Contagion and Uninvadability in Local Interaction Games: The Bilingual Game and General Supermodular Games

Daisuke Oyama
Faculty of Economics, University of Tokyo

and

Satoru Takahashi
Department of Economics, National University of Singapore


Abstract
In a setting where an infinite population of players interact locally and repeatedly, we study the impacts of payoff structures and network structures on contagion of a convention beyond 2 × 2 coordination games. First, we consider the ``bilingual game'', where each player chooses one of two conventions or adopts both (i.e., chooses the ``bilingual option'') at an additional cost. For this game, we completely characterize when a convention spreads contagiously from a finite subset of players to the entire population in some network, and conversely, when a convention is never invaded by the other convention in any network. We show that the Pareto-dominant (risk-dominant, resp.) convention is contagious if the cost of bilingual option is low (high, resp.). Furthermore, if the cost is in a medium range, both conventions are each contagious in respective networks, and in particular, the Pareto-dominant convention is contagious only in some non-linear networks. Second, we consider general supermodular games, and compare networks in terms of their power of inducing contagion. We show that if there is a weight-preserving node identification from one network to another, then the latter is more contagion-inducing than the former in all supermodular games. Journal of Economic Literature Classification Numbers: C72, C73, D83.
Key Words: equilibrium selection; strategic complementarity; bilingual game; network; contagion; uninvadability.


Forthcoming in Journal of Economic Theory.
First draft: December 31, 2010; this version: October 28, 2014. PDF file
(Older version: March 26, 2013. PDF file)

Former title: Contagion and Uninvadability in Social Networks with Bilingual Option