An exhaustive exploration of the parameter space of the Prisoners' Dilemma in one-dimensional cellular automata

TL;DR

This paper investigates the Prisoner's Dilemma in one-dimensional cellular automata, exploring how the number of neighbors influences the emergence of cooperation and system states.

Contribution

It provides an exhaustive analysis of parameter space, revealing the impact of neighbor count and parity on system dynamics in cellular automata.

Findings

Final states depend mainly on the number of neighbors z.

A significant difference exists between even and odd z values.

Results extend previous findings in regular lattices.

Abstract

The Prisoner's Dilemma (PD) is one of the most popular games of the Game Theory due to the emergence of cooperation among competitive rational players. In this paper, we present the PD played in cells of one-dimension cellular automata, where the number of possible neighbors that each cell interacts, z, can vary. This makes possible to retrieve results obtained previously in regular lattices. Exhaustive exploration of the parameters space is presented. We show that the final state of the system is governed mainly by the number of neighbors z and there is a drastic difference if it is even or odd.