Robust Cooperation in the Prisoner's Dilemma: Program Equilibrium via   Provability Logic
  We consider the one-shot Prisoner's Dilemma between algorithms with read-access to one anothers' source codes, and we use the modal logic of provability to build agents that can achieve mutual cooperation in a manner that is robust, in that cooperation does not require exact equality of the agents' source code, and unexploitable, meaning that such an agent never cooperates when its opponent defects. We construct a general framework for such "modal agents", and study their properties. 
Mihaly Barasz, Paul Christiano, Benja Fallenstein, Marcello   Herreshoff, Patrick LaVictoire, Eliezer Yudkowsky
cs.GT cs.LO