Evolution of State-Dependent Risk Preferences

Researchers have invested much effort in constructing models of the state-dependent (sometimes risk-averse and sometimes risk-prone) nature of human decision making. An important open question is how state-dependent risk behavior can arise and remain prominent in populations. We believe that one part of the answer is the interplay between risk-taking and sequentiality of choices in populations subject to evolutionary population dynamics. To support this hypothesis, we provide simulation and analytical results for evolutionary lottery games, including results on evolutionary stability. We consider a parameterized class of imitation dynamics in which the parameter 0 <= a <= 1 yields the replicator dynamic with alpha = 1 and the imitate-the-better dynamic with alpha = 0. Our results demonstrate that for every population dynamic in this class except for the replicator dynamic, the interplay between risk-taking and sequentiality of choices allows state-dependent risk behavior to have an evolutionary advantage over expected-value maximization.