The Evolution of Asymmetric Risk Preferences in Dynamic Competitions
This paper analyzes a dynamic competition in which two players gamble independently, and fairly to affect their wealths. At each instant in time, a prize is allocated to the player with the highest wealth. There is a unique equilibrium in which the player lagging in wealth takes maximal risks, while the leading player takes no risks at all. An evolutionary interpretation of the result is offered, which provides a foundation for reference-dependent, asymmetric risk preferences. In particular, when fitness is determined by such dynamic competitions, S-shaped Bernoulli utility functions emerge uniquely.