Research Article
A Phase Transition in Large Network Games
@INPROCEEDINGS{10.1007/978-3-031-23141-4_20, author={Abhishek Shende and Deepanshu Vasal and Sriram Vishwanath}, title={A Phase Transition in Large Network Games}, proceedings={Game Theory for Networks. 11th International EAI Conference, GameNets 2022, Virtual Event, July 7--8, 2022, Proceedings}, proceedings_a={GAMENETS}, year={2023}, month={1}, keywords={Game theory Network games Phase transition}, doi={10.1007/978-3-031-23141-4_20} }- Abhishek Shende
Deepanshu Vasal
Sriram Vishwanath
Year: 2023
A Phase Transition in Large Network Games
GAMENETS
Springer
DOI: 10.1007/978-3-031-23141-4_20
Abstract
In this paper, we use a model of large random network game where the agents plays selfishly and are affected by their neighbors, to explore the conditions under which the Nash equilibrium (NE) of the game is affected by a perturbation in the network. We use a phase transition phenomenon observed in finite rank deformations of large random matrices, to study how the NE changes on crossing critical threshold points. Our main contribution is as follows: when the perturbation strength is greater than a critical point, it impacts the NE of the game, whereas when this perturbation is below this critical point, the NE remains independent of the perturbation parameter. This demonstrates a phase transition in NE which alludes that perturbations can affect the behavior of the society only if their strength is above a critical threshold. We provide numerical examples for this result and present scenarios under which this phenomenon could potentially occur in real world applications.
