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The projection dynamic and the replicator dynamic

  • Sandholm, William H.
  • DokumacI, Emin
  • Lahkar, Ratul

We investigate a variety of connections between the projection dynamic and the replicator dynamic. At interior population states, the standard microfoundations for the replicator dynamic can be converted into foundations for the projection dynamic by replacing imitation of opponents with "revision driven by insecurity" and direct choice of alternative strategies. Both dynamics satisfy a condition called inflow-outflow symmetry, which causes them to select against strictly dominated strategies at interior states; still, because it is discontinuous at the boundary of the state space, the projection dynamic allows strictly dominated strategies to survive in perpetuity. The two dynamics exhibit qualitatively similar behavior in strictly stable and null stable games. Finally, the projection and replicator dynamics both can be viewed as gradient systems in potential games, the latter after an appropriate transformation of the state space.

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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 64 (2008)
Issue (Month): 2 (November)
Pages: 666-683

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Handle: RePEc:eee:gamebe:v:64:y:2008:i:2:p:666-683
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. Hofbauer, Josef & Weibull, Jîrgen W., 1995. "Evolutionary selection against dominated strategies," CEPREMAP Working Papers (Couverture Orange) 9506, CEPREMAP.
  2. 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.
  3. Hofbauer, Josef & Sandholm, William H., 2007. "Evolution in games with randomly disturbed payoffs," Journal of Economic Theory, Elsevier, vol. 132(1), pages 47-69, January.
  4. Sandholm, William H., 2001. "Potential Games with Continuous Player Sets," Journal of Economic Theory, Elsevier, vol. 97(1), pages 81-108, March.
  5. 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.
  6. Michel BenaÔm & J–rgen W. Weibull, 2003. "Deterministic Approximation of Stochastic Evolution in Games," Econometrica, Econometric Society, vol. 71(3), pages 873-903, 05.
  7. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
  8. Sandholm, William H., 2003. "Evolution and equilibrium under inexact information," Games and Economic Behavior, Elsevier, vol. 44(2), pages 343-378, August.
  9. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  10. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
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