A Community Compromised Approach to Combinatorial Coalition Problem

Buyer coalition with a combination of items is a group of buyers joining together to purchase a combination of items with a larger discount. The primary aim of existing buyer coalition with a combination of items research is to generate a large total discount. However, the aim is hard to achieve because this research is based on the assumption that each buyer completely knows other buyers' information or at least one buyer knows other buyers' information in a coalition by exchange of information. These assumption contrast with the real world environment where buyers join a coalition with incomplete information, i.e., they concerned only with their expected discounts. Therefore, this paper proposes a new buyer community coalition formation with a combination of items scheme, called the Community Compromised Combinatorial Coalition scheme, under such an environment of incomplete information. In order to generate a larger total discount, after buyers who want to join a coalition propose their minimum required saving, a coalition structure that gives a maximum total retail prices is formed. Then, the total discount division of the coalition is divided among buyers in the coalition depending on their minimum required saving and is a Pareto optimal. In mathematical analysis, we compare concepts of this scheme with concepts of the existing buyer coalition scheme. Our mathematical analysis results show that the total discount of the coalition in this scheme is larger than that in the existing buyer coalition scheme.