(Optional) Exercises S4 and U4 demonstrate that in
zero-sum games such as the Evert-Navratilova tennis rivalry, changes in a
player’s payoffs can sometimes lead to unexpected or unintuitive changes to her
equilibrium mixture. But what happens to the expected value of the game?
Consider the following general form of a two-player zero-sum game:
Assume that there is no Nash equilibrium in pure
strategies, and assume that a, b, c, and d are all greater than or equal to 0.
Can an increase in any one of a, b, c, or d lead to a lower expected value of
the game for Rowena? If not, prove why not. If so, provide an example.