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A Path Following Procedure for Finding a Point in the Core of a Balanced N-Person Game

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  • Ludo Van der Heyden

Abstract

A basic theorem in n-person game theory due to Scarf states that a balanced game has a nonempty core. Scarf's proof presents a procedure to find a point in the core of a discrete game, where every coalition disposes of a finite number of alternatives. The proof for a general game follows by passing to the limit. In this paper we present a procedure which works with the characteristic sets in original form. They no longer need to be approximated. The procedure consists in following a finite sequence of possibly nonlinear paths. The framework adopted for this paper is more general than needed to treat the core problem. This enables us to present a unified approach treating the latter problem as well as related problems in linear complementarity theory and fixed point computation.

Suggested Citation

  • Ludo Van der Heyden, 1980. "A Path Following Procedure for Finding a Point in the Core of a Balanced N-Person Game," Cowles Foundation Discussion Papers 575, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:575
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    References listed on IDEAS

    as
    1. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
    2. B. Curtis Eaves & Herbert Scarf, 1976. "The Solution of Systems of Piecewise Linear Equations," Mathematics of Operations Research, INFORMS, vol. 1(1), pages 1-27, February.
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