Question

Mask4Mask and MouthX are competing in the market for face masks.   The market size (total available profits) is $10 million per year. Each firm can choose whether to advertise on local television. If a firm chooses to advertise in a given year, it costs that firm $3 million. If one firm advertises and the other doesn’t, then the advertiser captures the whole market. If both firms advertise, they split the market 50:50. If both firms choose not to advertise, they also split the market 50:50.

a. Suppose the two firms know they will only compete for one year then go out of business. Write down the payoff matrix and find any PSNE.

b. Does the equilibrium change if it’s five years instead of one? Why?

c. Suppose the two firms repeat the game indefinitely and suppose each firm has a discount factor of 0.8 per year. Show that (not advertise, not advertise) is the SPNE of this indefinitely-repeated game.

Answer 1