Single-crossing condition

Example of two normal cumulative distribution functions F(x) and G(x) which satisfy the single-crossing condition.
Example of two cumulative distribution functions F(x) and G(x) which satisfy the single-crossing condition.

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.


Cite error: There are <ref group=note> tags on this page, but the references will not show without a {{reflist|group=note}} template (see the help page).

  1. ^ 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.
  2. ^ Karlin, Samuel (1968). Total positivity. Vol. 1. Stanford University Press. OCLC 751230710.
  3. ^ 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.
  4. ^ 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.
  5. ^ Gollier, Christian (2001). The Economics of Risk and Time. The MIT Press. p. 103. ISBN 9780262072151.