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Biform game: Reflection as a stochastic programming problem

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  • Summerfield, Nichalin S.
  • Dror, Moshe

Abstract

In this paper we examine the biform games modeling framework. More specifically, we recast biform games as two-stage stochastic programming with recourse. The two-stage stochastic programming view of biform games is demonstrated in this paper on an example from Brandenburger and Stuart (2007) regarding a coordination game. We claim that our stochastic programming format for biform games allows for a well established mathematical methodology to enrich the modeling options when applied to biform competitive and cooperative game options.

Suggested Citation

  • Summerfield, Nichalin S. & Dror, Moshe, 2013. "Biform game: Reflection as a stochastic programming problem," International Journal of Production Economics, Elsevier, vol. 142(1), pages 124-129.
    • Handle: RePEc:eee:proeco:v:142:y:2013:i:1:p:124-129
    DOI: 10.1016/j.ijpe.2012.10.021
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    References listed on IDEAS

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    1. Nichalin Suakkaphong & Moshe Dror, 2011. "Managing decentralized inventory and transshipment," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 480-506, December.
    2. Moldovanu, Benny, 1992. "Coalition-proof nash equilibria and the core in three-player games," Games and Economic Behavior, Elsevier, vol. 4(4), pages 565-581, October.
    3. Stuart, Harborne Jr., 2007. "Buyer symmetry in monopoly," International Journal of Industrial Organization, Elsevier, vol. 25(3), pages 615-630, June.
    4. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
    5. Adam Brandenburger & Harborne Stuart, 2007. "Biform Games," Management Science, INFORMS, vol. 53(4), pages 537-549, April.
    6. George B. Dantzig, 1955. "Linear Programming under Uncertainty," Management Science, INFORMS, vol. 1(3-4), pages 197-206, 04-07.
    7. Harborne W. Stuart, Jr., 2005. "Biform Analysis of Inventory Competition," Manufacturing & Service Operations Management, INFORMS, vol. 7(4), pages 347-359, July.
    8. Stuart Jr., Harborne W., 2007. "Creating monopoly power," International Journal of Industrial Organization, Elsevier, vol. 25(5), pages 1011-1025, October.
    9. Summerfield, Nichalin S. & Dror, Moshe, 2012. "Stochastic programming for decentralized newsvendor with transshipment," International Journal of Production Economics, Elsevier, vol. 137(2), pages 292-303.
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    Cited by:

    1. van Beek, Andries & Malmberg, Benjamin & Borm, Peter & Quant, Marieke & Schouten, Jop, 2021. "Cooperation and Competition in Linear Production and Sequencing Processes," Other publications TiSEM fd7a301b-7ef3-4142-835d-a, Tilburg University, School of Economics and Management.
    2. Chenwei Liu & Shuwen Xiang & Yanlong Yang, 2021. "A Biform Game Model with the Shapley Allocation Functions," Mathematics, MDPI, vol. 9(16), pages 1-14, August.
    3. Jia, Fu & Zhang, Shiyuan & Zheng, Xiao-Xue & Choi, Tsan-Ming, 2023. "A novel coordination mechanism to coordinate the multi-agent reverse supply chain with fairness concerns," International Journal of Production Economics, Elsevier, vol. 265(C).
    4. Gupta, Narain & Dutta, Goutam & Fourer, Robert, 2014. "A Multi-Period Two Stage Stochastic Programming Based Decision Support System for Strategic Planning in Process Industries: A Case of an Integrated Iron and Steel Company," IIMA Working Papers WP2014-04-04, Indian Institute of Management Ahmedabad, Research and Publication Department.
    5. Fuentes González, Fabián & van der Weijde, Adriaan Hendrik & Sauma, Enzo, 2020. "The promotion of community energy projects in Chile and Scotland: An economic approach using biform games," Energy Economics, Elsevier, vol. 86(C).
    6. van Beek, Andries & Malmberg, Benjamin & Borm, Peter & Quant, Marieke & Schouten, Jop, 2023. "Competition and cooperation in linear production and sequencing processes," Games and Economic Behavior, Elsevier, vol. 139(C), pages 117-132.

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    Keywords

    Stochastic programming; Biform games;

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