Small groups and long memories promote cooperation

Abstract

Complex social behaviors lie at the heart of many of the challenges facing evolutionary biology, sociology, economics, and beyond. For evolutionary biologists the question is often how group behaviors such as collective action, or decision making that accounts for memories of past experience, can emerge and persist in an evolving system. Evolutionary game theory provides a framework for formalizing these questions and admitting them to rigorous study. Here we develop such a framework to study the evolution of sustained collective action in multi-player public-goods games, in which players have arbitrarily long memories of prior rounds of play and can react to their experience in an arbitrary way. We construct a coordinate system for memory-m strategies in iterated n-player games that permits us to characterize all cooperative strategies that resist invasion by any mutant strategy, and stabilize cooperative behavior. We show that, especially when groups are small, longer-memory strategies make cooperation easier to evolve, by increasing the number of ways to stabilize cooperation. We also explore the co-evolution of behavior and memory. We find that even when memory has a cost, longer-memory strategies often evolve, which in turn drives the evolution of cooperation, even when the benefits for cooperation are low.

Memory- n strategies of direct reciprocity

“…Overall, our study suggests that memory-n strategies are particularly valuable when the benefit of cooperation is small or intermediate (for b/c ≥ 2, already, the simple memory-1 strategy WSLS allows for full cooperation). In such cases, we may well expect to observe selection for longer memory as suggested by previous simulations (8), provided that the expected gains are worth the higher cognitive costs (49). In principle, our results suggest that cooperation is feasible in any multiplayer dilemma, provided that the interaction is sufficiently relevant for subjects to memorize their coplayers' past actions.…”

“…Evolutionary models, on the other hand, often take the opposite approach. With a few notable exceptions (5)(6)(7)(8), evolutionary models focus on naive subjects who can only choose from a restricted set of strategies (9)(10)(11)(12)(13), or who do not remember anything beyond the outcome of the very last round (14)(15)(16)(17)(18)(19)(20)(21).…”

Self-organizing Complex Networks: individual versus global rules

“…Another sociological concept, currently adopted to illustrate the conflict between the use of limited shared resources and individual self-interest (Hauser et al, 2014), “the tragedy of the commons”, has been used (Stewart and Plotkin, 2016) to discuss the evolution of cooperation in ecological networks.…”

Friendly-rivalry solution to the iteratedn-person public-goods game

“…However, which class is more favored by selection depends on environmental conditions such as the population size and the benefit-to-cost ratio of cooperation: If the population is small and cooperation is costly, it is better off to play a rival strategy than to play a partner strategy, and vice versa [11,14,20]. If a single strategy acts as a partner and a rival simultaneously, it has important implications in evolutionary dynamics because it possesses evolutionary robustness regardless of the environmental conditions, in the sense that no mutant strategy can invade a population of this strategy with greater fixation probability than that of neutral drift [11,[20][21][22]. To indicate the partner-rival duality, such a strategy will be called a 'friendly rival' [22].…”