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A PARAMETRIC, RESOURCE-BOUNDED GENERALIZATION OF LÖB’S THEOREM, AND A ROBUST COOPERATION CRITERION FOR OPEN-SOURCE GAME THEORY

Published online by Cambridge University Press:  02 April 2019

ANDREW CRITCH
ANDREW CRITCH*
Affiliation:
MACHINE INTELLIGENCE RESEARCH INSTITUTE 2030 ADDISON STREET, BERKELEY, CA94704, USA E-mail: [email protected]: http://intelligence.org/
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Abstract

This article presents two theorems: (1) a generalization of Löb’s Theorem that applies to formal proof systems operating with bounded computational resources, such as formal verification software or theorem provers, and (2) a theorem on the robust cooperation of agents that employ proofs about one another’s source code as unexploitable criteria for cooperation. The latter illustrates a capacity for outperforming classical Nash equilibria and correlated equilibria, attaining mutually cooperative program equilibrium in the Prisoner’s Dilemma while remaining unexploitable, i.e., sometimes achieving the outcome (Cooperate, Cooperate), and never receiving the outcome (Cooperate, Defect) as player 1.

Keywords

03B7003B4503F0368T2791A3562C9991A0591A0691A10Löbian cooperationbounded rationalityprogram equilibriumproof lengthPrisoner’s Dilemma
Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 4 , December 2019 , pp. 1368 - 1381
Copyright
Copyright © The Association for Symbolic Logic 2019 

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References

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