Phase diagram of Symmetric Iterated Prisoner's Dilemma of Two-Companies with Partial Imitation Rule

TL;DR

This paper analyzes the phase diagram of a symmetric two-company Iterated Prisoner's Dilemma model with partial imitation, revealing how noise and temptation influence players' strategies.

Contribution

It reduces the two-company case to an effective one-company model and constructs phase diagrams using mean value equations and simulations.

Findings

Players tend to adopt Grim Trigger strategy with increased noise.

Intra-group temptation to defect influences strategy adoption.

The phase diagram aligns well with simulation results.

Abstract

The problem of two companies of agents with one-step memory playing game is investigated in the context of the Iterated Prisoner's Dilemma under the partial imitation rule, where a player can imitate only those moves that he has observed in his games with his opponent. We limit our study to the special case where the players in the two groups enjoy the same conditions on a fully connected network, so that there are only two payoff matrices required: one for players playing games with members of the same company, and the other one for players playing games with members from a different company. We show that this symmetric case of two companies of players can be reduced to the one-company case with an effective payoff matrix, from which a phase diagram for the players using the two dominant strategies, Pavlov and Grim Trigger can be constructed. The phase diagram is computed by numerical integration of the approximate mean value equations. The results are in good agreement with simulations of the two-company model. The phase diagram leads to an interesting conclusion that a player will more likely become a Grim Trigger, regardless of their affiliated company, when the noise level increases so that he is more irrational, or when the intra-group temptation to defect increases.