Smart Proofs via Recursive Information Gathering: Decentralized Refereeing by Smart Contracts

Abstract

We introduce the SPRIG (Smart Proofs via Recursive Information Gathering) protocol. SPRIG allows agents to propose, question, and defend mathematical proofs in a decentralized fashion. A structure of stakes and bounties aims at producing debates in good faith and if those persist, they must go down to machine-level details, where they can be settled automatically. This combination of economic incentives and an oracle is designed to promote succinct and informative proofs. SPRIG can run autonomously as a smart contract on a blockchain platform, and hence it does not rely on a central trusted institution.

We translate SPRIG into a general game-theoretic model and prove that the protocol satisfies two desirable properties: no spamming and monotonicity. We then characterize analytically the equilibrium of a simple two-player specification of the model: this provides important insights into the impact of the protocol's parameters on the probabilities that it induces type I/II errors. We conclude by discussing the main attacks SPRIG's designers will need to take into account.

Keywords: information economics, blockchain, smart contracts, mathematical proof, formal verification, incentivization, game theory, perfect Bayesian equilibrium

JEL Classification: C72, D82, D89