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Price of Anarchy in Sequencing Situations and the Impossibility to Coordinate

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  • Herbert Hamers
  • Flip Klijn
  • Marco Slikker

Abstract

Scheduling jobs of decentralized decision makers that are in competition will usually lead to cost inefficiencies. This cost inefficiency is studied using the Price of Anarchy (PoA), i.e., the ratio between the worst Nash equilibrium cost and the cost attained at the centralized optimum. First, we provide a tight upperbound for the PoA that depends on the number of machines involved. Second, we show that it is impossible to design a scheduled-based coordinating mechanism in which a Nash equilibrium enforces the centralized or first best optimum. Finally, by simulations we illustrate that on average the PoA is relatively small with respect to the established tight upperbound.

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Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 709.

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Date of creation: Aug 2013
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Handle: RePEc:bge:wpaper:709

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Keywords: sequencing situations; outsourcing; first best solution; game theory; price of anarchy; coordinating mechanism;

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  1. Heydenreich Birgit & Müller, Rudolf & Uetz, Marc, 2006. "Decentralization and Mechanism Design for Online Machine Scheduling," Research Memorandum 007, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Yossi Bukchin & Eran Hanany, 2007. "Decentralization Cost in Scheduling: A Game-Theoretic Approach," Manufacturing & Service Operations Management, INFORMS, vol. 9(3), pages 263-275, October.
  3. George L. Vairaktarakis, 2013. "Noncooperative Games for Subcontracting Operations," Manufacturing & Service Operations Management, INFORMS, vol. 15(1), pages 148-158, September.
  4. Tolga Aydinliyim & George L. Vairaktarakis, 2010. "Coordination of Outsourced Operations to Minimize Weighted Flow Time and Capacity Booking Costs," Manufacturing & Service Operations Management, INFORMS, vol. 12(2), pages 236-255, January.
  5. Curiel, Imma & Pederzoli, Giorgio & Tijs, Stef, 1989. "Sequencing games," European Journal of Operational Research, Elsevier, vol. 40(3), pages 344-351, June.
  6. Estevez Fernandez, M.A. & Borm, P.E.M. & Calleja, P. & Hamers, H.J.M., 2004. "Sequencing Games with Repeated Players," Discussion Paper 2004-128, Tilburg University, Center for Economic Research.
  7. Manipushpak Mitra & Roland Hain, 2001. "Simple Sequencing Problems with Interdependent Costs," Bonn Econ Discussion Papers bgse20_2001, University of Bonn, Germany.
  8. van den Nouweland, Anne & Krabbenborg, Marc & Potters, Jos, 1992. "Flow-shops with a dominant machine," European Journal of Operational Research, Elsevier, vol. 62(1), pages 38-46, October.
  9. Curiel, I. & Pederzoli, G. & Tijs, S.H., 1989. "Sequencing games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154243, Tilburg University.
  10. Curiel, I. & Potters, J.A.M. & Rajendra Prasad, V. & Tijs, S.H. & Veltman, B., 1994. "Sequencing and cooperation," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154192, Tilburg University.
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