Dynamic realization games in newsvendor inventory centralization

M. Dror, L. A. Guardiola, A. Meca, J. Puerto

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Consider a set N of n (> 1) stores with single-item and single-period nondeterministic demands like in a classic newsvendor setting with holding and penalty costs only. Assume a risk-pooling single-warehouse centralized inventory ordering option. Allocation of costs in the centralized inventory ordering corresponds to modelling it as a cooperative cost game whose players are the stores. It has been shown that when holding and penalty costs are identical for all subsets of stores, the game based on optimal expected costs has a non empty core (Hartman et al. 2000, Games Econ Behav 31:26-49; Muller et al. 2002, Games Econ Behav 38:118-126). In this paper we examine a related inventory centralization game based on demand realizations that has, in general, an empty core even with identical penalty and holding costs (Hartman and Dror 2005, IIE Trans Scheduling Logistics 37:93-107). We propose a repeated cost allocation scheme for dynamic realization games based on allocation processes introduced by Lehrer (2002a, Int J Game Theor 31:341-351). We prove that the cost subsequences of the dynamic realization game process, based on Lehrer's rules, converge almost surely to either a least square value or the core of the expected game. We extend the above results to more general dynamic cost games and relax the independence hypothesis of the sequence of players' demands at different stages.

Original languageEnglish (US)
Pages (from-to)139-153
Number of pages15
JournalInternational Journal of Game Theory
Volume37
Issue number1
DOIs
StatePublished - Apr 1 2008

Keywords

  • Allocation process
  • Cooperative game
  • Core
  • Dynamic realization games
  • Least square value
  • Newsvedor centralization game

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (miscellaneous)
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

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