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| The '''Myerson–Satterthwaite theorem''' is an important result in [[mechanism design]] and the economics of [[information asymmetry|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.
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| Formally, the theorem applies if a prospective buyer ''A'' has a valuation <math>v_A \in [x_a,y_a]</math>, and the prospective seller ''B'' has an independent valuation <math>v_B \in [x_b,y_b]</math>, such that the intervals <math>[x_a,y_a]</math> and <math>[x_b,y_b]</math> overlap, and the [[probability density function|probability densities]] for the valuations are strictly positive on those intervals. Under those conditions, there is no [[Bayesian game|Bayesian]] [[incentive compatibility|incentive compatible]] [[social choice function]] that is guaranteed in advance to produce [[Pareto efficiency|efficient]] outcomes and [[participation constraint (mechanism design)|guarantees buyers and sellers non-negative returns]] regardless of <math>v_a</math> and <math>v_b</math>.
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| 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 impossibility theorem|Arrow's earlier result on the impossibility of satisfactory electoral systems]].
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| ==References==
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| * {{cite journal |last=Myerson |first=Roger B. |authorlink=Roger B. Myerson |coauthors=Mark A. Satterthwaite |year=1983 |month= |title=Efficient Mechanisms for Bilateral Trading |journal=Journal of Economic Theory |volume=29 |issue= 2|pages=265–281 |id= |url= |accessdate=2008-08-16 |doi=10.1016/0022-0531(83)90048-0 }}
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| {{DEFAULTSORT:Myerson-Satterthwaite theorem}}
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| [[Category:Mechanism design]]
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| [[Category:Game theory]]
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Latest revision as of 14:03, 6 November 2014
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