Program Equilibrium in the Prisoner’s Dilemma via Löb’s Theorem

Applications of game theory often neglect that real-world agents normally have some amount of out-of-band informa-tion about each other. We consider the limiting case of a one-shot Prisoner’s Dilemma between algorithms with read-access to one anothers ’ source code. Previous work has shown that cooperation is possible at a Nash equilibrium in this setting, but existing constructions require interacting agents to be identical or near-identical. We show that a nat-ural class of agents are able to achieve mutual cooperation at Nash equilibrium without any prior coordination of this sort.