This is the bargaining question for Game Theory.

Consider a bargaining set S

Exercise 5.2 Consider a bargaining set S with threat point (0,0). Let a > 0, b > 0, and let S' = {(au,bv) | (u,v) E S}. The set S' is the set of utility pairs in S rescaled by a for player I and by b for player 1]. Recall that one axiomatic property of the bargaining solution is independence from these scale factors. Show that the Nash product fulls this property, that is, the Nash bargaining solution from S obtained by maximising the Nash product re-scales to become the solution for S'. Note: Don't panic! This is extremely easy once you state in the right way what it means that something maximises something. You may nd it useful to consider rst the simpler case b = 1