Glassworks and Clearsmooth compete in the local market
for windshield repairs. 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 former
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 windshield-repair firms know they
will compete for just one year. Write down the payoff matrix for this game.
Find the Nash equilibrium strategies.
(b) Suppose the firms play this game for five years in a
row, and they know that at the end of five years, both firms plan to go out of
business. What is the subgame-perfect equilibrium for this five-period game?
(c) What would be a tit-for-tat strategy in the game
described in part (b)?
(d) Suppose the firms play this game repeatedly forever,
and suppose that future profits are discounted with an interest rate of 20% per
year. Can you find a subgame-perfect equilibrium that involves higher annual
payoffs than the equilibrium in part (b)? If so, explain what strategies are
involved. If not, explain why not.