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Cooperation in a Multi-Dimensional Local Interaction Model

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Author Info
Alexander F. Tieman () (Vrije Universiteit Amsterdam)
Harold Houba () (Vrije Universiteit Amsterdam)
Gerard van der Laan () (Vrije Universiteit Amsterdam)

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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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Publisher Info
Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 98-024/1.

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Date of creation: 04 Mar 1998
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Handle: RePEc:dgr:uvatin:19980024

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Web page: http://www.tinbergen.nl/

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Related research
Keywords: Evolution Local Interaction Cooperation > Prisoner's Dilemma.

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Find related papers by JEL classification:
C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

References listed on IDEAS
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  1. Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June. [Downloadable!] (restricted)
  2. Camerer, Colin, . "Progress and Behavioral Game Theory," Working Papers 1004, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  3. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September. [Downloadable!] (restricted)
  4. Karl H. Schlag, . "Why Imitate, and if so, How? A Bounded Rational Approach to Multi- Armed Bandits," ELSE working papers 028, ESRC Centre on Economics Learning and Social Evolution. [Downloadable!]
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  5. 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. [Downloadable!] (restricted)
  6. Binmore, Ken, and Larry Samuelson, 1994. "Muddling Through: Noisy Equilibrium Selection," Discussion Paper Serie B 275, University of Bonn, Germany.
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  7. 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. [Downloadable!] (restricted)
  8. Binmore, K. & Samuelson, L., 1991. "Evolutionary Stability in Repeated Game Played by Finite Automata," Papers 9131, Tilburg - Center for Economic Research.
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  9. repec:att:wimass:199612r is not listed on IDEAS
  10. 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.
  11. Rabin, Matthew, 1993. "Incorporating Fairness into Game Theory and Economics," American Economic Review, American Economic Association, vol. 83(5), pages 1281-1302, December. [Downloadable!] (restricted)
  12. Camerer, Colin F, 1997. "Progress in Behavioral Game Theory," Journal of Economic Perspectives, American Economic Association, vol. 11(4), pages 167-88, Fall. [Downloadable!] (restricted)
  13. Selten, Reinhard, 1991. "Evolution, learning, and economic behavior," Games and Economic Behavior, Elsevier, vol. 3(1), pages 3-24, February. [Downloadable!] (restricted)
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  1. Giorgio Fagiolo & Luigi Marengo & Marco Valente, 2003. "Endogenous Networks in Random Population Games," LEM Papers Series 2003/03, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy. [Downloadable!]
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