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Prove that there exists a unique efficient alternative

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Reference no: EM131333098

Let (S, d) ∈ F be a bargaining game.

(a) Prove that there exists a unique efficient alternative in S minimizing the absolute value |(x1 - d1) - (x2 - d2)|. Denote this alternative by x∗.

Let Y be the collection of efficient alternatives y in S satisfying the property that the sum of their coordinates y1 + y2 is maximal.

(b) Show that the Nash solution N (S, d) is on the efficient boundary between x∗ and the point in Y that is closest to x. In particular, if x∗ ∈ Y then x∗ = N (S, d).

Reference no: EM131333098

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