This paper studies the impact of a small probability event on strategic behavior in incomplete information games with non-common priors. It is shown that the global impact of a small probability event (i.e., its propensity to affect strategic behavior at all states in the state space) has an upper bound that is an increasing function of a measure of discrepancy from the common prior assumption. In particular, its global impact can be arbitrarily large under non-common priors, but is bounded from above under common priors. These results quantify the different implications common prior and non-common prior models have on the (infinite) hierarchies of beliefs. Journal of Economic Literature Classification Numbers: C72, D82.

Key Words: common prior assumption; higher order belief; rationalizability; contagion; belief potential.

Former title: Strategic Implications of (Non-)Common Priors I: Belief Potential

First draft: December 31, 2005; this version: July 3, 2007. PDF file (Slides)

oyama@econ.hit-u.ac.jp