The Stable Marriage Problem: an Interdisciplinary Review from the Physicist's Perspective

Abstract: We present a fascinating model that has lately caught attention among physicists working in complexity related fields. Though it originated from mathematics and later from economics, the model is very enlightening in many aspects that we shall highlight in this review. It is called The Stable Marriage Problem (though the marriage metaphor can be generalized to many other contexts), and it consists of matching men and women, considering preference-lists where individuals express their preference over the members of the opposite gender. This problem appeared for the first time in 1962 in the seminal paper of Gale and Shapley and has aroused interest in many fields of science, including economics, game theory, computer science, etc. Recently it has also attracted many physicists who, using the powerful tools of statistical mechanics, have also approached it as an optimization problem. Here we present a complete overview of the Stable Marriage Problem emphasizing its multidisciplinary aspect, and reviewing the key results in the disciplines that it has influenced most. We focus, in particular, in the old and recent results achieved by physicists, finally introducing two new promising models inspired by the philosophy of the Stable Marriage Problem. Moreover, we present an innovative reinterpretation of the problem, useful to highlight the revolutionary role of information in the contemporary economy.