Equilibrium Analysis of Conformity and Influence on a Social Network

Abstract Desiring conformity but lacking common labels with which to identify the different options, a population employs reliable social connections to identify paths through which decisions can disseminate. A leader serves the population by coordinating adoption and therefore increasing conformity. A premium for adopting the popular option in advance of others in the population ensures that the cooperative solution generates asymmetry in the payoffs. Motivated by an inquiry into the role of individuals and group connectivity in the emergence of social phenomenon, the present paper identifies the set of social structures that are the product of equilibrium strategy profiles. While individual best response strategy and reward depend on the player's position in the social network of the particular equilibrium realized, the features that characterize the equilibrium structure are found to be universal