Bounded Size Coalition Formation: Stability, Fairness, and Complexity

Format: On Campus
Number of Interns: 2 undergraduate students
Duration of the Internship: 6 Weeks
Start Date: June 29, 2026
Finish Date: August 14, 2026
Application Deadline: The deadline announced by the university
Project Supervisor: Dr. Seçkin Özbilen
Project Description:

This project is related to cooperative game theory and focuses on hedonic coalition formation problems. Such problems arise in many real-life situations. For example, when allocating university students to dormitory rooms, creating shifts and project groups for employees in a workplace, or assigning homework and project groups in a classroom, administrators, managers, and teachers aim to divide individuals into groups so that no one feels dissatisfied or raises objections. However, in practice, some individuals may prefer to form new teams or exchange positions with others. This dynamic forces decision-makers to search for systematic solutions that balance preferences and fairness. These examples can be viewed as instances of hedonic coalition formation.

Formally, a hedonic coalition formation problem (in short problem) consists of a finite set of agents. A coalition is a non-empty subset of this agent set, and each agent has complete and transitive preferences over the collection of coalitions that include them. An outcome of the problem is a partition of the agents into mutually disjoint coalitions, which is called a coalition structure.

At the first stage of the project, we will analyze the stability properties of coalition structures in these problems. At the second stage, we will design algorithms that generate coalition structures which are stable, optimal, and fair. In the final stage, the computational complexity of these problems will be studied, providing insights into the algorithmic limits of coalition formation.

Research Intern Responsibilities:

• Conduct literature review on coalition formation.
• Understand and write examples and counter examples related to stability, fairness, and optimality in coalition structures.
• Prepare written reports and present findings to the supervisor and peers.
• Collaborate with other interns to compare theoretical results with computational experiments.

Required Skills and Qualifications:

• Strong background in mathematics. Interest in microeconomics and game theory.
• Familiarity with programming languages such as Python, MATLAB, or similar.
• Ability to work independently and in a team environment.
• Good communication and academic writing skills in English.

Expected Learning Outcomes:

• Deeper understanding of cooperative game theory and coalition formation problems.
• Ability to design and implement algorithms for stability and fairness analysis.
• Experience in connecting mathematical theory with computational practice.
• Improved teamwork, research, and presentation skills.
• Awareness of computational complexity issues in coalition formation.

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