Monotone and Local Potential Maximizers in
Symmetric 3 × 3 Supermodular Games

Daisuke Oyama
Graduate School of Economics, Hitotsubashi University


Satoru Takahashi
Department of Economics, Princeton University

Generalized notions of potential maximizer, monotone potential maximizer (MP-maximizer) and local potential maximizer (LP-maximizer), are studied. It is known that 2 × 2 coordination games generically have a potential maximizer, while symmetric 4 × 4 supermodular games may have no MP- or LP-maximizer. This note considers the case inbetween, namely the class of (generic) symmetric 3 × 3 supermodular coordination games. This class of games are shown to always have a unique MP-maximizer, and its complete characterization is given. A nondegenerate example demonstrates that own-action quasiconcave supermodular games may have more than one LP-maximizers. Journal of Economic Literature Classification Numbers: C72.
Key Words: equilibrium selection; supermodular game; monotone potential; MP-maximizer; local potential; LP-maximizer.

Economics Bulletin 29, No.3, 2132-2144 (2009). PDF file