, Volume 15, Issue 2, pp 322–340 | Cite as

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

Original Paper


We introduce a new class of totally balanced cooperative TU games, namely p-additive games. It is inspired by the class of inventory games that arises from inventory situations with temporary discounts (Toledo Ph.D. thesis, Universidad Miguel Hernández de Elche, 2002) and contains the class of inventory cost games (Meca et al. Math. Methods Oper. Res. 57:481–493, 2003). It is shown that every p-additive game and its corresponding subgames have a nonempty core. We also focus on studying the character of concave or convex and monotone p-additive games. In addition, the modified SOC-rule is proposed as a solution for p-additive games. This solution is suitable for p-additive games, since it is a core-allocation which can be reached through a population monotonic allocation scheme. Moreover, two characterizations of the modified SOC-rule are provided.


p-additive games Inventory situations with temporary discounts Totally balanced cooperative TU games Modified SOC-rule Core-allocations 

Mathematics Subject Classification (2000)

91A12 90B05 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bondareva ON (1963) Some applications of linear programming methods to the theory of cooperative games. Probl Kibern 10:119–139, in Russian Google Scholar
  2. Granot DG, Huberman G (1982) The relation between convex games and minimal cost spanning tree games: a case for permutationally convex games. SIAM J Algebraic Discrete Methods 3:288–292 CrossRefGoogle Scholar
  3. Meca A, García-Jurado I, Borm PEM (2003) Cooperation and competition in inventory games. Math Methods Oper Res 57:481–493 Google Scholar
  4. Meca A, Timmer J, García-Jurado I, Borm PEM (2004) Inventory games. Eur J Oper Res 156:127–139 CrossRefGoogle Scholar
  5. Mosquera MA, García-Jurado I, Fiestras-Janeiro MG (2007) A note on coalitional manipulation and centralized inventory management. Ann Oper Res (to appear) Google Scholar
  6. Shapley LS, (1953) A value for n-person games. In: Kuhn H, Tucker AW (eds) Contributions to the theory of games II. Princeton University Press, Princeton, pp 307–317 Google Scholar
  7. Shapley LS (1967) On balanced sets and cores. Nav Res Logist Quarterly 14:453–460 CrossRefGoogle Scholar
  8. Shapley LS (1971) Cores of convex games. Int J Game Theory 1:11–26 CrossRefGoogle Scholar
  9. Sprumont Y (1990) Population monotonic allocation schemes for cooperative games with transferable utility. Games Econ Behav 2:378–394 CrossRefGoogle Scholar
  10. Tersine RJ (1994) Principles of inventory and material management. Elsevier/North-Holland, Amsterdam Google Scholar
  11. Toledo A (2002) Problemas de inventario con descuento desde la perspectiva de la teoría de juegos. Ph.D. thesis, Universidad Miguel Hernández de Elche Google Scholar

Copyright information

© Sociedad de Estadística e Investigación Operativa 2007

Authors and Affiliations

  1. 1.Operations Research CenterUniversidad Miguel Hernández, Edificio TorretamaritElcheSpain
  2. 2.Dpto. de Estudios de COHISPANIACompañía Hispania de Tasaciones y Valoraciones S.A.MadridSpain

Personalised recommendations