A LARGE POPULATION, GAME THEORETIC MODEL OF JOB-SEARCH WITH DISCOUNTING

Abstract

This paper considers a large population, game theoretic job-search problem, in which the ratio of job searchers to jobs is α. There are n distinct types of jobs, each with an associated value. Each searcher can only accept one job and cannot recall a job previously rejected. Once a searcher accepts a job, no other searcher can obtain that particular job. The reward to a searcher is taken to be the value of the job he/she obtains discounted by a factor of e-γt, where t is the time spent searching and γ > 0. It is shown that a unique evolutionarily stable strategy (ESS) exists for such problems. Two iterative algorithms for approximating the ESS are considered. In the case where there are only two types of job, the ESS can be calculated directly.