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Non-Cooperative Rational Interactive Proofs

Authors Jing Chen, Samuel McCauley, Shikha Singh

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Author Details

Jing Chen
  • Stony Brook University, Stony Brook, NY 11794-4400, USA
Samuel McCauley
  • Williams College, Williamstown, MA 01267, USA
Shikha Singh
  • Williams College, Williamstown, MA 01267, USA

Funding

This work has been partially supported by NSF CAREER Award CCF 1553385, CNS 1408695, CCF 1439084, IIS 1247726, IIS 1251137, CCF 1217708, by Sandia National Laboratories, by the European Research Council under the European Union’s 7th Framework Programme (FP7/2007-2013) / ERC grant agreement no. 614331, and a Zuckerman STEM Fellowship.

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Jing Chen, Samuel McCauley, and Shikha Singh. Non-Cooperative Rational Interactive Proofs. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ESA.2019.29

Abstract

Interactive-proof games model the scenario where an honest party interacts with powerful but strategic provers, to elicit from them the correct answer to a computational question. Interactive proofs are increasingly used as a framework to design protocols for computation outsourcing.
Existing interactive-proof games largely fall into two categories: either as games of cooperation such as multi-prover interactive proofs and cooperative rational proofs, where the provers work together as a team; or as games of conflict such as refereed games, where the provers directly compete with each other in a zero-sum game. Neither of these extremes truly capture the strategic nature of service providers in outsourcing applications. How to design and analyze non-cooperative interactive proofs is an important open problem. 
In this paper, we introduce a mechanism-design approach to define a multi-prover interactive-proof model in which the provers are rational and non-cooperative - they act to maximize their expected utility given others' strategies. We define a strong notion of backwards induction as our solution concept to analyze the resulting extensive-form game with imperfect information.
We fully characterize the complexity of our proof system under different utility gap guarantees. (At a high level, a utility gap of u means that the protocol is robust against provers that may not care about a utility loss of 1/u.) We show, for example, that the power of non-cooperative rational interactive proofs with a polynomial utility gap is exactly equal to the complexity class P^{NEXP}.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory and mechanism design
  • Theory of computation → Interactive proof systems
  • Theory of computation → Computational complexity and cryptography
Keywords
  • non-cooperative game theory
  • extensive-form games with imperfect information
  • refined sequential equilibrium
  • rational proofs
  • interactive proofs

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