Adversity and cooperation in heterogeneous pairs

The consequences of switching strategies in a two-player iterated survival game

We consider two-player iterated survival games in which players are able to switch from a more cooperative behavior to a less cooperative one at some step of an n-step game. Payoffs are survival probabilities and lone individuals have to finish the game on their own. We explore the potential of these games to support cooperation, focusing on the case in which each single step is a Prisoner’s Dilemma. We find that incentives for or against cooperation depend on the number of defections at the end of the game, as opposed to the number of steps in the game. Broadly, cooperation is supported when the survival prospects of lone individuals are relatively bleak. Specifically, we find three critical values or cutoffs for the loner survival probability which, in concert with other survival parameters, determine the incentives for or against cooperation. One cutoff determines the existence of an optimal number of defections against a fully cooperative partner, one determines whether additional defections eventually become disfavored as the number of defections by the partner increases, and one determines whether additional cooperations eventually become favored as the number of defections by the partner increases. We obtain expressions for these switch-points and for optimal numbers of defections against partners with various strategies. These typically involve small numbers of defections even in very long games. We show that potentially long stretches of equilibria may exist, in which there is no incentive to defect more or cooperate more. We describe how individuals find equilibria in best-response walks among n-step strategies.

Social rank modulates how environmental quality influences cooperation and conflict within animal societies

Although dominance hierarchies occur in most societies, our understanding of how these power structures influence individual investment in cooperative and competitive behaviours remains elusive. Both conflict and cooperation in animal societies are often environmentally regulated, yet how individuals alter their cooperative and competitive investments as environmental quality changes remain unclear. Using game theoretic modelling, we predict that individuals of all ranks will invest more in cooperation and less in social conflict in harsh environments than individuals of the same ranks in benign environments. Counterintuitively, low-ranking subordinates should increase their investment in cooperation proportionally more than high-ranking dominants, suggesting that subordinates contribute relatively more when facing environmental challenges. We then test and confirm these predictions experimentally using the Asian burying beetle Nicrophorus nepalensis. Ultimately, we demonstrate how social rank modulates the relationships between environmental quality and cooperative and competitive behaviours, a topic crucial for understanding the evolution of complex societies.