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

TL;DR

This paper explores how tit-for-tat strategies can lead to cooperative equilibrium in the iterated prisoner's dilemma, emphasizing the impact of memory length and strategy evolution on cooperation.

Contribution

It demonstrates that extending memory horizons and strategy filtering promote cooperation, highlighting the role of modified tit-for-tat strategies in evolutionary dynamics.

Findings

Cooperation emerges as a dominant strategy with one-step memory.

Extended memory horizons facilitate the filtering of poor strategies.

Modified tit-for-tat strategies are crucial for stable cooperation.

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.