A note on coalitional manipulation and centralized inventory management

Abstract

In this note we deal with inventory games as defined in Meca et al. (Math. Methods Oper. Res. 57:483-491, 2003). In that context we introduce the property of immunity to coalitional manipulation, and demonstrate that the SOC-rule (Share the Ordering Cost) is the unique allocation rule for inventory games which satisfies this property.

Survey of cooperative inventory games and extensions

“…Immunity to such manipulations is relevant in practice. Mosquera et al (2008) demonstrate that the allocation rule p i is immune to coalitional manipulation.…”

“…By adding features to the two games, changing assumptions, and asking pertinent questions, the games become more complex and their analysis more involved. We begin with the EOQ game presented in Meca et al (2004), a note on coalitional manipulation (Mosquera et al, 2008), and proceed with two different versions of a similar game by Anily and Haviv (2007) and Dror and Hartman (2007). We continue with a short summary of economic lot-size games of Van den Heuvel et al (2007) and production-inventory games of Guardiola et al (2008Guardiola et al ( , 2009).…”

“…Definition (Mosquera et al, 2008) Take c a AI U , c b AI M and a non-empty set SCU. c b is an S-manipulation of c a if, for each i S AS:…”

Supply Chain Collaboration

“…Moreover, an alternative characterization of the SOC-rule is provided there. Mosquera et al (2007) introduce the property of immunity to coalition manipulation and demonstrate that the SOC-rule is the unique solution for inventory cost games that satisfies this property. In addition, Meca et al (2004) shows that holding cost games are permutationally concave.…”

p-additive games: a class of totally balanced games arising from inventory situations with temporary discounts

“…Moreover, an alternative characterization of the SOC-rule is provided there. Mosquera et al (2007) introduce the property of immunity to coalition manipulation and demonstrate that the SOC-rule is the unique solution for inventory cost games which satisfies this property. Toledo (2002) analyzes the class of inventory games that arises from inventory problems with special sale prices.…”