# Universalized Prisoner's Dilemma With Risk

**Authors:** Paul Studtmann  
**arXiv:** [1510.00665](https://arxiv.org/abs/1510.00665)  
**Date:** 2015-09-15  
**Summary page:** https://www.summarizepaper.com/en/paper/1510.00665v1/

## 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.