Accumulation of individual fitness or wealth as a population game

Abstract

The accumulation of individual fitness or wealth is modelled as a population game in which pairs of individuals are recurrently and randomly matched to play a game over a resource. In addition, all individuals have random access to a constant background resource, and their fitness or wealth depreciates over time. For brevity we focus on the well-known Hawk-Dove game. In the base-line model, the probability of winning a fight (that is, when both play Hawk) is the same for both parties. In an extended version, the individual with higher current fitness or wealth has a higher probability of winning. Analytical results are given for the fitness/wealth distribution at any given time, for the evolution of average fitness/wealth over time, and for the asymptotics with respect to time and population size. Long-run average fitness/wealth is non-monotonic in the value of the resource, thus providing a potential explanation of the curse of the riches.