February 7, 2024 – 3 PM
The Stable Marriage Problem: properties and models
In this talk, I will begin by providing an overview of the Stable Marriage Problem (SMP): a game-theoretical model that addresses the stable matching of individuals based on their preference lists. Initially introduced by mathematicians Gale and Shapley in 1962, the SMP has attracted interest across various fields, including economics, biology, and statistical physics. I will discuss its fundamental properties and highlight its multidisciplinary influence and advancements.
Following this, I will introduce an evolutionary model representing the dynamic counterpart of the SMP. This model examines how agents interact locally and selfishly to maximize their benefits and explores whether these local dynamics inhibit agents from achieving the stable solution in the classical SMP. I will present analytical findings that indicate considerable deviations from both the ground and stable states, influenced by factors such as the number of agents and the symmetry of their preference lists.