Endogenous coordination and discoordination games: Multiculturalism and assimilation

We argue that many strategic interactions are chosen by, rather than imposed upon, agents. The endogeneity of the implicit game substantially alters the incentive structure faced by agents. If agents can refuse to play a game and instead seek a different partner, then it becomes in their interest to be the sort of player with whom a high quality partner will agree to play. Formally, we explore games which are endogenous in the sense that players first choose to learn a specific set of strategies to play with future partners, and then enter a matching process to find a suitable partner. We find that in coordination games, the only equilibria involve all agents learning the exact same single strategy and playing this with the first partner they meet. Applying this to culture and language, our results imply that if there are benefits from interacting with similar agents then there is a strong bias towards assimilation and the emergence of a single culture (that is, all agents use the endogenous game structure to learn or adopt only a single common culture or language). This result can be overturned, however, by such factors as heritage, cultural affinities, caste, and government policies. Finally, we show that if agents benefit from interacting with agents dissimilar from themselves (we call this a “discoordination game”), not only will different cultures coexist, but also there must necessarily arise a class of “cultural market makers” who specialize in bridging the cultural divide.