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We consider the one-shot Prisoner's Dilemma between algorithms withread-access to one anothers' source codes, and we use the modal logic ofprovability to build agents that can achieve mutual cooperation in a mannerthat is robust, in that cooperation does not require exact equality of theagents' source code, and unexploitable, meaning that such an agent nevercooperates when its opponent defects. We construct a general framework for such"modal agents", and study their properties.

Robust Cooperation in the Prisoner's Dilemma: Program Equilibrium via Provability Logic