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Generalized Replicator Dynamics as a Model of Specialization and Diversity in Societies

Author

Listed:
  • Vivek S. Borkar

    (Department of Computer Science and Automation, Indian Institute of Science, Bangalore 560 012, India)

  • Sanjay Jain

    (Centre for Theoretical Studies, Indian Institute of Science, Bangalore 560 012, India)

  • Govindan Rangarajan

    (Department of Mathematics and Centre for Theoretical Studies, Indian Institute of Science, Bangalore 560 012, India)

Abstract

We consider a generalization of replicator dynamics as a non-cooperative evolutionary game-theoretic model of a community ofNagents. All agents update their individual mixed strategy profiles to increase their total payoff from the rest of the community. The properties of attractors in this dynamics are studied. Evidence is presented that under certain conditions the typical attractors of the system are corners of state space where each agent has specialized to a pure strategy, and/or the community exhibits diversity, i.e., all strategies are represented in the final states. The model suggests that new pure strategies whose payoff matrix elements satisfy suitable inequalities with respect to the existing ones can destabilize existing attractors ifNis sufficiently large, and be regarded as innovations that enhance the diversity of the community.

Suggested Citation

  • Vivek S. Borkar & Sanjay Jain & Govindan Rangarajan, 1999. "Generalized Replicator Dynamics as a Model of Specialization and Diversity in Societies," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 1(04), pages 325-359.
    • Handle: RePEc:wsi:acsxxx:v:01:y:1999:i:04:n:s0219525998000211
    DOI: 10.1142/S0219525998000211
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