Conclusion

We combine our interpersonal utility expression with the direct utility expression to identify the total utility a player receives as the sum of these components. We label this function as reciprocal utility:

uRi ai; aj � � ¼ uDi ai; aj� �|fflfflfflfflfflffl{zfflfflfflfflfflffl}

Player i0s direct utility

þ βi Rij aj � �

uDj ai; aj � �|fflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

Player i0s interpersonal utility; uIi

(3)

In the context of a collective commitment to risk sharing, the term on the left of Equation (3) represents the direct utility player i receives from consumption after disutility from taxation has been subtracted. These damages are a function of total costs of relief for all players. The term on the right, conversely, represents the additional utility that player i receives from reciprocal assessment of player j’s behavior. Assuming that player i views public relief policies positively and their recipients as deserving, she will receive more utility when other highly supportive players also receive utility. This term represents the player’s utility from their perception of reciprocity, but not the utility they gain from the other players’ actual investment in the public good (this portion of utility is expressed in the direct utility term, as a part of the direct effect of the public relief). In this framework, individuals maximize their reciprocal utility by choosing support levels taking into account both impacts from damages from hurricanes or financial losses, but also any potential gains or losses from how other players perceive their supportiveness. The results will differ from the direct-utility framework because support for taxation for public relief affects the best-response functions of each player in both the direct and the interpersonal or reciprocal terms, allowing contributions above those predicted by the free-rider hypothesis.