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| Abstract |
The conjugate point was introduced by Jacobi to derive a sufficient optimality condition for a variational problem. One of the authors defined the conjugate point for an extremal problem in R^n. The k...ey of the conjugate point is a coalition of variables. Namely, when there exists a conjugate point for a stationary solution x ∊ R^n, the solution is improved by suitably changing some of the variables. This fact leads us to a cooperative game. One of the solution concepts for cooperative games is the Shapley value. It evaluates player's contribution in the cooperative game. However, its calculation is usually very hard. The purpose of this paper is to provide a cooperative game, which we call the conjugate-point game, whose Shapley value can be explicitly computed.show more
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