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Consider two firms that can either advertise or not advertise. If they both advertise they each earn a profit of 5. If one advertises and the other does not, then the firm that advertises earns 10 and the other firm earns 3. If neither advertises, then each earns an amount a, where 5 < a < 10. Firms make their decisions on advertising simultaneously.
(a) Suppose this game is played once. Show that both firms will advertise.
(b) Now suppose this game is to be played an unknown number of times. Both firms know that there is a probability .1 that the current play of the game will be the last time the game will be played. So there is a probability 1.0 that the game will be played at least once, a probability .9 that the game will be played at least twice, a probability .81 that it will be played at least three times, and so on. Consider the following trigger strategy. A firm does not advertise the first time the game is played. In later periods, it does not advertise if its opponent has not advertised in every period up to that point; otherwise it advertises. The discount factor is 1 (i.e., the interest rate is 0). For what range of values of a do these trigger strategies constitute a subgame perfect equilibrium?
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Provide brief but theoretically sound explanation for each of the following.
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