# Reactive means in the Iterated Prisoner's Dilemma

## TL;DR

This paper introduces morality metrics for the Iterated Prisoner's Dilemma, focusing on reactive strategies, to evaluate fairness and goodness, aiding the comparison of advanced strategies based on these moral measures.

## Contribution

It proposes a set of morality metrics and computes reactive means for these metrics, providing a new way to assess strategies in IPD and ISG.

## Key findings

- Reactive means for morality metrics are computed.
- Certain morality functions are anticorrelated with success.
- Metrics help compare strategies based on fairness and goodness.

## Abstract

The Iterated Prisoner's Dilemma (IPD) is a well studied framework for understanding direct reciprocity and cooperation in pairwise encounters. However, measuring the morality of various IPD strategies is still largely lacking. Here, we partially address this issue by proposing a suit of plausible morality metrics to quantify four aspects of justice. We focus our closed-form calculation on the class of reactive strategies because of their mathematical tractability and expressive power. We define reactive means as a tool for studying how actors in the IPD and Iterated Snowdrift Game (ISG) behave under typical circumstances. We compute reactive means for four functions intended to capture human intuitions about ``goodness'' and ``fair play''. Two of these functions are strongly anticorrelated with success in the IPD and ISG, and the other two are weakly anticorrelated with success. Our results will aid in evaluating and comparing powerful IPD strategies based on machine learning algorithms, using simple and intuitive morality metrics.