Coordination, Local Interactions, and Endogenous Neighborhood Formation

The details of the process governing the co-evolution of expectations formation, individual choices and interaction structure can crucially affect the long-run social structure emerging in coordination games repeatedly played in large populations. To investigate this issue, we present a model of local coordination in which agents can simultaneously choose both stage-game strategies and the partners with whom to play the game. We consider a population of myopic (adaptive) individuals located on a one-dimensional lattice with periodic boundaries who repeatedly play a pure coordination game with their 'nearest neighbors'. We assume that holding neighbors is costly and that, from time to time, agents are allowed to slightly shrink (or enlarge) the 'radius' of their current neighborhood by maximizing expected net payoffs. We study the behavior of the model in settings characterized by both positive and negative network externalities. After having characterized the set of steady states and conditions for convergence, we show that both full coordination and coexistence of conventions may be possible in the long-run. Nevertheless, as computer simulations show, the system is able to reach very high average coordination levels, together with small neighborhood sizes, for a large region of the parameter space. By means of extensive Montecarlo analyses, we find that the rate of neighborhood updating negatively affects average coordination levels. This raises the question of how coordination levels with endogenous neighborhoods compare to the case in which interaction structures are static. Simulations indicate that, for a large class of exogenously given interaction structures and system parameters, a population with a small but positive rate of endogenous neighborhood formation always reaches higher coordination. Furthermore, we find that large societies perform better than small ones provided that individuals initially hold, on average, large neighborhoods. We also discuss the role played by negative network externalities in system dynamics. Finally, we test the robustness of the model to departures from the basic setup. In particular, we study what happens to long-run patterns of coordination when agents: (i) might enjoy positive network externalities for all neighborhood sizes; (ii) are located in higher-dimensional lattices; (iii) play coordination stage-games where a trade-off arises between Pareto-efficient and risk-dominant Nash equilibria.