Assignment
3 Questions about Cigarette Advertising.
Philip Morris and R. J. Reynolds are the largest cigarette manufacturers.
To simplify our analysis, assume the cigarette market is a duopoly, i.e., Philip Morris and R. J. Reynolds are the only manufacturers in the market.
Suppose the annual demand for cigarettes is 4 billion packs, and each pack can generate a profit of $1 dollar (before paying any advertising expenses).
The market share of a company depends on how much it spends on advertising relative to what its rival spends. Let AP denote the advertising expenditures of Philip Morris and AR denote the advertising expenditures of R. J. Reynolds.
Assume that the market share of Philip Morris equals
Ap/Ap+Ar
Accordingly, the profit (payoff) of Philip Morris is equal to $1* 4billion* Ap/Ap+Ar -Ap and the profit (payoff) of R. J. Reynolds is $1* 4billion* Ar/Ap+Ar -Ar:
Assume there are four levels of advertising: $200 million, $400 million, $600 million, and $800 million.
(a) Construct the payoff matrix for this advertising game.
(b) Find all Nash equilibria of this game.
(c) Suppose now the government bans cigarette advertising on TV, and hence makes it infeasible for the cigarette companies to spend $800 million on advertising. Find all Nash equilibria in this new advertising game. Are Philip Morris and R. J. Reynolds better or worse from the ban?