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Characterizing Stability Properties in Games with Strategic Substitutes

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  • Sunanda Roy

    (Department of Economics, Iowa State University)

  • Tarun Sabarwal

    (Department of Economics, University of Kansas)

Abstract

In games with strategic substitutes (GSS), convergence of the best response dynamic starting from the inf (or sup) of the strategy space is equivalent to global stability (convergence of every adaptive dynamic to the same pure strategy Nash equilibrium). Consequently, in GSS, global stability can be analyzed using a single best response dynamic. Moreover, in GSS, global stability is equivalent to dominance solvability, showing that in this class of games, two different foundations for robustness of predicted outcomes are equivalent, and both can be checked using a single best response dynamic. These equivalences are useful to study stability of equilibria in a variety of applications. Furthermore, in parameterized GSS, under natural conditions, dynamically stable equilibrium selections can be viewed in terms of monotone selections of equilibria. Several examples are provided.

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Bibliographic Info

Paper provided by University of Kansas, Department of Economics in its series WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS with number 201003.

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Length: 29 pages
Date of creation: Jul 2010
Date of revision: Oct 2011
Handle: RePEc:kan:wpaper:201003

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Keywords: Global stability; adaptive dynamics; strategic substitutes; dominance solvable; learning; monotone comparative statics; Correspondence principle;

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Cited by:
  1. Acemoglu, Daron & Jensen, Martin Kaae, 2009. "Aggregate Comparative Statics," CEPR Discussion Papers 7254, C.E.P.R. Discussion Papers.
  2. Eric Hoffmann, 2013. "Global Games Selection in Games with Strategic Substitutes or Complements," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201308, University of Kansas, Department of Economics.

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