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A Linear Programming Framework for Network Games

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  • A.B. Gamble
  • A.I. Pazgal

Abstract

In this paper we present a linear programming game that is motivated by the assignment game of Shapley and Shubik. This new game is a very natural generalization of many of the network optimization games that have been well studied in the past. We first show that for this general class of games the core is nonempty. In fact any dual optimal solution of the underlying linear programming probem gives rise to a core allocation. We also show that for a particular subclass of games (which include the assignment, max flow and location games) the core exactly coincides with the set of optimal dual solutions. Additionally we study the relationship between this linear programming game and the production game of Owen.

Suggested Citation

  • A.B. Gamble & A.I. Pazgal, 1995. "A Linear Programming Framework for Network Games," Discussion Papers 1119, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:1119
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    References listed on IDEAS

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    1. Ehud Kalai & Eitan Zemel, 1980. "On Totally Balanced Games and Games of Flow," Discussion Papers 413, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Dov Samet & Eitan Zemel, 1984. "On the Core and Dual Set of Linear Programming Games," Mathematics of Operations Research, INFORMS, vol. 9(2), pages 309-316, May.
    3. Pradeep Dubey & Lloyd S. Shapley, 1982. "Totally Balanced Games Arising from Controlled Programming Problems," UCLA Economics Working Papers 262, UCLA Department of Economics.
    4. Curiel, I. & Tijs, S.H., 1986. "Assignment games and permutation games," Other publications TiSEM c9a47c3b-28d3-4874-b0a2-f, Tilburg University, School of Economics and Management.
    5. Ehud Kalai & Eitan Zemel, 1982. "Generalized Network Problems Yielding Totally Balanced Games," Operations Research, INFORMS, vol. 30(5), pages 998-1008, October.
    6. Xiaotie Deng & Christos H. Papadimitriou, 1994. "On the Complexity of Cooperative Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 19(2), pages 257-266, May.
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    Cited by:

    1. Mariusz Kaleta & Eugeniusz Toczyłowski, 2009. "A cost allocation framework for LP and GLP games," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 19(4), pages 27-46.
    2. Mariusz Kaleta & Eugeniusz Toczylowski, 2009. "A cost allocation framework for lp and glp games," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, vol. 4, pages 27-46.

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