Supermodular function: Difference between revisions

Revision as of 03:38, 4 April 2011

Revision as of 23:17, 9 August 2011

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If −''f'' is supermodular then ''f'' is called '''submodular''', and if the inequality is changed to an equality the function is '''modular'''.

If ''f'' is smoothtwice continuously differentiable, then supermodularity is equivalent to the condition<ref>The equivalence between the definition of supermodularity and its calculus formulation is sometimes called ''Topkis' Characterization Theorem''. See Paul Milgrom and John Roberts (1990), 'Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities', ''Econometrica'' 58 (6), page 1261.</ref>

:<math> \frac{\partial ^2 f}{\partial z_i\, \partial z_j} \geq 0 \mbox{ for all } i \neq j.</math>