The above movie shows a representative simulation run for two families (i.e. two kinds of genetically related individuals), populating 60% of a 50x50 spatial grid without periodic boundary conditions. We find the emergence of cooperation in both families, and most remarkably, also a cooperation between members of different families (i.e. "cooperation between strangers"). The initial friendliness in the orange-turquoise family is 0, and in the red-blue family it is assumed to be 0.2 (but it could be chosen 0 as well, see Grund et al. (2013)). One finds the emergence of cooperation in both families (represented by blue or turquoise), which cannot occur for the “homo economicus”. Hence, cooperation implies a “homo socialis”. Remarkably, there are clusters in which members of different families cooperate (i.e. a “cooperation between strangers” evolves).
Individuals play 2-person prisoner’s dilemma games with all neighbors in their respective Moore neighborhoods (but similar results are expected for some other social dilemma games as well). The payoff parameters are the “Reward” R = 1 for the cooperation of both interaction partners, the “Punishment” P = 0 for non-cooperative behavior on both sides, the “Temptation” T = 1.1 for a defector exploiting a cooperator, and the “Sucker’s Payoff” S = 1 for an exploited cooperator. Each agent’s utility function weights the payoffs of the neighbors with the “friendliness” ρ_i, i.e. the utility function U_i of an agent i is assumed to be U_i = (1-ρ_i) P_i + ρ_i , where P_i is the payoff of individual i and the average payoff of the neighbors. For all agents, the initial friendliness is set to ρ_i = 0 (corresponding to a “homo economicus”) and the initial behavior (“strategy”) is assumed to be defective (orange or red). The behaviors of all individuals are simultaneously updated based on a best response rule, which implies a behavior that maximizes the individual utility based on the behaviors of the neighbors. Only with a probability of 0.05 do individuals take other decisions than the best response rule suggests.
To allow for evolution, while keeping population size constant, individuals die at random with the probability β = 0.05, but the same number of offspring is born by living individuals. The likelihood to give birth to an offspring is proportional to the actual payoff in the previous round (i.e. not proportional to the utility). With probability ν, the offspring is born in the closest empty site to the parent, while with probability (1-ν), the offspring moves to a randomly selected empty site (here: ν = 0.95). Offspring inherit a trait called friendliness ρ_i from their parents, which is subject to random mutations. (With probability 0.8 the offspring’s friendliness is “reset” to a uniformly distributed random value between 0 and the friendliness ρ_i of the parent, and with probability 0.2 it takes on a uniformly distributed value between ρ_i and 1.) The local reproduction rate ν determines, whether a transition from a “homo economicus” with self-regarding preferences to a “homo socialis” with other-regarding preferences takes place, see Fig. 2 in Grund et al. (2013). We expect that reputation-based interactions (see Milinski, M., D. Semmann, and H. J. Krambeck (2002) Reputation helps solve the tragedy of the commons, Nature 415, 424-426) would be another mechanism promoting other-regarding behavior.
At the beginning of our computer simulation, defectors are more successful than cooperators, as they receive higher payoffs on average. Yet, after the transition from a "homo economics" to a "homo socialis" occurred, the payoffs for cooperating agents increases even more than the payoff of defectors, which allows the "homo socialis" to spread thanks to a reproduction rate that is now higher than that of the "homo economicus". Note that due to population dynamics and intergenerational migration, it might happen that families die out before high levels of cooperation are reached.