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Cooperation in a Multi-Dimensional Local Interaction Model

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Author Info

  • Alexander F. Tieman

    (Tinbergen Institute & Free University)

  • Harold Houba

    (Free University)

  • Gerard van der Laan

    (Tinbergen Institute & Free University)

Abstract

We consider a local interaction model with a population on an h dimensional torus, in which in each round of play a random player gets a learning draw. This player plays a k+1 action stage game with players in his neighborhood, compares his own average payoff with the average payoff of the neighbors he played against and updates his action based on this comparison. Individuals use the update rule `Win Cooperate, Lose Defect', a multi-player variant of Tit-for-Tat. We prove that there are exactly k+1 stable states and that all of these can be reached with positive probability, for any dimension h of the torus. Furthermore, we prove that when k+1=2, both stable states will be reached with probability 1/2. For k+1>2 we provide some insight in the probability of reaching each of the stable states by presenting simulation results.

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Bibliographic Info

Paper provided by EconWPA in its series Game Theory and Information with number 9803002.

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Length: 27 pages
Date of creation: 24 Mar 1998
Date of revision:
Handle: RePEc:wpa:wuwpga:9803002

Note: Type of Document - dvi (compiled TeX); prepared on IBM PC - Scientific Workplace 2.5; to print on HP/PostScript; pages: 27 ; figures: included. Tinbergen Institute Discussion Paper
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Related research

Keywords: Evolution; Local Interaction; Cooperation; Prisoner's Dilemma.;

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References

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  1. Matthew Rabin., 1992. "Incorporating Fairness into Game Theory and Economics," Economics Working Papers 92-199, University of California at Berkeley.
  2. Binmore, K. & Samuelson, L., 1991. "Evolutionary Stability in Repeated Game Played by Finite Automata," Papers 9131, Tilburg - Center for Economic Research.
  3. Schlag, Karl H., 1994. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Discussion Paper Serie B 296, University of Bonn, Germany.
  4. Fernando Vega-Redondo & Frédéric Palomino, 1999. "Convergence of aspirations and (partial) cooperation in the prisoner's dilemma," International Journal of Game Theory, Springer, vol. 28(4), pages 465-488.
  5. Ken Binmore & Larry Samuelson, 1994. "Muddling Through: Noisy Equilibrium Selection," Game Theory and Information 9410002, EconWPA.
  6. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September.
  7. Colin F. Camerer, 1997. "Progress in Behavioral Game Theory," Journal of Economic Perspectives, American Economic Association, vol. 11(4), pages 167-188, Fall.
  8. Milgrom, Paul & Roberts, John, 1995. "Complementarities and fit strategy, structure, and organizational change in manufacturing," Journal of Accounting and Economics, Elsevier, vol. 19(2-3), pages 179-208, April.
  9. Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
  10. Karl H. Schlag, 1995. "Why Imitate, and if so, How? A Bounded Rational Approach to Multi-Armed Bandits," Discussion Paper Serie B 361, University of Bonn, Germany, revised Mar 1996.
  11. repec:att:wimass:9612 is not listed on IDEAS
  12. Offerman, Theo & Sonnemans, Joep & Schram, Arthur, 1996. "Value Orientations, Expectations and Voluntary Contributions in Public Goods," Economic Journal, Royal Economic Society, vol. 106(437), pages 817-45, July.
  13. Ellison, G., 1996. "Basins of Attraction, Long Run Equilibria, and the Speed of Step-by- Step Evolution," Working papers 96-4, Massachusetts Institute of Technology (MIT), Department of Economics.
  14. Selten, Reinhard, 1991. "Evolution, learning, and economic behavior," Games and Economic Behavior, Elsevier, vol. 3(1), pages 3-24, February.
  15. Eshel, I. & Samuelson, L. & Shaked, A., 1996. "Altruists, Egoists and Hooligans in a Local Interaction Model," Working papers 9612r, Wisconsin Madison - Social Systems.
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Cited by:
  1. Marco Valente & Giorgio Fagiolo & Luigi Marengo, 2003. "Endogenous Networks in Random Population Games," Computing in Economics and Finance 2003 68, Society for Computational Economics.

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