Concave utility functions on finite sets

  • Yakar Kannai | Weizmann Institute of Science

Concave utility functions are widely used in applied economics and in economic theory. A complete characterization of preferences representable by such utility functions has been known for some time, provided that the preferences are defined on infinite convex sets. The real world is finite. This motivates recent work by Richter and Wong concerning convex preferences defined on finite sets. We provide geometric constructions and clarify the relation with older algorithms in demand theory. We also show that certain natural objects (such as least concave utility functions) do not exist in general in the finite context.

Speaker Details

Yakar Kannai studies mainly linear partial differential equations (Ph.D. under the supervision of S.Agmon) and Game Theory/Mathematical Economics (got initiated to the subject by R.J.Aumann). Currently, he is involved in two longstanding projects:1. Studying second order equations of various types, in particular constructing kernels associated with (functions of) degenerate hypoelliptic operators;2. Convexity properties of an individual preferences as manifest in her demand behavior.

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