Social Norms, Local Interaction, and Neighborhood Planning

This paper examines optimal social linkage when each individual's repeated interaction with each of his neighbors creates spillovers. Individuals differ across rates of time preference. A planner must choose a local interaction system or neighborhood design before observing the realization of these rates. Given the planner's choice of design and a realization of discount factors, each individual plays a repeated Prisoner's Dilemma game with his neighbors. We introduce the concept of a local trigger strategy equilibrium (LTSE) to describe a stationary sequential equilibrium in which, for any realization of discount factors, each individual conditions his cooperation on the cooperation of at least one "acceptable" group of neighbors. The presence of impatient types implies that some free riding may be tolerated in equilibrium. When residents' discount factors are known to the planner, the optimal design exhibits a cooperative "core" and an uncooperative "fringe." Uncooperative (impatient) types are connected to cooperative ones who tolerate their free riding so that social conflict is kept to a minimum. By contrast, when residents' discount factors are independently distributed, the optimal design partitions individuals into maximally connected cliques (e.g., cul-de-sacs). In that case, each person's cooperation decision becomes a pure local public good. Finally, if types are correlated, then incomplete graphs with small overlap (e.g., grids) are possible.