Cooperative game analysis of retail space-exchange problems

Mingming LENG, Mahmut PARLAR, Dengfeng ZHANG

Research output: Journal PublicationsJournal Article (refereed)

5 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)393-404
Number of pages12
JournalEuropean Journal of Operational Research
Volume232
Issue number2
Early online date22 Jul 2013
DOIs
Publication statusPublished - 16 Jan 2014

Fingerprint

Cooperative Game
Profitability
Bargaining
Profit
Shapley Value
Coalitions
Retail
Cooperative game
Game analysis
Retailers
Characteristic Function
Excess
Game
Resources

Keywords

  • Retail space-exchange
  • Bargaining power
  • Generalized Nash bargaining scheme
  • Weighted Shapley value

Cite this

LENG, Mingming ; PARLAR, Mahmut ; ZHANG, Dengfeng. / Cooperative game analysis of retail space-exchange problems. In: European Journal of Operational Research. 2014 ; Vol. 232, No. 2. pp. 393-404.
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Cooperative game analysis of retail space-exchange problems. / LENG, Mingming; PARLAR, Mahmut; ZHANG, Dengfeng.

In: European Journal of Operational Research, Vol. 232, No. 2, 16.01.2014, p. 393-404.

Research output: Journal PublicationsJournal Article (refereed)

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N2 - 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.

AB - 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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