Intelligent tit-for-tat in the iterated prisoner's dilemma game

Abstract

We seek a route to the equilibrium where all the agents cooperate in the iterated prisoner's dilemma game on a two-dimensional plane, focusing on the role of tit-for-tat strategy. When a time horizon, within which a strategy can recall the past, is one time step, an equilibrium can be achieved as cooperating strategies dominate the whole population via proliferation of tit-for-tat. Extending the time horizon, we filter out poor strategies by simplified replicator dynamics and observe a similar evolutionary pattern to reach the cooperating equilibrium. In particular, the rise of a modified tit-for-tat strategy plays a central role, which implies how a robust strategy is adopted when provided with an enhanced memory capacity.

arXiv comment9 pages, 14 figures

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• Five rules for friendly rivalry in direct reciprocity
• Local stability of cooperation in a continuous model of indirect reciprocity
• Friendly-rivalry solution to the iterated $n$-person public-goods game
• Limitation of network inhomogeneity in improving cooperation in coevolutionary dynamics
• Network Structures between Strategies in Iterated Prisoners' Dilemma Games
• The world of strategies with memory
• Dynamic Motifs of Strategies in Prisoner's Dilemma Games
• A Round-Robin Tournament of the Iterated Prisoner's Dilemma with Complete Memory-Size-Three Strategies