P-stable equilibrium : definition and some properties
Desgranges, Gabriel and Ghosal, Sayantan (2010) P-stable equilibrium : definition and some properties. Working Paper. Coventry: University of Warwick. Dept. of Economics. (Warwick economics research paper series (TWERPS), Vol.2010).
WRAP_Ghosal_twerp_952.pdf - Other - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Official URL: http://www2.warwick.ac.uk/fac/soc/economics/resear...
We define a continuous index of strategic stability, p-stability, which requires equilibrium to be the unique outcome compatible with common knowledge of rationality and common knowledge of p-beliefs (beliefs that put probability at least p on the equilibrium profile). We show that every equilibrium (within a large class) is p-stable for some p < 1 and justify, in smooth settings, the intuition that the slope of the best response map is related to the stability of equilibrium. We show that adding incomplete information on fundamentals could decrease the degree of strategic stability. In two applications to large markets we (i) show that a unique equilibrium globally unstable (under tâtonnement dynamics) has, nevertheless, a measure of strategic stability, (ii) characterize the conditions under which enhanced equilibrium efficiency results in decreased strategic stability.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||H Social Sciences > HB Economic Theory
Q Science > QA Mathematics
|Divisions:||Faculty of Social Sciences > Economics|
|Library of Congress Subject Headings (LCSH):||Equilibrium (Economics), Stability|
|Series Name:||Warwick economics research paper series (TWERPS)|
|Publisher:||University of Warwick. Dept. of Economics|
|Place of Publication:||Coventry|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|References:|| Artstein Z. (1979), "A note on Fatou's lemma in several dimensions", Journal of Mathematical Economics, 6(3), 277-282.  Aumann R. and A. Brandenburger (1995), "Epistemic Conditions for Nash Equilibrium", Econometrica, 63, 5, 1161-1180.  Busetto, F., G. Codognato and S. Ghosal (2010), "Noncooperative oligopoly in markets with a continuum of traders", Games and Economic Behavior, forthcoming, doi:10.1016/j.geb.2010.06.009.  Carlsson H. and E. van Damme (1993), "Global Games and Equilibrium Selection", Econometrica, 61,5, 998-1018.  Codognato G., Ghosal S. (2000), "Cournot-Nash equilibria in limit exchange economies with complete markets and consistent prices," Journal of Mathematical Economics 34, 39-53.  Dubey P., Shapley L.S. (1994), "Noncooperative general exchange with a continuum of traders: two models, " Journal of Mathematical Economics, 23, 253-293.  Dudley, R.M. (1989), Real Analysis and Probability, Wadsworth & Brooks/Cole Advanced Books and Software, Wadsworth Inc. Belmont, California.  Guesnerie R. (1992), "An Exploration of the Eductive Justifications of the Rational Expectations Hypothesis", American Economic Review, 82,5, 1254-1278.  Hu T.W. (2007), "On p-rationalizability and approximate common certainty of rationality", Journal of Economic Theory, 136 (1), 379-391.  Mas-Colell A. (1984), "On a theorem of Schmeidler", Journal of Mathematical Economics, 13, 201-206  Mertens J.F. and S. Zamir (1985), "Formulation of Bayesian analysis for games with incomplete information", International Journal of Game Theory, Volume 14, Number 1 / March, 1985.  Morris S., R. Rob and H.S. Shin (1995), "p-Dominance and Belief Potential", Econometrica, 63,1, 145-157.  Morris S. and H.S. Shin (1998), "Unique equilibrium in a model of self-fulfilling currency attacks", American Economic Review, 88, 587-597.  Sahi S., Yao S. (1989), "The noncooperative equilibria of a trading economy with complete markets and consistent prices," Journal of Mathematical Economics 18, 325-346.  Scarf H. (1960), "Some Examples of Global Instability of the Competitive Equilibrium", International Economic Review, 1(3), 157-172.  Shapley L.S., Shubik M. (1977), "Trade using one commodity as a means of payment," Journal of Political Economy 85, 937-968.  Tan T. and S. Werlang (1988), "On Aumann's Notion of Common Knowledge, an Alternative Approach", Journal of Economic Theory, 45: 370-91.  Tercieux O. (2006), "p-Best response set", Journal of Economic Theory, 131(1), 45-70.|
Actions (login required)