Explaining contributions to public goods: Formalizing the social exchange heuristic

The public good game is a popular model of cooperation problems. Rational egoism predicts that in finitely repeated public good games no contributions are made. At least 4 observations are inconsistent with this prediction: contributions (i) are frequently positive, (ii) increase in the marginal rate of return of the public good, (iii) increase in the expected contributions of others, and (iv) decrease as the public good game is repeated. I build a rational choice model that explains these observations, extending and formalizing the social exchange heuristic. The model does not assume a specific utility function. I assume that total utility is a strictly increasing function of monetary and social utility, and then show that concave utility functions and a positive cross-partial derivate of total utility to monetary and social utility are sufficient conditions to arrive at a model compatible with the 4 observations. Directions for future (experimental) research are discussed.