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Cooperative game analysis of retail space-exchange problems

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  • Leng, Mingming
  • Parlar, Mahmut
  • Zhang, Dengfeng

Abstract

We analyze retail space-exchange problems where two or more retailers exchange their excess retail spaces to improve the utilization of their space resource. We first investigate the two-retailer space exchange problem. In order to entice both retailers with different bargaining powers to exchange their spaces, we use the generalized Nash bargaining scheme to allocate the total profit surplus between the two retailers. Next, we consider the space-exchange problem involving three or more retailers, and construct a cooperative game in characteristic function form. We show that the game is essential and superadditive, and also prove that the core is non-empty. Moreover, in order to find a unique allocation scheme that ensures the stability of the grand coalition, we propose a new approach to compute a weighted Shapley value that satisfies the core conditions and also reflects retailers’ bargaining powers. Our analysis indicates that the space exchange by more retailers can result in a higher system-wide profit surplus and thus a higher allocation to each retailer under a fair scheme.

Suggested Citation

  • Leng, Mingming & Parlar, Mahmut & Zhang, Dengfeng, 2014. "Cooperative game analysis of retail space-exchange problems," European Journal of Operational Research, Elsevier, vol. 232(2), pages 393-404.
    • Handle: RePEc:eee:ejores:v:232:y:2014:i:2:p:393-404
    DOI: 10.1016/j.ejor.2013.07.013
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    2. Masoud Rabbani & Navid Salmanzadeh-Meydani & Amir Farshbaf-Geranmayeh & Vahed Fadakar-Gabalou, 2018. "Profit maximizing through 3D shelf space allocation of 2D display orientation items with variable heights of the shelves," OPSEARCH, Springer;Operational Research Society of India, vol. 55(2), pages 337-360, June.
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    4. Luo, Chunlin & Zhou, Xiaoyang & Lev, Benjamin, 2022. "Core, shapley value, nucleolus and nash bargaining solution: A Survey of recent developments and applications in operations management," Omega, Elsevier, vol. 110(C).
    5. Erick González & Rafael Alejandro Espín & Eduardo Fernández, 2016. "Negotiation Based on Fuzzy Logic and Knowledge Engineering: Some Case Studies," Group Decision and Negotiation, Springer, vol. 25(2), pages 373-397, March.

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