Decision making under uncertainty and the evolution of interdependent preferences

This paper finds support for the evolution of interdependent preferences un der natural selection from a (perhaps) surprising source: decision making u nder uncertainty. Individuals choose from sets of risky alternatives. The l otteries may involve either idiosyncratic risk or aggregate uncertainty or both. Robson (J. Econ. Theory 68 (1996), 397-324) gives the evaluation crit erion for lotteries that maximizes reproductive value and shows that it doe s not satisfy the expected utility theorem. Cooper and Kaplan (J. Theoret. Biol. 94 (1982). 135-151) have demonstrated that when lotteries are aggrega te. the optimal decision rule involves randomization. This paper reexamines Robson's evaluation criterion. using it to solve fur the optimal amount of randomization. The solution is characterized and an interpretation is offe red that links maximizing reproductive value to maximizing expected relativ e offspring. It is shown that when agents preferences arise from their own offspring relative to the average within the population, a game is construc ted out of the choice of lotteries and that the unique Nash equilibrium dis tribution of actions maximizes reproductive value. (C) 2001 Academic Press.