Figure 1 shows computer simulations of a population consisting of n players. The strategies are given by ki and the image levels by si. At the beginning of each generation, the image levels of all players are zero (assuming that children do not inherit the image of their parents). In succession, m donor–recipient pairs are chosen. A donor, i, cooperates with a recipient, j, if ki # sj. The fitness of a player is given by the total number of points received during the m interactions. Some players may never be chosen, in which case their payoff from the game will be zero. On average, a player will be chosen 2m/n times, either as donor or as recipient. At the end of each generation, players leave offspring in proportion to the their fitness. We find that if the game is played for many generations, then eventually all players will adopt the same strategy. If the k value of this strategy is 0 or less then cooperation is established; if the value is 1 or more then defection has won. Cooperation is more likely to win if the number of interactions, m, per generation is large.

Builds on: "The image score of a recipient does not change."

Nowak, M. A., & Sigmund, K, Evolution of Indirect Recip…, loc. 38