Population Dynamics of Centipede Game using an Energy Based Evolutionary Algorithm

In the context of Evolutionary Game Theory, we have developed an evolutionary algorithm without an explicit fitness function or selection function. Instead players obtain energy by playing games. Clonal reproduction subject to mutation occurs when a player’s energy exceeds some threshold. To avoid exponential growth of the population there is a death event that depends on population size. By tweaking with the relation between payoff and energy and with death event, we create another dilemma that a population must overcome: extinction. We demonstrate this phenomena in the Centipede game. Simulations show that if players can only play one of the two positions of this asymmetric game extinctions are common. If players are versatile and can play both positions there are no extinctions.