Drug Ads:
A pharmaceutical company (player 1) introduces a new cold medicine. The medicine may either be highly effective (H) or have little effect (L). The company knows the effectiveness of the drug, but a representative consumer (player 2) knows only that the prior probability that it is highly effective is 1/2.
The company can choose either to advertise the drug excessively (A), at a cost c > 0, or not to advertise (N), which costs nothing. The representative consumer decides whether or not to buy the product after observing whether the company advertised the drug. The net payoff to the representative consumer from buying the drug is 1 if it is highly effective and -1 if it has little effect, and his payoff from not buying the drug is 0.
If the drug is highly effective then if consumers buy the drug once they will learn of its efficacy and buy it many more times, in which case the company earns a high payoff equal to R>c. If instead consumers learn that the drug has little effect then the company will sell the drug to them only once, and the company's returns are equal to r > 0. If the representative consumer does not buy the drug then the revenue of the company is 0. Assume that R>c>r> 0.
a. Write down the extensive-form game tree.
b. Find a separating perfect Bayesian Nash equilibrium in which the company chooses a different action depending on the drug's efficacy.
c. Find a pooling perfect Bayesian Nash equilibrium in which the company chooses the same action regardless of the drug's efficacy.
d. What changes when R>r>c> 0?