The Myerson–Satterthwaite theorem is an important result in
mechanism design
Mechanism design is a field in economics and game theory that takes an objectives-first approach to designing economic mechanisms or incentives, toward desired objectives, in strategic settings, where players act rationally. Because it starts a ...
and the economics of
asymmetric information
In contract theory and economics, information asymmetry deals with the study of decisions in transactions where one party has more or better information than the other.
Information asymmetry creates an imbalance of power in transactions, which can ...
, and named for
Roger Myerson
Roger Bruce Myerson (born March 29, 1951) is an American economist and professor at the University of Chicago. He holds the title of the David L. Pearson Distinguished Service Professor of Global Conflict Studies at The Pearson Institute for the ...
and
Mark Satterthwaite
Mark Allen Satterthwaite is an economist at the Kellogg School of Management at Northwestern University in Evanston, Illinois. He is currently A.C. Buehler Professor in Hospital & Health Services Management, Professor of Strategic Management & Ma ...
. 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
There are two fundamental theorems of welfare economics. The first states that in economic equilibrium, a set of complete markets, with complete information, and in perfect competition, will be Pareto optimal (in the sense that no further exchang ...
. It is, however, much less famous than those results or
Arrow's earlier result on the impossibility of satisfactory electoral systems.
Notation
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:
* For Sally, the value of Bob is represented by a
probability density
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can ...
function
which is positive in the range