In this post, I explore the evolutionarily adaptive risk preferences under various conditions.
Fair wager model
To understand the long term effects of risk aversion vs risk neutrality, we consider an evolutionary player with 10 apples initially who repeatedly makes a series of wagers that gets one apple half of the time and pays one apple half of the time. The wager is considered “fair” since the expected payoff is 0. In a population, every player is presented with the same wagers but the results of the wagers are independent or idiosyncratic. The player stops playing when he loses all the apples and dies. The wager repeats 10000 times in a short time and we record the number of apples owned at the end, which is proportional to the population size or fitness. Three thousand simulations are run and the distribution of the number of apples is plotted in figure 1.1.
As plotted in figure 1.1, in the long run the player almost surely dies. The distribution is severely skewed right. The single period expected payoff and long run expected payoff are both 0 apples because starvation does not change expected future payoff since whether wagering or dead, the expected payoff remains 0. Can we say evolution disfavors this kind of wagers since the extinction rate is high? Without additional assumptions, the answer is no. If individuals in a population either always accept this wager or decline this wager, then after many generations more than 99% of the lineages will be from the risk averse ones who decline the wager, which makes risk aversion seem like the dominant strategy. However, if counting the number of surviving individuals, the two risk preferences are equally successful by having equal total population sizes since the expected payoff of both risk preference equals 0. We will use this method to define fitness in the rest of the article and therefore we can assume what evolution maximizes is the long run expected number of offsprings produced. Assuming every offspring is the same, an organism selected by maximizing the long run fitness should maximize the number of his children (and kins) in his lifetime. Continue reading “The Evolution of Risk Preferences”