Escaping Prisoner's Dilemmas: From Discord to Harmony in the Landscape of 2x2 Games

TL;DR

This paper explores how changing payoffs in 2x2 games can transform social dilemmas like Prisoner's Dilemma into cooperative games, using a comprehensive topology to map these relationships and facilitate strategic analysis.

Contribution

It introduces a systematic topology of 2x2 games that maps relationships and transformation paths, enhancing understanding of social dilemma dynamics and game classification.

Findings

Payoff swaps can convert Prisoner's Dilemma into other game types.

The topology maps 144 strict and 38 symmetric 2x2 games.

Coordinates uniquely identify all asymmetric 2x2 games.

Abstract

Changes in payoffs can transform Prisoner's Dilemma and other social dilemmas into harmonious win-win games. Using the Robinson-Goforth topology of 2x2 games, this paper analyzes how payoff swaps turn Prisoner's Dilemma into other games, compares Prisoner's Dilemmas with other families of games, traces paths that affect the difficulty of transforming Prisoner's Dilemma and other social dilemmas into win-win games, and shows how ties connect simpler and more complex games. Charts illustrate the relationships between the 144 strict ordinal 2x2 games, the 38 symmetric 2x2 ordinal games with and without ties, and the complete set of 1,413 2x2 ordinal games. Payoffs from the symmetric ordinal 2x2 games combine to form asymmetric games, generating coordinates for a simple labeling scheme to uniquely identify and locate all asymmetric ordinal 2x2 games. The expanded topology elegantly maps relationships between 2x2 games with and without ties, enables a systematic understanding of the potential for transformations in social dilemmas and other strategic interactions, offers a tool for institutional analysis and design, and locates a variety of interesting games for further research.