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Where strategic and evolutionary stability depart - a study of minimal diversity games

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Author Info

  • Dieter Balkenborg

    (Department of Economics, University of Exeter)

  • Stefano Demichelis

    (Department of Mathematics, University of Pavia)

  • Dries Vermeulen

    (Department of Quantitative Economics, University Maastricht)

Abstract

A minimal diversity game is an n player strategic form game in which each player has m pure strategies at his disposal. The payoff to each player is always 1, unless all players select the same pure strategy, in which case all players receive zero payoff. Such a game has a unique isolated completely mixed Nash equilibrium in which each player plays each strategy with equal probability, and a connected component of Nash equilibria consisting of those strategy profiles in which each player receives payoff 1. The Pareto superior component is shown to be asymptotically stable under a wide class of evolutionary dynamics, while the isolated equilibrium is not. On the other hand, the isolated equilibrium is strategically stable, while the strategic stability of the Pareto efficient component depends on the dimension of the component, and hence on the number of players, and the number of pure strategies.

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File URL: http://people.exeter.ac.uk/cc371/RePEc/dpapers/DP1001.pdf
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Bibliographic Info

Paper provided by Exeter University, Department of Economics in its series Discussion Papers with number 1001.

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Date of creation: 2010
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Handle: RePEc:exe:wpaper:1001

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Related research

Keywords: Strategic form games; strategic stability; evolutionary stability;

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References

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  1. Guth, Werner & Huck, Steffen & Muller, Wieland, 2001. "The Relevance of Equal Splits in Ultimatum Games," Games and Economic Behavior, Elsevier, vol. 37(1), pages 161-169, October.
  2. Swinkels Jeroen M., 1993. "Adjustment Dynamics and Rational Play in Games," Games and Economic Behavior, Elsevier, vol. 5(3), pages 455-484, July.
  3. DEMICHELIS, Stefano & RITZBERGER, Klaus, 2000. "From evolutionary to strategic stability," CORE Discussion Papers 2000059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Sergiu Hart, 2006. "Discrete Colonel Blotto and General Lotto Games," Discussion Paper Series dp434, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  5. KOHLBERG, Elon & MERTENS, Jean-François, . "On the strategic stability of equilibria," CORE Discussion Papers RP -716, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  7. Balkenborg, Dieter & Schlag, Karl H., 2007. "On the evolutionary selection of sets of Nash equilibria," Journal of Economic Theory, Elsevier, vol. 133(1), pages 295-315, March.
  8. DE MICHELIS, Stefano & GERMANO, Fabrizio, 2000. "On the indices of zeros of nash fields," CORE Discussion Papers 2000017, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Ritzberger, Klaus, 1994. "The Theory of Normal Form Games form the Differentiable Viewpoint," International Journal of Game Theory, Springer, vol. 23(3), pages 207-36.
  10. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, January.
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Cited by:
  1. Man, Priscilla T.Y., 2012. "Efficiency and stochastic stability in normal form games," Games and Economic Behavior, Elsevier, vol. 76(1), pages 272-284.

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