Fig. 2: The evolutionary advantage of linkage.
a, b We simulated the dynamics when players simultaneously engage in a game with a high benefit of cooperation (Game 1, blue) and a game with a comparably low benefit (Game 2, red). We find that linking has a strongly positive effect in the low-benefit game and a weakly positive effect in the high-benefit game. c, d We recorded which behaviors the players exhibit by the end of each simulation. To this end, we define a strategy to be cooperative in a given game if the respective cooperation rate against itself is at least 80%. Similarly, we say a strategy is non-cooperative, if this cooperation rate is below 20%. This distinction gives rise to four behavioral classes, depending on whether players are cooperative in both games, cooperative in one game but non-cooperative in the other, or non-cooperative in both. Only when the two games are linked, players are most likely to be fully cooperative in both. e, f We analyze which strategies the players use when they are fully cooperative. Each bar shows the respective mean value, whereas dots represent 100 randomly sampled realizations of the simulation. In the linked case, players only exhibit a high mean cooperation probability (in either game) if their co-player previously cooperated in both games. As parameters we used b1 = 5, b2 = 3, and c1 = c2 = 1, in a population of size N = 50 using a selection strength parameter s = 2. The figure shows averages over 1000 simulations of the pairwise comparison process41,42 in the limit of rare mutations (see “Methods” for details).
