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A Game Theoretical Approach to Sharing Penalties and Rewards in Projects


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  • Estevez Fernandez, M.A.

    (Tilburg University, Center for Economic Research)


This paper analyzes situations in which a project consisting of several activities is not realized according to plan. If the project is expedited, a reward arises. Analogously, a penalty arises if the project is delayed. This paper considers the case of arbitrary monotonic 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 corresponding cooperative project game determines a set of stable allocations of the total reward (penalty). In the definition of project games, surplus (cost) sharing mechanisms are used to take into account the specific characteristics of the reward (penalty) function at hand. It turns outs 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 Tilburg University, Center for Economic Research in its series Discussion Paper with number 2008-84.

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Date of creation: 2008
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Handle: RePEc:dgr:kubcen:200884

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Keywords: Project planning; delay; expedition; cost sharing mechanism; surplus sharing mechanism; bankruptcy problems; taxation problems; cooperative game; core;

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  1. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September.
  2. 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.
  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. Nalini Dayanand & Rema Padman, 2001. "Project Contracts and Payment Schedules: The Client's Problem," Management Science, INFORMS, vol. 47(12), pages 1654-1667, December.
  5. 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.
  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. 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.
  8. Shenhar, Aaron J. & Dvir, Dov, 1996. "Toward a typological theory of project management," Research Policy, Elsevier, vol. 25(4), pages 607-632, June.
  9. Brânzei, R. & Ferrari, G. & Fragnelli, V. & Tijs, S.H., 2002. "Two approaches to the problem of sharing delay costs in joint projects," Open Access publications from Tilburg University urn:nbn:nl:ui:12-91324, Tilburg University.
  10. 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.
  11. Moulin, Herve, 1987. "Egalitarian-Equivalent Cost Sharing of a Public Good," Econometrica, Econometric Society, vol. 55(4), pages 963-76, July.
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