Social Networks and Stable Matchings in the Job Market

Abstract

Abstract. In this paper we introduce and study a model that considers the job market as a two-sided matching market, and accounts for the importance of social contacts in finding a new job. We assume that workers learn only about positions in firms through social contacts. Given that information structure, we study both static properties of what we call locally stable matchings, a solution concept derived from stable matchings, and dynamic properties through a reinterpretation of Gale-Shapley's algorithm as myopic best response dynamics.We prove that, in general, the set of locally stable matching strictly contains that of stable matchings and it is in fact NP-complete to determine if they are identical. We also show that the lattice structure of stable matchings is in general absent. Finally, we focus on myopic best response dynamics inspired by the Gale-Shapley algorithm. We study the efficiency loss due to the informational constraints, providing both lower and upper bounds.

Analysis of stochastic matching markets

“…This implies that any ergodic set (which is called absorbing set in [14] and [20]) of the corresponding Markov chain must contain some of the above matchings. Constructing this instance in PRISM, we find there are 308 matchings and a single ergodic set which consists of the matchings {M 4 , M 5 , M 6 , M 7 }, where M 7 = {(1, 2), (3,8), (4,6), (5, 7)}. This corresponds to the results presented in [20].…”

“…Roth and Vande Vate [30] prove that, given an instance of sm, starting from any unstable matching we can always obtain a stable matching by successively satisfying blocking pairs. 3 Diamantoudi et al [8] show that a similar result holds for the roommates problem, namely, for a given instance of sr that admits a stable matching and starting from any unstable matching, one can obtain a stable matching by successively satisfying blocking pairs. This essentially means that the corresponding stochastic processes (to be defined in Section 3) are absorbing Markov chains (for more details of these stochastic processes see, e.g.…”

“…This is a realistic assumption in case of some real P2P networks. Finally, Arcaute and Vassilvitskii [3] and Hoefer [12] studied similar stochastic market processes with the extra feature of an underlying social network that dynamically determine the accessible partners and the so-called locally stable matchings.…”

Locally Stable Marriage with Strict Preferences

“…Locally stable matchings were introduced by Arcaute and Vassilvitskii [5] in a two-sided job-market model, in which links exist only among one partition. The paper uses strong uniformity assumptions on the preference lists and addresses the lattice structure for stable matchings and a local GaleShapley algorithm.…”

“…A prominent and popular approach in all these areas is stable matching, as it captures aspects like distributed control and rationality of participants that arise in many assignment problems today. A variety of allocation problems in markets can be analyzed within the context of two-sided stable matching, e.g., the assignment of jobs to workers [5,28], organs to patients [36], or general buyers to sellers. In addition, stable marriage problems have been successfully used to study distributed resource allocation problems in networks [3,17,33].…”