Prove that set argmaxy is the image of the set argmaxx

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Let (S,c) be a bargaining game, and let (T,d) be the image of (S,c) under the positive affine transformation x #→ ax + b on R2; that is, T = aS + b and d = ac + b.

Prove that the set argmaxy∈T (y₁ - d₁)(y₂ - d₂) is the image of the set argmaxx∈S(x₁ - c₁)(x₂ - c₂) under this transformation.

Reference no: EM131333089

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