The Largesse design problem

Largesse design is a positive theory of what happens when players in a game, who have a limited willingness to sacrifice for the common good, can coordinate on a welfare-optimal solution. This theory provides an alternative to psychological theories in explaining why players engage in costly punishments and rewards. It also says that players will engage in other low-cost methods of encouraging pro-social behavior, for example, through reputation effects. In this paper, I study the properties and comparative statics of the largesse design problem. Despite a lack of concavity in the maximization problem, solutions are unique and continuous except on a lower-dimensional bifurcation set. In examples, I study these bifurcations, in which a small change in the parameters can lead to a large change in behavior or welfare.