The Super Bowl, the championship game in U.S. professional football, delivers the largest television audience of the year and as such is an important, but expensive, advertising opportunity for producers of consumer products. Beer brands Miller and Budweiser recognize the benefits of advertising during the Super Bowl but both must decide how much they will spend on Super Bowl advertising. An investment analyst prepared the following payoff matrix:
The numbers in the table are the additional profit that the brewing companies will earn if their budget for Super Bowl advertising is either "low" (a small number of commercials during the Super Bowl), "medium" or "high" (a large number of commercials during Super Bowl). The highlighted figures are the additional profits for Miller, and the non-bolded figures are the additional profits for Budweiser. All of the figures are expressed in millions of dollars. For example, the first cell indicates that if both Budweiser and Miller choose a low advertising budget for the Super Bowl, Miller will earn an additional $60 million of profit and Budweiser will earn an additional $45 million of profit.
Recall that a "dominant strategy" is a strategy that always provides the best outcome, independent of the choice of strategy by the other player.
(a) Does Miller have a dominant strategy? Why or why not?
(b) Does Budweiser have a dominant strategy? Why or why not?
(c) What is the equilibrium for this advertising strategy game? That is, in which cell will the firms end up?