Emergent Network Dynamics and Strategic Social Interactions

Abstract: In all social and economic interactions, individuals or coalitions choose not only with whom to interact but how to interact, and over time both the structure (the with whom) and the strategy (the how) of interactions change. Our objec-tives here are to model the structure and strategy of interactions prevailing at any point in time as a directed network and to address the following open question in the theory of social and economic network formation: given the rules of network formation, the preferences of individuals over networks, the strategic behavior of coalitions in forming networks, and the trembles of nature, what network dynamics are likely to emergence and persist. Our main contributions are (i) to formulate the problem of network formation as a dynamic, stochastic game, (ii) to show that this game possesses a stationary correlated equilibrium (in coalitional network formation strategies), and (iii) to show that, together with the trembles of nature, this station-ary correlated equilibrium determines a network dynamic which respects the rules of network formation and the preferences of individuals. Moreover, we show that this emergent network dynamic possesses a nonempty set of ergodic measures and gen