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The job search problem as an employer–candidate game

Published online by Cambridge University Press:  14 July 2016

J. M. Mcnamara  and
E. J. Collins
J. M. Mcnamara
Affiliation:
University of Bristol
E. J. Collins*
Affiliation:
University of Bristol
*
∗ Postal address for both authors: School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK.
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Abstract

In the standard job search problem a single decision-maker (say an employer) has to choose from a sequence of candidates of varying fitness. We extend this formulation to allow both employers and candidates to make choices. We consider an infinite population of employers and an infinite population of candidates. Each employer interviews a (possibly infinite) sequence of candidates for a post and has the choice of whether or not to offer a candidate the post. Each candidate is interviewed by a (possibly infinite) sequence of employers and can accept or reject each offer. Each employer seeks to maximise the fitness of the candidate appointed and each candidate seeks to maximise the fitness of their eventual employer. We allow both discounting and/or a cost per interview. We find that there is a unique pair of policies (for employers and candidates respectively) which is in Nash equilibrium. Under these policies each population is partitioned into a finite or countable sequence of subpopulations, such that an employer (candidate) in a given subpopulation ends up matched with the first candidate (employer) encountered from the corresponding subpopulation. In some cases the number of non-empty subpopulations in the two populations will differ and some members of one population will never be matched.

Keywords

SECRETARY PROBLEMMATE CHOICENASH EQUILIBRIUM
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 4 , December 1990 , pp. 815 - 827
Copyright
Copyright © Applied Probability Trust 1990 

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References

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