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Staffing problems with local network externalities

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  • Xiong, Yifan
  • Li, Ziyan

Abstract

This study examines how an organization assigns agents to interactive jobs embedded in a network. We employ a two-stage linear quadratic game with local complementarities, in which the underlying network represents the interrelated jobs that an organization seeks for staff. Under the assumption that employees have heterogeneous abilities, the organization assigns individuals to jobs in an attempt to maximize aggregate effort or aggregate payoff. Two problems are considered when maximizing the total effort. First, we assume that each agent’s ability is single dimensional and show that the planner should match the ordinal ranking of an agent’s ability level to the job indexed by the same ordinal level in the centrality ranking. Second, we assume that agents are experts in different jobs, implying that each agent’s ability is multidimensional. We show that the optimal staffing problem is essentially an assignment problem that can be solved by the Hungarian algorithm in polynomial time. Finally, we consider an optimal staffing scenario to maximize the total payoff. Finding all permutations of n agents has high computation time complexity. To solve this problem, we design a heuristic algorithm.

Suggested Citation

  • Xiong, Yifan & Li, Ziyan, 2022. "Staffing problems with local network externalities," Economics Letters, Elsevier, vol. 212(C).
  • Handle: RePEc:eee:ecolet:v:212:y:2022:i:c:s0165176522000386
    DOI: 10.1016/j.econlet.2022.110338
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    References listed on IDEAS

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    1. H. W. Kuhn, 1955. "The Hungarian method for the assignment problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 2(1‐2), pages 83-97, March.
    2. Coralio Ballester & Antoni Calvó-Armengol & Yves Zenou, 2006. "Who's Who in Networks. Wanted: The Key Player," Econometrica, Econometric Society, vol. 74(5), pages 1403-1417, September.
    3. Coralio Ballester & Antoni Calvó-Armengol & Yves Zenou, 2010. "Delinquent Networks," Journal of the European Economic Association, MIT Press, vol. 8(1), pages 34-61, March.
    4. Shai Bernstein & Eyal Winter, 2012. "Contracting with Heterogeneous Externalities," American Economic Journal: Microeconomics, American Economic Association, vol. 4(2), pages 50-76, May.
    5. Amir Ajorlou & Ali Jadbabaie & Ali Kakhbod, 2018. "Dynamic Pricing in Social Networks: The Word-of-Mouth Effect," Management Science, INFORMS, vol. 64(2), pages 971-979, February.
    6. Leo Katz, 1953. "A new status index derived from sociometric analysis," Psychometrika, Springer;The Psychometric Society, vol. 18(1), pages 39-43, March.
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    More about this item

    Keywords

    Network games; Staffing; Matching on networks; Interactions; Complementarities;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D23 - Microeconomics - - Production and Organizations - - - Organizational Behavior; Transaction Costs; Property Rights
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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