Question

Prove that in a mixed strategy Nash equilibrium of a finite strategic game, all the pure strategies that are assigned positive probabilities must have the same expected payoff.

Answer 1

Answer:Finite means limited in size.In nash equilibrium scenario we can say it "finite strategic games".It means players have finite strategies,players also need to be certain size or number.This theory don't applicable in every scenario It might be possible infinite players participate in games.Theorm only confirm that Nash Equilibrium exists in given condition which is not shocking.Cordination game and Stag hunt some of the examples we can put.Suppose mixed strategy is a best response then everytime each pure strategies is a best response.

Just assume there only one pure strategy it would be allocate to best return mix that provides a lower payoff.If there is more than one pure strategies we would be pick lower expected payoff.If i wipe out low-yield strategy from my mix,my expected pay off gets high.But original mixed strategy not worthy as we can find about new mixed strategy.So here this comes out as disagreement.