Universalized Prisoner's Dilemma With Risk

TL;DR

This paper introduces a novel mathematical model of the Prisoner's Dilemma incorporating a new action type called 'universalizing' and adds risk to analyze how trustworthiness affects agents' decisions, showing how risk levels influence outcomes.

Contribution

It presents a new recursive action type 'universalizing' and integrates risk into the Prisoner's Dilemma, offering a more nuanced model of trust and decision-making.

Findings

Agents can escape the dilemma with no risk.

High risk causes agents to succumb to the dilemma.

Universalizing expands strategic options in the Prisoner's Dilemma.

Abstract

In this paper I present a mathematically novel approach to the Prisoner's Dilemma. I do so by first defining recursively a distinct action type, what I call 'universalizing', that I add to the original prisoner's dilemma. Such a modified version of the Prisoner's Dilemma provides a very food productive model of the choices that would be made in a prisoner's dilemma by agents who trust each other. As I show, players playing a universalized prisoner's dilemma get as far out of the dilemma as is mathematically possible. I then add the concept of risk to the universalized version of prisoner's dilemma. Doing so provide a model that is sensitive to the trustworthiness of the agents in any prisoner's dilemma. As I show, with no risk, agents get out of the prisoners dilemma; and with maximal risk, the succumb to it. succumb to it.