In monotone comparative statics, the single-crossing condition or single-crossing property refers to a condition where the relationship between two or more functions[note 1] is such that they will only cross once.[1] For example, a mean-preserving spread will result in an altered probability distribution whose cumulative distribution function will intersect with the original's only once.
The single-crossing condition was posited in Samuel Karlin's 1968 monograph 'Total Positivity'.[2] It was later used by Peter Diamond, Joseph Stiglitz,[3] and Susan Athey,[4] in studying the economics of uncertainty.[5]
The single-crossing condition is also used in applications where there are a few agents or types of agents that have preferences over an ordered set. Such situations appear often in information economics, contract theory, social choice and political economics, among other fields.
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- ^ Athey, S. (2002-02-01). "Monotone Comparative Statics under Uncertainty". The Quarterly Journal of Economics. 117 (1): 187–223. doi:10.1162/003355302753399481. ISSN 0033-5533. S2CID 14098229.
- ^ Karlin, Samuel (1968). Total positivity. Vol. 1. Stanford University Press. OCLC 751230710.
- ^ Diamond, Peter A.; Stiglitz, Joseph E. (1974). "Increases in risk and in risk aversion". Journal of Economic Theory. 8 (3). Elsevier: 337–360. doi:10.1016/0022-0531(74)90090-8. hdl:1721.1/63799.
- ^ Athey, Susan (July 2001). "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information". Econometrica. 69 (4): 861–889. doi:10.1111/1468-0262.00223. hdl:1721.1/64195. ISSN 0012-9682.
- ^ Gollier, Christian (2001). The Economics of Risk and Time. The MIT Press. p. 103. ISBN 9780262072151.
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