Cooperation and Self-Regulation in a Model of Agents Playing Different Games

TL;DR

This paper introduces a simple agent-based model where selfish agents playing extended Prisoner's Dilemma games self-organize into cooperation or defection states, revealing counterintuitive results about payoff structures and cooperation levels.

Contribution

The study presents a novel model of agents with no memory or direct reciprocity, demonstrating how cooperation emerges in diverse game settings and challenging prior assumptions.

Findings

Certain payoff matrices lead to high cooperation despite favoring defection.

Some games expected to maximize cooperation do not produce the highest cooperation levels.

The system reaches stationary states with stable cooperation probabilities and incomes.

Abstract

A simple model for cooperation between "selfish" agents, which play an extended version of the Prisoner's Dilemma(PD) game, in which they use arbitrary payoffs, is presented and studied. A continuous variable, representing the probability of cooperation, $p_k(t) \in$ [0,1], is assigned to each agent $k$ at time $t$. At each time step $t$ a pair of agents, chosen at random, interact by playing the game. The players update their $p_k(t)$ using a criteria based on the comparison of their utilities with the simplest estimate for expected income. The agents have no memory and use strategies not based on direct reciprocity nor 'tags'. Depending on the payoff matrix, the systems self-organizes - after a transient - into stationary states characterized by their average probability of cooperation $\bar{p}_{eq}$ and average equilibrium per-capita-income $\bar{p}_{eq},\bar{U}_\infty$. It turns out that the model exhibit some results that contradict the intuition. In particular, some games which - {\it a priory}- seems to favor defection most, may produce a relatively high degree of cooperation. Conversely, other games, which one would bet that lead to maximum cooperation, indeed are not the optimal for producing cooperation.