We introduce a natural model for the iterated prisoner's dilemma in the presence of noise, where strategies are finite automata that at each step have a probability p of making a mistake. This leads us to model the result of two strategies playing against each other as a Markov chain. We prove that for a strategy to be evolutionarily stable in our setup, it has to be cooperative, in the sense that it has to cooperate when playing against a clone of itself. We conjecture that the Pavlov strategy is evolutionarily stable.
Besides the paper, this repository contains supporting code files, and the countless pages of notes taken in thinking about the problem. The code files are useful for evaluating the Markov chains and time average distributions referred to in the paper. The notes are mostly here just for fun.
The work was performed by Arvid Lunnemark during the Spring of 2020, under the guidance of Dr. Michael Sipser. I am thankful to Mike for granting me this opportunity, and for providing the idea behind the project.