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Sato–Crutchfield Formulation For Some Evolutionary Games

Author

Listed:
  • E. AHMED

    (Mathematics Department, Faculty of Science, 35516 Mansoura, Egypt;
    Mathematics Department, Faculty of Science, Al-Ain, P. O. Box 17551, UAE)

  • A. S. HEGAZI

    (Mathematics Department, Faculty of Science, 35516 Mansoura, Egypt)

  • A. S. ELGAZZAR

    (Mathematics Department, Faculty of Education, 45111 El-Arish, Egypt;
    Mathematics Department, College of Science - Al-Jouf, King Saud University, Kingdom of Saudi Arabia)

Abstract

The Sato–Crutchfield equations are analytically and numerically studied. The Sato–Crutchfield formulation corresponds to losing memory. Then the Sato–Crutchfield formulation is applied for some different types of games including hawk–dove, prisoner's dilemma and the battle of the sexes games. The Sato–Crutchfield formulation is found not to affect the evolutionarily stable strategy of the ordinary games. But choosing a strategy becomes purely random, independent of the previous experiences, initial conditions, and the rules of the game itself. The Sato–Crutchfield formulation for the prisoner's dilemma game can be considered as a theoretical explanation for the existence of cooperation in a population of defectors.

Suggested Citation

  • E. Ahmed & A. S. Hegazi & A. S. Elgazzar, 2003. "Sato–Crutchfield Formulation For Some Evolutionary Games," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 14(07), pages 963-971.
    • Handle: RePEc:wsi:ijmpcx:v:14:y:2003:i:07:n:s0129183103005091
    DOI: 10.1142/S0129183103005091
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    Cited by:

    1. Elgazzar, Ahmed S., 2020. "Quantum prisoner’s dilemma in a restricted one-parameter strategic space," Applied Mathematics and Computation, Elsevier, vol. 370(C).

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