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Cooperative game analysis of retail space-exchange problems
European Journal of Operational Research
  • Mingming LENG, Department of Computing and Decision Sciences, Faculty of Business, Lingnan University
  • Mahmut PARLAR, McMaster University
  • Dengfeng ZHANG, PingAn Bank, No. 5047 East Shen Nan Road, Shenzhen
Document Type
Journal article
Publication Date
Elsevier BV
  • Retail space-exchange; Bargaining power; Generalized Nash bargaining scheme; Weighted Shapley value

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.

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Citation Information
Leng, M., Parlar, M., & Zhang, D. (2014). Cooperative game analysis of retail space-exchange problems. European Journal of Operational Research, 232(2), 393-404. doi: 10.1016/j.ejor.2013.07.013