Cooperative Purchasing with General Discount: A Game Theoretical Approach

Jose A. García-Martínez (), Ana Meca and G. Alexander Vergara
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Jose A. García-Martínez: Departamento de. Estudios Económicos y Financieros, Universidad Miguel Hernández de Elche, 03202 Elche, Spain
Ana Meca: I. U. Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, 03202 Elche, Spain
G. Alexander Vergara: Interuniversity Doctorate in Economics (DEcIDE), I. U. Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, 03202 Elche, Spain

Mathematics, 2022, vol. 10, issue 22, 1-20

Abstract: In some situations, sellers of certain commodities usually provide price discounts for large orders according to a decreasing unit price function. Buyers of such commodities can cooperate and form purchasing groups to benefit from these price discounts. A natural way to allocate the corresponding cost reductions is the equal price rule. We analyze this situation as a cooperative game. We show that when the decreasing unit price function is linear, the equal price rule coincides with the Shapley value and the nucleolus of the cooperative game. However, some buyers may argue that the equal price rule is not acceptable because it favors those who buy just a few units of the product. This can be more problematic when the decreasing unit price function is nonlinear: In that case, the equal price rule loses some of its good properties and it no longer matches the Shapley value or the nucleolus. Unlike the linear case, in this nonlinear case, the Shapley value and nucleolus do not assign the same price to all agents, so there are different price rules. However, they have a computability problem, as both are very laborious to calculate for a large number of agents. To find a suitable alternative, we first study the properties that a different price rule should have in this situation. Second, we propose a family of different price rules that hold those properties and are easy to calculate for a large number of agents. This family of different price rules provides buyers (companies, institutions, consumers, etc.) with an easy-to-implement method which ensures stability in cooperative purchasing.

Keywords: cooperative purchasing; price discounts; equal price rule; different price rules; game theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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