Evolution of memes

Abstract

The paper considers the evolution of a population of individuals, where each one initially possesses a certain number of strategies the memory of which does not exceed a depth of 2. All individuals randomly enter into competition in pairs at each stage of evolution. A random pair of individuals conducts a competition between pairs of all their randomly selected strategies when they are interacting. These strategies compete in pairs according to the iterated prisoner's dilemma. In such struggle, strategies earn evolutionary advantage points according to a given payout matrix. The strategy with the most points wins. Two strategies come into this game twice to negate an impact of the first move. The first game starts by one strategy, the second game starts by another one. The winnings are determined by the outcome of both these games. After this competition the winning strategy of one individual replaces the corresponding losing strategy of another individual. Thus, there is an exchange of more "successful" strategies between individuals with the loss of lost strategies. The evolution of the population of such individuals was carried out until the stage of stationary state. There were established patterns of changes in basic properties of strategies of average individual during evolution. It is shown that in the process of evolution the aggression of an individual increases, tenting to the maximum value. The stationary set of strategies of an individual consists of strategies of maximum memory depth and complexity with a certain number of primitive strategies. The complexity and memory depth of an individual's strategies turns out to be evolutionary beneficial. In the stationary state the number of primitive strategies in an individual depends on their initial distribution to individuals. The paper considers two initial distributions, where the first corresponds to the equal probability of any strategy in the distribution by individuals, and the seconds corresponds to equally probable choice in terms of memory depth. The variety of strategies in the process of evolution decreases significantly, making up only a small part of the initial strategies present in the population.