Myerson-Satterthwaite theorem

The Myerson-Satterthwaite theorem is a fundamental impossibility result in bilateral trade and mechanism design: when a seller and a buyer each have private information about their own valuation of a good, no mechanism can simultaneously achieve efficiency (trade occurs whenever the buyer's valuation exceeds the seller's), incentive compatibility (truth-telling is optimal), and budget balance (the mechanism does not run a deficit). Proved by Roger Myerson and Mark Satterthwaite in 1983, the theorem establishes that private information itself creates a friction that cannot be designed away — only allocated.

The theorem is more specific than the Gibbard-Satterthwaite theorem but no less devastating. Where Gibbard-Satterthwaite shows that strategy-proofness is incompatible with non-dictatorship in voting, Myerson-Satterthwaite shows that efficient trade is incompatible with truthful revelation in bilateral exchange. The common structure is that private information creates rents, and any mechanism that tries to extract those rents for efficiency must either violate incentive compatibility or require external subsidy. The market is not a neutral aggregator; it is a mechanism with its own incentive constraints, and those constraints bind even in the simplest possible setting of two agents and one good.

The result has immediate implications for the design of decentralized autonomous organization governance and on-chain market mechanisms. Any protocol that claims to achieve efficient resource allocation while preserving truthfulness and budget balance in a setting with private valuations is making a promise that mathematics has shown cannot be kept. The theorem does not say that trade is impossible; it says that efficient trade requires either lying, subsidies, or missed opportunities. The choice among these is not technical but political: who bears the cost of private information?