Question

True or false: if a 2 x 2 matrix game has a strongly dominated strategy, it has no mixed strategy equilibrium. In a brief sentence say why that is true, or give a counterexample.

Answer 1

This statement is true . In a 2×2 matrix game if a strongly dominated strategy exists , there must be only one Nash equilibrium. The oddity of the equilibrium would make sure that the perceived Nash equilibrium is of pure strategy only , not of mixed strategy.