Abstract
An implicit assumption underpins basic models of the evolution of cooperation, mutualism and altruism: The benefits (or pay-offs) of cooperation and defection are defined by the current frequency or distribution of cooperators. In social dilemmas involving durable public goods (group resources that can persist in the environment–ubiquitous from microbes to humans) this assumption is violated. Here, we examine the consequences of relaxing this assumption, allowing pay-offs to depend on both current and past numbers of cooperators. We explicitly trace the dynamic of a public good created by cooperators, and define pay-offs in terms of the current public good. By raising the importance of cooperative history in determining the current fate of cooperators, durable public goods cause novel dynamics (e.g., transient increases in cooperation in Prisoner's Dilemmas, oscillations in Snowdrift Games, or shifts in invasion thresholds in Stag-hunt Games), while changes in durability can transform one game into another, by moving invasion thresholds for cooperation or conditions for coexistence with defectors. This enlarged view challenges our understanding of social cheats. For instance, groups of cooperators can do worse than groups of defectors, if they inherit fewer public goods, while a rise in defectors no longer entails a loss of social benefits, at least not in the present moment (as highlighted by concerns over environmental lags). Wherever durable public goods have yet to reach a steady state (for instance due to external perturbations), the history of cooperation will define the ongoing dynamics of cooperators.
Highlights
IntroductionThe simplest and most common models of cooperation present two interacting players with a simple and symmetric choice, to cooperate or to defect [4]
If we normalise the payoffs for mutual cooperation R and mutual defection P to 1 and 0 respectively, social dilemmas can be described in game theoretic terms by two key parameters, the ‘temptation’ to cheat, T, and the ‘sucker’ reward for unilateral cooperation, S [10,29] (Fig. 1a, methods)
Building on the simplest models of social dilemmas, we have moved from a world consisting only of cooperators and defectors, to a world of cooperators, defectors and their environmental consequences
Summary
The simplest and most common models of cooperation present two interacting players with a simple and symmetric choice, to cooperate or to defect [4]. If they both cooperate, they each receive a reward, R, which is larger than the punishment, P, obtained if they both defect. If one defects while the other cooperates, the defector receives the ‘temptation’ payoff, T, and the cooperator receives the sucker’s payoff S (methods) This terminology was introduced for the Prisoner’s Dilemma, which is defined by the ranking T.R.P.S. Given the relative magnitude of the payoff values, a rational player should always defect in one-off encounters, regardless of whether the other player cooperates or not. The problematic outcome is total defection, despite a higher pay-off occurring when everyone cooperates. (maintenance of cooperation in the Prisoner’s Dilemma requires additional mechanisms that ensure cooperators are more likely to encounter other cooperators than expected by chance [5])
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