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A Game Theoretical Approach to Sharing Penalties and Rewards in Projects

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  • Arantza Est�vez-Fern�ndez

    (VU University Amsterdam)

Abstract

This paper analyzes situations in which a project consisting of several activities is not realized according to plan. Ifthe project is expedited, a reward arises. Analogously, a penalty arises if the project is delayed. This paper considersthe case of arbitrary nondecreasing reward and penalty functions on the total expedition and delay, respectively.Attention is focused on how to divide the total reward (penalty) among the activities: the core of a correspondingcooperative project game determines a set of stable allocations of the total reward (penalty). In the definition ofproject games, surplus (cost) sharing mechanisms are used to take into account the specific characteristics of thereward (penalty) function at hand. It turns out that project games are related to bankruptcy and taxation games.This relation allows us to establish the nonemptiness of the core of project games.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 09-090/1.

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Date of creation: 20 Oct 2009
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Handle: RePEc:dgr:uvatin:20090090

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Keywords: Project planning; delay; expedition; cost sharing mechanism; surplus sharing mechanism; bankruptcy;

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  1. Brânzei, R. & Ferrari, G. & Fragnelli, V. & Tijs, S.H., 2001. "Two Approaches to the Problem of Sharing Delay Costs in Joint Projects," Discussion Paper 2001-22, Tilburg University, Center for Economic Research.
  2. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 9(2), pages 139-199, December.
  3. Estevez Fernandez, M.A. & Borm, P.E.M. & Hamers, H.J.M., 2005. "Project Games," Discussion Paper 2005-91, Tilburg University, Center for Economic Research.
  4. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September.
  5. Shenhar, Aaron J. & Dvir, Dov, 1996. "Toward a typological theory of project management," Research Policy, Elsevier, vol. 25(4), pages 607-632, June.
  6. Koster, M.A.L., 1999. "Cost Sharing in Production Situations and Network Exploitation," Open Access publications from Tilburg University urn:nbn:nl:ui:12-80718, Tilburg University.
  7. Moulin, Herve, 1987. "Egalitarian-Equivalent Cost Sharing of a Public Good," Econometrica, Econometric Society, vol. 55(4), pages 963-76, July.
  8. Nalini Dayanand & Rema Padman, 2001. "Project Contracts and Payment Schedules: The Client's Problem," Management Science, INFORMS, vol. 47(12), pages 1654-1667, December.
  9. Weglarz, Jan & Józefowska, Joanna & Mika, Marek & Waligóra, Grzegorz, 2011. "Project scheduling with finite or infinite number of activity processing modes - A survey," European Journal of Operational Research, Elsevier, vol. 208(3), pages 177-205, February.
  10. Hartmann, Sönke & Briskorn, Dirk, 2010. "A survey of variants and extensions of the resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 207(1), pages 1-14, November.
  11. Rolf H. Möhring & Andreas S. Schulz & Frederik Stork & Marc Uetz, 2003. "Solving Project Scheduling Problems by Minimum Cut Computations," Management Science, INFORMS, vol. 49(3), pages 330-350, March.
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