Too much of a good thing? The dynamics of trust and loyalty.
Abstract: Motivated by the study of household dynamics, we analyze a stochastic partnership model with a view to determining how the mean duration of the partnership depends on the distribution of the partners’ monetary earnings. Every period, the partners’ preferences for each other are revised stochastically, and the partners have the opportunity to choose to continue the relationship and renegotiate the allocation of their earning, or to part ways and permanently collect their autarky payoffs. Since the extent of such transfers is limited by the size of the partners’ earnings, the degree of effective transferability is determined both by the distribution of earnings and the nature of the shocks most likely to require compensation. We characterize equilibria of the infinitely repeated game with a fixed discount factor. The main result is that the expected duration of the partnership is decreasing in the inequality of monetary earnings if the shock distribution satisfies a monotone hazard rate condition.