Convex Choice

TL;DR

This paper explores convex choice in multidimensional Euclidean spaces, linking it to local incentive constraints and showing its implications for expected-utility preferences and multidimensional mechanism design.

Contribution

It characterizes convex choice via local incentive constraints and connects it to directional single-crossing differences, advancing understanding in multidimensional mechanism design.

Findings

Convex choice characterizes the sufficiency of local incentive constraints.

DSCD implies preferences are either one-dimensional or affine.

The work provides a new perspective on multidimensional mechanism design.

Abstract

For multidimensional Euclidean type spaces, we study convex choice: from any choice set, the set of types that make the same choice is convex. We establish that, in a suitable sense, this property characterizes the sufficiency of local incentive constraints. Convex choice is also of interest more broadly. We tie convex choice to a notion of directional single-crossing differences (DSCD). For an expected-utility agent choosing among lotteries, DSCD implies that preferences are either one-dimensional or must take the affine form that has been tractable in multidimensional mechanism design.