Let be a zero-sum matrix game, and let p ′ , p ″ be mixed strategies for Rose and q ′ , q ″ mixed strategies for Colin. Suppose the expected payoff when Rose plays p ′ and Colin plays q ′ is ′ and the expected payoff when Rose plays p ″ and Colin plays q ″ is ″ . If ′ < < ″ , show that there exist mixed strategies p for Rose and q for Colin so that the expected payoff when Rose plays p and Colin plays q is .
I am studying Game Theory: A Playful Introduction Book by Deborah A. Kent and Matthew Jared DeVos. I need to solve this question using only basic concepts like expected payoff, mixed strategy, and Minimax theorem. The question reminds me of the intermediate value property.
Any hints please?