Universalized Prisoner's Dilemma With Risk

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.