Impact of Higher-Order Uncertainty

38 Pages Posted: 14 Apr 2003

Date Written: March 2003

Abstract

In some games, the impact of higher-order uncertainty is very large, implying that present economic theories may be misleading as these theories assume common knowledge of the type structure after specifying the first or the second orders of beliefs. Focusing on normal-form games in which the players' strategy spaces are compact metric spaces, we show that our key condition, called "global stability under uncertainty," implies a variety of results to the effect that the impact of higher-order uncertainty is small. Our central result states that, under global stability, the maximum change in equilibrium strategies due to changes in players' beliefs at orders higher than k is exponentially decreasing in k. Therefore, given any need for precision, we can approximate equilibrium strategies by specifying only finitely many orders of beliefs.

Keywords: Higher-order Uncertainty, Stability, Incomplete Information, Equilibrium

JEL Classification: C72, C73

Suggested Citation

Weinstein, Jonathan and Yildiz, Muhamet, Impact of Higher-Order Uncertainty (March 2003). MIT Department of Economics Working Paper No. 03-14. Available at SSRN: https://ssrn.com/abstract=394841 or http://dx.doi.org/10.2139/ssrn.394841

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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