URAP Project Descriptions

Open Theoretical Research Project in Economic Theory / Operations Research (Publication-Oriented)

Ilan Morgenstern, Professor
Business, Haas School

Applications for Spring 2026 are closed for this project.

This project studies a classic problem in economic theory known as a bankruptcy (or claims) problem: how to allocate a limited resource among agents who have competing claims over the same resources. Such problems arise in economics, operations research, and fair division, and are central to the theory of cooperative games.

A well-known solution concept in this literature is the random arrival rule, which assigns resources based on the expected outcome of agents arriving in a random order. An earlier work of mine (Morgenstern & Domínguez, Economics Letters) provides a partial result that characterizes this rule as the only solution that satisfies a structural property called feasible set additivity, together with fairness conditions. However, this result has only been proved in restricted cases (e.g., small numbers of agents), and whether it extends to general settings remains an open question.

The goal of this project is to explore whether this characterization can be extended to a general multi-agent environment, using tools from convex analysis and game theory. If successful, this work could lead to a publishable theoretical result.

Role: The undergraduate researcher will work closely with the faculty supervisor on this theoretical research project. The student’s responsibilities will include:

1. Reading and understanding existing literature on bankruptcy problems and fair division

2. Studying a proposed proof strategy that extends existing results to a more general setting.

3. Attempting to formalize, refine, and extend this proof, including identifying missing steps, clarifying assumptions, or constructing counterexamples where appropriate.

4. Writing up intermediate results clearly and rigorously, potentially contributing to a working paper or academic publication.

By the end of the project, the student will:

A. Gain deep exposure to economic theory and axiomatic reasoning

B. Learn how to read and critically engage with research-level economics papers

C. Develop experience in constructing and evaluating formal mathematical proofs

D. Experience what it is like to work on an open research problem at the frontier of the literature

This work is especially a good fit for students looking to build preparation for graduate study (PhD) in economics, mathematics, computer science, or operations research.

Qualifications: 1. Strong background in mathematics, including real analysis, linear algebra, and proofs.

2. Comfort with abstract reasoning and formal mathematical arguments.

3. Interest in economic theory, game theory, or operations research.

4. Prior coursework in economics, mathematics, computer science, or related fields is required.

Hours: 9-11 hrs

Social Sciences

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