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Myerson–Satterthwaite theorem


The Myerson–Satterthwaite theorem is an important result in mechanism design and the economics of asymmetric information, due to Roger Myerson and Mark Satterthwaite. Informally, the result says that there is no efficient way for two parties to trade a good when they each have secret and probabilistically varying valuations for it, without the risk of forcing one party to trade at a loss.

The Myerson–Satterthwaite theorem is among the most remarkable and universally applicable negative results in economics — a kind of negative mirror to the fundamental theorems of welfare economics. It is, however, much less famous than those results or Arrow's earlier result on the impossibility of satisfactory electoral systems.

There are two agents: Sally (the seller) and Bob (the buyer). Sally holds an item that is valuable for both her and Bob. Each agent values the item differently: Bob values it as and Sally as . Each agent knows his/her own valuation with certainty, but knows the valuation of the other agent only probabilistically:


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