Two-Sided Matching with Bounded Rationality: A Stochastic Framework for Personnel Selection

Saeed Najafi-Zangeneh, Naser Shams-Gharneh () and Olivier Gossner
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Saeed Najafi-Zangeneh: Industrial Engineering Department, Amirkabir University of Technology, Tehran 1591634311, Iran
Naser Shams-Gharneh: CNRS-CREST, Ecole Polytechnique and London School of Economics, 91120 Palaiseau, France
Olivier Gossner: CNRS-CREST, Ecole Polytechnique and London School of Economics, 91120 Palaiseau, France

Mathematics, 2025, vol. 13, issue 19, 1-26

Abstract: Personnel selection represents a two-sided matching problem in which firms compete for qualified candidates by designing job-offer packages. While traditional models assume fully rational agents, real-world decision-makers often face bounded rationality due to limited information and cognitive constraints. This study develops a matching framework that incorporates bounded rationality through the Quantal Response Equilibrium, where firms and candidates act as probabilistic rather than perfect optimizers under uncertainty. Using Maximum Likelihood Estimation and organizational hiring data, we validate that both sides display bounded rational behavior and that rationality increases as the selection process advances. Building on these findings, we propose a two-stage stochastic optimization approach to determine optimal job-offer packages that balance organizational policies with candidate competencies. The optimization problem is solved using particle swarm optimization, which efficiently explores the solution space under uncertainty. Data analysis reveals that only 23.10% of low-level hiring decisions align with rational choice predictions, compared to 64.32% for high-level positions. In our case study, bounded rationality increases package costs by 26%, while modular compensation packages can reduce costs by up to 25%. These findings highlight the cost implications of bounded rationality, the advantages of flexible offers, and the systematic behavioral differences across job levels. The framework provides theoretical contributions to matching under bounded rationality and offers practical insights to help organizations refine their personnel selection strategies and attract suitable candidates more effectively.

Keywords: two-sided matching; quantal response equilibrium; bounded rationality; two-stage stochastic approach; particle swarm optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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