The Myerson–Satterthwaite theorem is an important result in mechanism design and the economics of asymmetric information, and named for Roger Myerson and Mark Satterthwaite.
[1] 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.
Formally, it is represented by two functions: Note that, thanks to the revelation principle, the assumption that the mechanism is direct does not lose generality.
Hence: Myerson and Satterthwaite study the following requirements that an ideal mechanism should satisfy.
If the following two assumptions are true: then, there is no mechanism which satisfies the four properties mentioned above (IR, WBB, NEIC and PE).