Random tags can sustain high heterophily levels
We consider a spatial model of the emergence of cooperation with synchronous births and deaths. Agents bear a tag and interact with their neighbors by playing the prisoner's dilemma game with strategies depending on their own and opponent's tags. An agent's payoff determines its chances of reproducing and passing on its strategy. We show that when tags are assigned at random rather than inherited, a significant heterophilic population of about 40~\% of the whole can emerge and persist. Heterophilics defect on agents bearing the same tag as theirs and cooperate with others. In our setting, the emergence of heterophily is explained by the correlation between an agent's payoff and its neighbors' payoffs. The advantage of heterophily over homophily (cooperating with agents bearing one's tag and defecting with others) when tags are assigned at random makes the emergence of the later an even more interesting phenomenon than previously thought.