Weak acyclicity of the iterated prisoner’s dilemma with a memory of one period.

I develop a Python algorithm that visualizes the combined state values of the ϵ-greedy policies of an iterated prisoner’s dilemma with a memory of one period. From this one can read the best response to a given policy of the opposing player. I also attempt to show that the iterated prisoner’s dilemma is weakly acyclic. This can be done by constructing a potential function for the game. The two candidate functions explored turn out not to be potential functions. The approach developed here does however lend itself to extensions to games with more states and actions.