A Combinatorial Optimization Model for Transmission of Job Information through Contact Networks

A combinatorial network model is constructed to describe the information structure of job finding in a homogeneous job market. A fundamental distinction is drawn between strong and weak contacts: strong contacts are assumed to have strict priority as recipients of information about the existence of job vacancies, while maintenance of a given strong contact requires more time than does maintenance of a weak contact. Facing a limited time-budget, each individual confronts a tradeoff between these two possible ways of investing time. In the model presently investigated, each individual is assumed to develop his contacts so as to maximize probability of getting some new job in the event that he loses his present job. Concepts of both stability and optimality are defined. It is found that if the probability of becoming jobless is low (u <<1), then a situation where all individuals choose only weak ties ("all-weak network") will be stable and will be a Pareto optimum under the maximizing behavior assumed. Also, all-weak networks are the only Pareto optima in this case. For u near 1, a different situation obtains: now networks containing only strong ties will be stable and all-weak networks will be unstable. In this second limiting case, however, stability and optimality do not coincide: all-strong networks are not Pareto optimal.