A model of informal favor exchange on networks

We develop a model of informal favor exchange within a social network where the cost of providing a favor is stochastic. The community has a norm, which specifies a cost threshold under which one should perform a favor if asked, as well as a punishment—exclusion from the network of the “noncompliers,” that is, of those who do not perform favors despite their cost being below the threshold, and those who refuse to punish nonperformers. We show that there always exists a cost threshold such that all agents participating in the favor exchange system receive strictly positive expected utility, and the system is a stable system. For systems involving stars and regular networks, we provide an ordering of the highest cost threshold supporting their stability. We also identify the conditions under which systems are efficient and show that, among all efficient systems, the one with the complete network provides the highest sum of expected utilities. An efficient system, however, need not be stable.