Finite-Order Implications of Any Equilibrium

36 Pages Posted: 7 Feb 2004

Date Written: January 2004


Present economic theories make a common-knowledge assumption that implies that the first or the second-order beliefs determine all higher order beliefs. We analyze the role of such closing assumptions at finite orders by instead allowing higher orders to vary arbitrarily. Assuming that the space of underlying uncertainty is sufficiently rich, we show that the resulting set of possible outcomes, under an arbitrary fixed equilibrium, must include all outcomes that survive iterated elimination of strategies that are never a strict best reply. For many games, this implies that, unless the game is dominance solvable, every equilibrium will be highly sensitive to higher-order beliefs, and thus economic theories based on such equilibria may be misleading. Moreover, every equilibrium is discontinuous at each type for which two or more actions survive our elimination process.

Keywords: higher-order uncertainty, rationalizability, incomplete information, equilibrium, robustness

JEL Classification: C72, C73

Suggested Citation

Weinstein, Jonathan and Yildiz, Muhamet, Finite-Order Implications of Any Equilibrium (January 2004). MIT Economics Working Paper No. 04-06. Available at SSRN: or

Jonathan Weinstein

Northwestern University - Department of Managerial Economics and Decision Sciences (MEDS) ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

Muhamet Yildiz (Contact Author)

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

50 Memorial Drive
Room E52-522
Cambridge, MA 02142
United States
617-253-5331 (Phone)
617-253-6915 (Fax)

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