Introduction

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**Iterated Prisoner's Dilemma**

Prisoner's Dilemma (PD) may be used to model many conflict-of-interest interactions, where a group of individuals would be best off cooperating with each other, yet the cooperation does not always develop. The name itself comes from imagining a situation where two prisoners are interrogated in separate rooms, and encouraged to incriminate each other (i.e. to defect). The payoffs take the form of larger or smaller prison sentences, and follow the relationship outlined in the previous slide. It would be in the prisoners' best interest to somehow agree to cooperate. Luckily for the interrogators, if the prisoners are only concerned with their own well-being, they will instead both defect in such a one-time instance of the PD game, for the reasons discussed in the previous slides.

However, most of the time we would like to model instances of *Iterated
Prisoner's Dilemma* instead, where the players play the PD game more than just once. One important example, a
nuclear arms race between countries such as the US and the Soviet Union, may be analyzed along the lines
of an Iterated PD. In this case, each player's decision is based not only on the present payoffs, but also
on the past history of moves by each player and the possibilities contained in the future. For instance,
one of the countries may decide to reduce its nuclear arsenal if it saw the other one do the same in the
previous years.

In the rest of this tutorial, we model players that engage in instances of the Iterated PD. We will
introduce *δ*, the probability that such an instance continues after each Prisoner's Dilemma round.
δ, often called the *shadow of the future,* determines the average number of PD rounds in a single
instance of Iterated PD.

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