Asymmetric sequential search under incomplete information

• Date: 01 June 2018
• Author: Yizhaq Minchuk,Aner Sela
• DOI: http://doi.org/10.1111/jems.12242
• Published date: 01 June 2018

Received: 1 August 2016 Revised: 11 January 2018 Accepted: 11 January 2018

DOI: 10.1111/jems.12242

ORIGINAL ARTICLE

Asymmetric sequential search under incomplete information

Yizhaq Minchuk1Aner Sela2

1Department of Industrial Engineering

and Management, Shamoon College

of Engineering, Beer-Sheva, Israel

(Email: yizhami@sce.ac.il)

2Department of Economics, Ben-Gurion

Universityof the Negev, Beer-Sheva, Israel

(Email: anersela@bgu.ac.il)

Abstract

We study a multistage sequential search model with 𝑛agents who compete for one

job. The agents arrive sequentially, each one in a different stage.The agents' abilities,

which are private information, are derived from heterogeneous distribution functions.

In each stage, the designer chooses an ability threshold. If an agent has a higher ability

than the threshold in the stage in which he arrives, he gets the job and the search is

over.The agent's ability is not revealed when he wins the job and the designer has only

an estimation of this ability according to the threshold placed by him. We analyze the

optimal ability thresholds imposed by the designer who wishes to maximize the ability

estimation of the agent who gets the job net of the search cost. Wealso investigate the

relation between the optimal ability thresholds as well as the optimal order of agents

in all stages according to the agents' distributions of abilities.

1INTRODUCTION

A well-known economic search problem concerns the academic job market. It usually takes the following form: New Ph.D.

candidates are sequentially invited for an examination that usually includes an interview and a presentation of the candidate's

job market paper.The candidates's abilities are unknown before the examinationand as t heycome from different universities and

sometimes from different countries, their distributions of abilities are asymmetric and are not even correlated. If the candidate

successfully passes the examination, the search process ends. However, the department must bear in mind that because of the

intense competition between the numerous number of universities, when a candidate does not get an immediate job offer, there

is a high probability that in the meantime he might accept an offer form a different department. This example conveys the idea

of the sequential search that we deal with in this paper.

We study a simple model of assignment in which𝑛asymmetr ic agentscompete for one job. The agents arrive sequentially one

after the other. The designer wishes to give the job to the agent with the highest ability, but he also has to take into account that

he has a search cost 𝑐>0in each stagesuch that his incentive is to shorten the lengt h of the search.The designer does not know

the agents' abilities, but does know their distribution functions that are heterogeneous. In the first stage, the designer chooses an

ability threshold. Then, the first agent arrives and if his ability is higher than or equal to the ability threshold imposed by the

designer he wins the job and the 𝑛-stage sequential search is over. Otherwise, in the second stage, the designer again imposes

an ability threshold that is not necessarily equal to the previous one. Then, the second agent arrives, and if his ability is higher

than or equal to the second ability threshold, he wins the job and so on. If, on the other hand, all the agents' abilities are lower

than their ability thresholds, no one wins the job and the payoff of the designer is negative and is equal to the sum of the search

costs in all the stages. The designer knows whether or not an agent wins the job and he also knows that his ability is higher than

the ability threshold he faced, but he does not exactly know the ability of this agent. As the higher the ability threshold of the

winner is, the higher is his expected ability, the designer will want to maximize a monotonic function of the threshold that the

winner faced (net of the search cost).

We begin by investigating the relation between the ability thresholds imposed by the designer in the 𝑛stages of the sequential

search.1As we are dealing with a model with a finite number stages, in the late stages the designer might compromise about

J Econ Manage Strat. 2018;27:315–325. © 2018 WileyPeriodicals, Inc. 315wileyonlinelibrary.com/journal/jems