Comparing reactive and memory-one strategies of direct reciprocity

Abstract

Direct reciprocity is a mechanism for the evolution of cooperation based on repeated interactions. When individuals meet repeatedly, they can use conditional strategies to enforce cooperative outcomes that would not be feasible in one-shot social dilemmas. Direct reciprocity requires that individuals keep track of their past interactions and find the right response. However, there are natural bounds on strategic complexity: Humans find it difficult to remember past interactions accurately, especially over long timespans. Given these limitations, it is natural to ask how complex strategies need to be for cooperation to evolve. Here, we study stochastic evolutionary game dynamics in finite populations to systematically compare the evolutionary performance of reactive strategies, which only respond to the co-player's previous move, and memory-one strategies, which take into account the own and the co-player's previous move. In both cases, we compare deterministic strategy and stochastic strategy spaces. For reactive strategies and small costs, we find that stochasticity benefits cooperation, because it allows for generous-tit-for-tat. For memory one strategies and small costs, we find that stochasticity does not increase the propensity for cooperation, because the deterministic rule of win-stay, lose-shift works best. For memory one strategies and large costs, however, stochasticity can augment cooperation.

18 pages, 7 figures

References in corpus (7)

• Zero-determinant alliances in multiplayer social dilemmas
• Mutation-selection equilibrium in games with multiple strategies
• Defection and extortion as unexpected catalysts of unconditional cooperation in structured populations
• Optional games on cycles and complete graphs
• Win-stay lose-shift strategy in formation changes in football
• Intelligent tit-for-tat in the iterated prisoner's dilemma game
• Network Structures between Strategies in Iterated Prisoners' Dilemma Games

Cited by in corpus (19)

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• Combination with anti-tit-for-tat remedies problems of tit-for-tat
• Mutation enhances cooperation in direct reciprocity
• Seven rules to avoid the tragedy of the commons
• Evolution Reinforces Cooperation with the Emergence of Self-Recognition Mechanisms: an empirical study of the Moran process for the iterated Prisoner's dilemma
• Reactive learning strategies for iterated games
• Evolution of direct reciprocity in group-structured populations
• Local stability of cooperation in a continuous model of indirect reciprocity
• Win-Stay-Lose-Shift as a self-confirming equilibrium in the iterated Prisoner's Dilemma
• Signalling boosts the evolution of cooperation in repeated group interactions
• Chaos and unpredictability in evolution of cooperation in continuous time
• Duality between cooperation and defection in the presence of tit-for-tat in replicator dynamics
• Friendly-rivalry solution to the iterated $n$-person public-goods game
• Grouping promotes both partnership and rivalry with long memory in direct reciprocity
• Single Equalizer Strategy with no Information Transfer for Conflict Escalation
• The role of memory in transition from direct to indirect reciprocity
• Payoff landscapes and the robustness of selfish optimization in iterated games
• Exploitation by asymmetry of information reference in coevolutionary learning in prisoner's dilemma game
• Inferring Strategies from Observations in Long Iterated Prisoner's Dilemma Experiments