Fear of Loss, Inframodularity, and Transfers

Abstract

There exist several characterizations of concavity for univariate functions. One of them states that a function is concave if and only if it has non-increasing differences. This definition provides a natural generalization of concavity for multivariate functions, called inframodularity. This paper shows that a finite lottery is preferred to another by all expected utility maximizers with an inframodular utility if and only if the first measure can be obtained from the second via a sequence of suitable transfers. This result is a natural multivariate generalization of Rothschild and Stiglitz's construction based on mean preserving spreads.

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