A Genetic Algorithm for Nash Equilibrium Analysis of Competitive Course Bidding Mechanisms

Runfeng Yang

2025

Abstract

This paper analyzes a real course-bidding game that features a discrete and finite strategy set with incomplete information. Course-bidding systems are widely adopted in academic institutions to allocate limited resources, yet their strategic dynamics under incomplete information remain understudied. Due to the discrete nature of the game, a pure strategy derived from Nash Equilibrium is intractable. To address this challenge, this study employs a Genetic Algorithm (GA) to approximate equilibrium strategies, given the game’s discrete and finite strategy space. Due to the discrete nature of the game, pure-strategy Nash Equilibria (PSNE) is intractable. This paper investigates the long-term evolution of strategic tendencies, examining their features and implications. This study shows that the course-bidding strategy tends to a more concentrated allocation of the bidding resources. As agents learn to prioritize high-value courses, the resulting strategy leads to higher variance of the bidding ratios between courses, as well as lowering the width of the courses that are invested. This analysis reveals structural deficiencies in the model, highlighting the need for mechanisms to mitigate over-concentration, such as bid caps or quota adjustments.

Paper Citation

in Harvard Style

Yang R. (2025). A Genetic Algorithm for Nash Equilibrium Analysis of Competitive Course Bidding Mechanisms. In Proceedings of the 2nd International Conference on Innovations in Applied Mathematics, Physics, and Astronomy - Volume 1: IAMPA; ISBN 978-989-758-774-0, SciTePress, pages 584-588. DOI: 10.5220/0013833600004708

in Bibtex Style

@conference{iampa25,
author={Runfeng Yang},
title={A Genetic Algorithm for Nash Equilibrium Analysis of Competitive Course Bidding Mechanisms},
booktitle={Proceedings of the 2nd International Conference on Innovations in Applied Mathematics, Physics, and Astronomy - Volume 1: IAMPA},
year={2025},
pages={584-588},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013833600004708},
isbn={978-989-758-774-0},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 2nd International Conference on Innovations in Applied Mathematics, Physics, and Astronomy - Volume 1: IAMPA
TI - A Genetic Algorithm for Nash Equilibrium Analysis of Competitive Course Bidding Mechanisms
SN - 978-989-758-774-0
AU - Yang R.
PY - 2025
SP - 584
EP - 588
DO - 10.5220/0013833600004708
PB - SciTePress