Single-Crossing Differences in Convex Environments

Navin Kartik, SangMok Lee and Daniel Rappoport

Papers from arXiv.org

Abstract: An agent's preferences depend on an ordered parameter or type. We characterize the set of utility functions with single-crossing differences (SCD) in convex environments. These include preferences over lotteries, both in expected utility and rank-dependent utility frameworks, and preferences over bundles of goods and over consumption streams. Our notion of SCD does not presume an order on the choice space. This unordered SCD is necessary and sufficient for ''interval choice'' comparative statics. We present applications to cheap talk, observational learning, and collective choice, showing how convex environments arise in these problems and how SCD/interval choice are useful. Methodologically, our main characterization stems from a result on linear aggregations of single-crossing functions.

Date: 2022-12, Revised 2023-06
New Economics Papers: this item is included in nep-mic and nep-upt
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Journal Article: Single-Crossing Differences in Convex Environments (2024)
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