A Lagrangian Approach to Optimal Lotteries in Non-Convex Economies

Chengfeng Shen, Felix Kubler, Yucheng Yang and Zhennan Zhou
Additional contact information
Chengfeng Shen: Peking University
Felix Kubler: University of Zurich
Yucheng Yang: University of Zurich; Swiss Finance Institute
Zhennan Zhou: Westlake University

No 25-48, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

Abstract: We develop a new method to efficiently solve for optimal lotteries in models with non-convexities. In order to employ a Lagrangian framework, we prove that the value of the saddle point that characterizes the optimal lottery is the same as the value of the dual of the deterministic problem. Our algorithm solves the dual of the deterministic problem via sub-gradient descent. We prove that the optimal lottery can be directly computed from the deterministic optima that occur along the iterations. We analyze the computational complexity of our algorithm and show that the worst-case complexity is often orders of magnitude better than the one arising from a linear programming approach. We apply the method to two canonical problems with private information. First, we solve a principal-agent moral-hazard problem, demonstrating that our approach delivers substantial improvements in speed and scalability over traditional linear programming methods. Second, we study an optimal taxation problem with hidden types, which was previously considered computationally infeasible, and examine under which conditions the optimal contract will involve lotteries.

Keywords: Private Information; Adverse Selection; Moral Hazard; Non-Convexities; Lotteries; Lagrangian Iteration (search for similar items in EconPapers)
JEL-codes: C61 C63 D61 D82 (search for similar items in EconPapers)
Pages: 62 pages
Date: 2025-04
New Economics Papers: this item is included in nep-cta and nep-mic
References: Add references at CitEc
Citations:

Downloads: (external link)
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5233164 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp2548

Access Statistics for this paper

More papers in Swiss Finance Institute Research Paper Series from Swiss Finance Institute Contact information at EDIRC.
Bibliographic data for series maintained by Ridima Mittal ().