Let ?1 and ?2 be two solution concepts for the family of bargaining games F. Define another solution concept ? for the family of bargaining games F as follows:
Ψ(S, d) = 1/2 Ψ1(S, d) + 1/2 Ψ2(S, d).
For each of the following properties, prove or disprove the following claim: if ?1 and ?2 satisfy the property, then the solution concept ? also satisfies the same property
(a) Symmetry.
(b) Efficiency.
(c) Independence of irrelevant alternatives.
(d) Covariance under positive affine transformations.