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Metastable Equilibria

  • Srihari Govindan
  • Robert Wilson

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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Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 122247000000001211.

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Date of creation: 03 Mar 2006
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Handle: RePEc:cla:levrem:122247000000001211
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  1. MERTENS, Jean-François, 1990. "The "small worlds" axiom for stable equilibria," CORE Discussion Papers 1990007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. David Kreps & Robert Wilson, 1998. "Sequential Equilibria," Levine's Working Paper Archive 237, David K. Levine.
  3. E. Kohlberg & J.-F. Mertens, 1998. "On the Strategic Stability of Equilibria," Levine's Working Paper Archive 445, David K. Levine.
  4. Mclennan, A., 1989. "Selected Topics In The Theory Of Fixed Points," Papers 251, Minnesota - Center for Economic Research.
  5. 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.
  6. Govindan, Srihari & Wilson, Robert B., 2007. "Stable Outcomes of Generic Games in Extensive Form," Research Papers 1933r, Stanford University, Graduate School of Business.
  7. Srihari Govindan & Robert Wilson, 2006. "Sufficient Conditions for Stable Equilibria," Levine's Bibliography 784828000000000267, UCLA Department of Economics.
  8. 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.
  9. Srihari Govindan & Robert Wilson, 2006. "Essential Equilibria," Levine's Bibliography 122247000000001035, UCLA Department of Economics.
  10. Hillas, John, 1990. "On the Definition of the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 58(6), pages 1365-90, November.
  11. Mertens, J.-F., 1988. "Stable equilibria - a reformulation," CORE Discussion Papers 1988038, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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