“Private Information of Nonpaternalistic Altruism: Exaggeration of Generosity and Reciprocal Behavior” by Yuk-Fai FONG
Agents who care about each other's utilities are matched pairwise to exchange gifts once. Matched agents do not have reciprocity or equity concern, and their degrees of altruism are statistically independent. When degrees of altruism are common knowledge, donors' gift sizes are also statistically independent. When second donors' degrees of altruism are private information, however, their gift amounts may become larger than under perfect information, and tend to increase in the gifts they receive from first donors. Such exaggeration of generosity and reciprocal behavior by the last mover are observed whenever the possible degrees of altruism in the population are relatively similar, or if a fraction of agents are sufficiently altruistic.