Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Mattheos K. Protopapas
    • 1
  • Francesco Battaglia
    • 1
  • Elias B. Kosmatopoulos
    • 2
  1. 1.Department of StatisticsUniversity of Rome “La Sapienza”RomeItaly
  2. 2.Department of Production Engineering and ManagementTechnical University of CreteAgiou Titou Square

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