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Totally balanced games arising from controlled programming problems

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Abstract

A cooperative game in characteristic-function form is obtained by allowing a number of individuals to esercise partial control over the constraints of a (generally nonlinear) mathematical programming problem, either directly or through committee voting. Conditions are imposed on the functions defining the programming problem and the control system which suffice to make the game totally balanced. This assures a nonempty core and hence a stable allocation of the full value of the programming problem among the controlling palyers. In the linear case the core is closely related to the solutions of the dual problem. Applications are made to a variety of economic models, including the transferable utility trading economies of Shapley and Shubik and a multishipper one-commodity transshipment model with convex cost functions and concave revenue functions. Dropping the assumption of transferable utility leads to a class of controlled multiobjective or ‘Pareto programming’ problems, which again yield totally balanced games.

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Authors and Affiliations

  1. Cowles Foundation for Research in Economics, Yale University, 06520, New Haven, CT, USA

    Pradeep Dubey

  2. Departments of Mathematics and Economics, University of California at Los Angeles, 90024, Los Angeles, CA, USA

    Lloyd S. Shapley

Authors
  1. Pradeep Dubey
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  2. Lloyd S. Shapley
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Dubey, P., Shapley, L.S. Totally balanced games arising from controlled programming problems. Mathematical Programming 29, 245–267 (1984). https://doi.org/10.1007/BF02591996

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  • DOI: https://doi.org/10.1007/BF02591996

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