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Direct reciprocity in structured populations.

ABSTRACT: Reciprocity and repeated games have been at the center of attention when studying the evolution of human cooperation. Direct reciprocity is considered to be a powerful mechanism for the evolution of cooperation, and it is generally assumed that it can lead to high levels of cooperation. Here we explore an open-ended, infinite strategy space, where every strategy that can be encoded by a finite state automaton is a possible mutant. Surprisingly, we find that direct reciprocity alone does not lead to high levels of cooperation. Instead we observe perpetual oscillations between cooperation and defection, with defection being substantially more frequent than cooperation. The reason for this is that "indirect invasions" remove equilibrium strategies: every strategy has neutral mutants, which in turn can be invaded by other strategies. However, reciprocity is not the only way to promote cooperation. Another mechanism for the evolution of cooperation, which has received as much attention, is assortment because of population structure. Here we develop a theory that allows us to study the synergistic interaction between direct reciprocity and assortment. This framework is particularly well suited for understanding human interactions, which are typically repeated and occur in relatively fluid but not unstructured populations. We show that if repeated games are combined with only a small amount of assortment, then natural selection favors the behavior typically observed among humans: high levels of cooperation implemented using conditional strategies.

SUBMITTER: van Veelen M

PROVIDER: S-EPMC3382515 | biostudies-literature | 2012 Jun

REPOSITORIES: biostudies-literature

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Direct reciprocity in structured populations.

van Veelen Matthijs M García Julián J Rand David G DG Rand David G DG Nowak Martin A MA

Proceedings of the National Academy of Sciences of the United States of America 20120604 25

Reciprocity and repeated games have been at the center of attention when studying the evolution of human cooperation. Direct reciprocity is considered to be a powerful mechanism for the evolution of cooperation, and it is generally assumed that it can lead to high levels of cooperation. Here we explore an open-ended, infinite strategy space, where every strategy that can be encoded by a finite state automaton is a possible mutant. Surprisingly, we find that direct reciprocity alone does not lead ...[more]

PMID: 22665767

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Project description:In repeated interactions, players can use strategies that respond to the outcome of previous rounds. Much of the existing literature on direct reciprocity assumes that all competing individuals use the same strategy space. Here, we study both learning and evolutionary dynamics of players that differ in the strategy space they explore. We focus on the infinitely repeated donation game and compare three natural strategy spaces: memory-1 strategies, which consider the last moves of both players, reactive strategies, which respond to the last move of the co-player, and unconditional strategies. These three strategy spaces differ in the memory capacity that is needed. We compute the long term average payoff that is achieved in a pairwise learning process. We find that smaller strategy spaces can dominate larger ones. For weak selection, unconditional players dominate both reactive and memory-1 players. For intermediate selection, reactive players dominate memory-1 players. Only for strong selection and low cost-to-benefit ratio, memory-1 players dominate the others. We observe that the supergame between strategy spaces can be a social dilemma: maximum payoff is achieved if both players explore a larger strategy space, but smaller strategy spaces dominate. Author summary Direct reciprocity can lead to cooperation between individuals who meet in repeated encounters. The shadow of the future casts an incentive to cooperate. If I cooperate today, you may cooperate tomorrow. But if I defect today, you may defect tomorrow. In most studies of direct reciprocity it is assumed that both players explore the same space of possible strategies. In contrast, here we study interactions between players that use different strategy spaces and therefore utilize different memory capacities. Surprisingly, we find that more complex strategy spaces often lose out against simpler ones. The social optimum, however, is achieved if all players use the more complex space. Therefore, the game between strategy spaces becomes a higher order social dilemma.

Dataset Information

Direct reciprocity in structured populations.

Publications

Direct reciprocity in structured populations.

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