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Metastable Equilibria

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  • Govindan, Srihari

    (U of Iowa)

  • Wilson, Robert B.

    (Stanford U)

Abstract

We define a refinement of Nash equilibria called metastability. This refinement supposes that the given game might be embedded within any global game that leaves its local bestreply correspondence unaffected. A selected set of equilibria is metastable if it is robust against perturbations of every such global game; viz., every sufficiently small perturbation of the best-reply correspondence of each global game has an equilibrium that projects arbitrarily near the selected set. Metastability satisfies the standard decisiontheoretic axioms obtained by Mertens' (1989) refinement (the strongest proposed refinement), and it satisfies the projection property in Mertens' small-worlds axiom: a metastable set of a global game projects to a metastable set of a local game. But the converse is slightly weaker than Mertens' decomposition property: a metastable set of a local game contains a metastable set that is the projection of a metastable set of a global game. This is inevitable given our demonstration that metastability is equivalent to a strong form of homotopic essentiality. Mertens' definition invokes homological essentiality whereas we derive homotopic essentiality from primitives (robustness for every embedding). We argue that this weak version of decomposition has a natural gametheoretic interpretation.

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Bibliographic Info

Paper provided by Stanford University, Graduate School of Business in its series Research Papers with number 1934r.

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Date of creation: May 2007
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Handle: RePEc:ecl:stabus:1934r

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  1. David Kreps & Robert Wilson, 1998. "Sequential Equilibria," Levine's Working Paper Archive 237, David K. Levine.
  2. Wilson, Robert B. & Govindan, Srihari, 2006. "Sufficient conditions for stable equilibria," Theoretical Economics, Econometric Society, vol. 1(2), pages 167-206, June.
  3. Srihari Govindan & Jean-François Mertens, 2004. "An equivalent definition of stable Equilibria," International Journal of Game Theory, Springer, vol. 32(3), pages 339-357, 06.
  4. Hillas, John & Kohlberg, Elon, 2002. "Foundations of strategic equilibrium," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 42, pages 1597-1663 Elsevier.
  5. MERTENS, Jean-François, . "The small worlds axiom for stable equilibria," CORE Discussion Papers RP -1015, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. E. Kohlberg & J.-F. Mertens, 1998. "On the Strategic Stability of Equilibria," Levine's Working Paper Archive 445, David K. Levine.
  7. Mertens, J.-F., 1988. "Stable equilibria - a reformulation," CORE Discussion Papers 1988038, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Hillas, John, 1990. "On the Definition of the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 58(6), pages 1365-90, November.
  9. Govindan, Srihari & Wilson, Robert B., 2007. "Stable Outcomes of Generic Games in Extensive Form," Research Papers 1933r, Stanford University, Graduate School of Business.
  10. Srihari Govindan & Robert Wilson, 2006. "Essential Equilibria," Levine's Bibliography 122247000000001035, UCLA Department of Economics.
  11. Mclennan, A., 1989. "Selected Topics In The Theory Of Fixed Points," Papers 251, Minnesota - Center for Economic Research.
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Cited by:
  1. Srihari Govindan & Robert Wilson, 2009. "Axiomatic Equilibrium Selection for Generic two-player games," Levine's Working Paper Archive 814577000000000231, David K. Levine.
  2. Govindan, Srihari & Wilson, Robert B., 2008. "Axiomatic Theory of Equilibrium Selection in Signaling Games with Generic Payoffs," Research Papers 2000, Stanford University, Graduate School of Business.
  3. Govindan, Srihari & Wilson, Robert B., 2007. "Stable Outcomes of Generic Games in Extensive Form," Research Papers 1933r, Stanford University, Graduate School of Business.

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