Prisoner's Dilemma: non-trivial results for the lowest temptation level in the Darwinian and Pavlovian evolutionary strategies

TL;DR

This paper reveals that the lowest temptation level in the Prisoner's Dilemma is non-trivial when players interact with multiple opponents, leading to diverse behaviors under different evolutionary strategies.

Contribution

It demonstrates that the triviality of T=1 is limited to single-player interactions, showing complex dynamics in multi-player scenarios for both Darwinian and Pavlovian strategies.

Findings

Multiple behaviors observed at T=1 in multi-player interactions

Cooperative, chaotic, or defective phases under Darwinian strategy

Cooperative or quasi-regular phases under Pavlovian strategy

Abstract

The lowest temptation level (T = 1) is considered a trivial case for the Prisoner's Dilemma. Here, we show that this statement is true only for a very particular case, where the players interact with only one player. Otherwise, if the players interact with more than one player, the system presents the same possible behaviors observed for $T > 1$. In the steady state, the system can reach the cooperative, chaotic or defective phases, when adopting the Darwinian Evolutionary Strategy and the cooperative or quasi-regular phases, adopting the Pavlovian Evolutionary Strategy.