Competing conventions

This paper studies a new coordination game, the Language Game, of a large but finite population. The population is partitioned into two groups of identical agents. Each player shares a common two-action strategy set and interacts pairwise with everyone else. Both symmetric profiles are pareto-efficient strict equilibria, but the groups rank them differently. The profile where successful coordination occurs only within-group, with each group adopting their most preferred action, is also an equilibrium provided the smaller group’s preferences are sufficiently strong. In all dynamically stable long run outcomes, players in the same group adopt the same action. Three properties, that do not matter for equilibrium selection in the homogeneous agent models of Kandori, Mailath, and Rob (1993) and Young (1993), do matter in the Language Game. These are: group size, preference over alternative equilibria, and rates of group adaptiveness (“group dynamism”). A relative increase in group dynamism is always weakly beneficial. ∗I would like to thank Sarada, Nageeb Ali, Prashant Bharadwaj, Tiffany Chou, Vince Crawford, Silke Januszewski Forbes, Dalia Ghanem, Roger Gordon, Youjin Hahn, Oana Hirakawa, Michihiro Kandori, Chulyoung Kim, Daniel Lima, Stephen Morris, Paul Niehaus, Frances Ruane, Bill Sandholm, Lucas Siga, James Slevin, Hee-Seung Yang, and Peyton Young for helpful comments. I would especially like to thank Joel Sobel for all his help. Remaining errors are mine. †Email : [email protected]; Web: http://econ.ucsd.edu/∼pneary/; Address: Department of Economics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0508.