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Robustness to Strategic Uncertainty

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Author Info

  • Andersson, Ola

    ()
    (Research Institute of Industrial Economics (IFN))

  • Argenton, Cédric

    ()
    (CentER & TILEC)

  • Weibull, Jörgen W.

    ()
    (Stockholm School of Economics)

Abstract

In games with continuum strategy sets, we model a player’s uncertainty about another player’s strategy, as an atomless probability distribution over the other player’s strategy set. We call a strategy profile (strictly) robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence (all sequences) of strategy profiles in which every player’s strategy is optimal under his or her uncertainty about the others. General properties of this robustness criterion are derived and it is shown that it is a refinement of Nash equilibrium when payoff functions are continuous. We apply the criterion to a class of Bertrand competition games. These are discontinuous games that admit a continuum of Nash equilibria. Our robustness criterion selects a unique Nash equilibrium, and this selection agrees with recent experimental findings.

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Bibliographic Info

Paper provided by Research Institute of Industrial Economics in its series Working Paper Series with number 910.

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Length: 27 pages
Date of creation: 30 Mar 2012
Date of revision:
Handle: RePEc:hhs:iuiwop:0910

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Related research

Keywords: Nash equilibrium; Refinement; Strategic uncertainty; Bertrand competition; Log-concavity;

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  1. Frank Heinemann & Rosemarie Nagel & Peter Ockenfels, 2004. "Measuring strategic uncertainty in coordination games," Economics Working Papers 804, Department of Economics and Business, Universitat Pompeu Fabra.
  2. Simon, Leo K & Stinchcombe, Maxwell B, 1995. "Equilibrium Refinement for Infinite Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1421-43, November.
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  8. John B Van Huyck & Raymond C Battalio & Richard O Beil, 1997. "Tacit coordination games, strategic uncertainty, and coordination failure," Levine's Working Paper Archive 1225, David K. Levine.
  9. Carlsson, Hans & Ganslandt, Mattias, 1998. "Noisy equilibrium selection in coordination games," Economics Letters, Elsevier, vol. 60(1), pages 23-34, July.
  10. Spulber, Daniel F, 1995. "Bertrand Competition When Rivals' Costs Are Unknown," Journal of Industrial Economics, Wiley Blackwell, vol. 43(1), pages 1-11, March.
  11. Bagnoli, M. & Bergstrom, T., 1989. "Log-Concave Probability And Its Applications," Papers 89-23, Michigan - Center for Research on Economic & Social Theory.
  12. Antonio Cabrales & Raffaele Miniaci & Marco Piovesan & Giovanni Ponti, 2008. "Social Preferences and Strategic Uncertainty: An Experiment on Markets and Contracts," Discussion Papers 08-06, University of Copenhagen. Department of Economics.
  13. Dastidar, Krishnendu Ghosh, 1995. "On the Existence of Pure Strategy Bertrand Equilibrium," Economic Theory, Springer, vol. 5(1), pages 19-32, January.
  14. Argenton, C. & Müller, W., 2009. "Collusion in Experimental Bertrand Duopolies with Convex Costs: The Role of Information and Cost Asymmetry," Discussion Paper 2009-87, Tilburg University, Center for Economic Research.
  15. Bagnoli, Mark & Lipman, Barton L, 1989. "Provision of Public Goods: Fully Implementing the Core through Private Contributions," Review of Economic Studies, Wiley Blackwell, vol. 56(4), pages 583-601, October.
  16. Abbink, Klaus & Brandts, Jordi, 2008. "24. Pricing in Bertrand competition with increasing marginal costs," Games and Economic Behavior, Elsevier, vol. 63(1), pages 1-31, May.
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