Dynamic Phase Transition in Prisoner's Dilemma on a Lattice with Stochastic Modifications

TL;DR

This paper investigates a stochastic variant of the prisoner's dilemma on a lattice, revealing a phase transition to all-defectors that belongs to the directed percolation universality class, with persistence properties influenced by dynamics.

Contribution

It introduces two stochastic variants of the prisoner's dilemma on a lattice and demonstrates a phase transition belonging to the directed percolation universality class.

Findings

Transition to all-defectors at high stochasticity p

Transition belongs to directed percolation universality class

Persistence exponents are higher than previous studies

Abstract

We present a detailed study of prisoner's dilemma game with stochastic modifications on a two-dimensional lattice, in presence of evolutionary dynamics. By very nature of the rules, the cooperators have incentive to cheat and the fear to being cheated in prisoner's dilemma and may cheat even when not dictated by evolutionary dynamics. We consider two variants. In either case, the agents mimic the action (cooperation or defection) in the previous timestep of the most successful agent in the neighborhood. Over and above this, the fraction p of cooperators spontaneously change their strategy to pure defector at every time step in the first variant. In the second variant, there are no pure cooperators. All cooperators keep defecting with probability p at every time-step. In both cases, the system switches from coexistence state to an all-defector state for higher values of p. We show that the transition between these states unambiguously belongs to directed percolation universality class in 2 + 1 dimension. We also study the local persistence and the persistence exponents are higher than ones obtained in previous studies underlining their dependence on details of dynamics