New paper on bounded Löb and robust cooperation of bounded agents - Machine Intelligence Research Institute

Löb's theorem and Gödel's theorem make predictions about the behavior of systems capable of self-reference with unbounded computational resources with which to write and evaluate proofs. However, in the real world, systems capable of self-reference will have limited memory and processing speed, so in this paper we introduce an effective version of Löb's theorem which is applicable given such bounded resources. These results have powerful implications for the game theory of bounded agents who are able to write proofs about themselves and one another, including the capacity to out-perform classical Nash equilibria and correlated equilibria, attaining mutually cooperative program equilibrium in the Prisoner's Dilemma. Previous cooperative program equilibria studied by Tennenholtz and Fortnow have depended on tests for program equality, a fragile condition, whereas "Löbian" cooperation is much more robust and agnostic of the opponent's implementation. Tennenholtz (2004) showed that cooperative equilibria exist in the Prisoner's Dilemma between agents with transparent source code.