Voluntary reciprocity as an informal social insurance mechanism : a game theoretic approach

Abstract

Informal social insurance mechanisms known as gift giving, reciprocal transfer payments, mutual assistance and contingent credit are analysed as consumption smoothing mechanisms by means of reciprocal transfer payments without the use of a binding contract. The objective of this study is to provide an explanation for the following: the existence of reciprocal transfer payments without the use of a binding contract, the non-existence of full insurance when there are no informational problems, and the effect of the occurrence of common risks on the feasibility of the mechanism. Based on the theory of decision making under uncertainty in a noncooperative game with complete information, three new elements are introduced. They are: first, the decision to pay a transfer is made after current income is known; second, the equilibrium of the infinitely repeated game must be non-renegotiable even when each player can terminate the agreement unilaterally; and third, the players are confronted with idiosyncratic and common income risks. The model shows that when the decision to pay a transfer is made after income uncertainty is revealed, co-operation is possible if the ratio between the gain from co-operating and the gain from not co-operating is sufficiently high. The transfer which maximises the expected payoff of the player who has to pay is the sustainable equilibrium. This equilibrium which is strictly lower than the level of transfer which yields full insurance is reached with delay if the bargaining process has low friction. The occurrence of both idiosyncratic and common risks does not impede co-operation if the agreement is dependent on the prevailing common state.