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Endogenous Homophily and Segregation in Networks: When Birds of a Feather (Don’t) Necessarily Flock Together

This work studies a strategic game with incomplete information in which a finite number of players simultaneously choose actions and form either unilaterally or bilaterally relationships. The players' payoffs are supermodular in actions but do exhibit neither negative nor positive spillovers; specifically, for a given network of relationships, the players have preferences for matching or coordinating their actions with the actions of those with whom they are related. The work highlights the roles that players' knowledge and beliefs, as well as the laterality of link formation, play for the geometry of the emerging network, and in particular its segregation pattern. A special case of the strategic game represents one possible microeconomic foundation of the so-called linear-in-means model. The analysis of this game carries a profound implication: endogenous effects are not identifiable in the linear-in-means model if the network of relationships and the players' outcomes constitute a stable play of the game.