Two firms compete repeatedly in a market of homogeneous goods. Each year, the firms can choose to charge a low or high price. The following payoff table summarizes their payoffs each year. The competition goes on indefinitely. Let & E (0, 1) denote the discount factor for both firms. Firm 2 Low High Low 0, 0 5, 0 High 0, 5 4, 4 Firm 1 Consider an n-period punishment trigger strategy s: • Play "High price" in the first stage. 4L our price" in the last neriod when he 5.

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5.
Two firms compete repeatedly in a market of homogeneous goods. Each
year, the firms can choose to charge a low or high price. The following payoff table
summarizes their payoffs each year. The competition goes on indefinitely. Let 5 E (0, 1)
denote the discount factor for both firms.
Firm 2
Low High
Low
0, 0
5, 0
Firm 1
High 0, 5 4, 4
Consider an n-period punishment trigger strategy s:
• Play "High price" in the first stage.
• In stage t> 2, if some player deviated to "Low price" in the last period when he
is supposed to play "High price", then play "Low price" for n periods and then
restart the game. In other words, after playing "Low price" for n periods, play
"High price" in the next stage as if it is the first stage of the game. Otherwise, play
"High price".
Find the necessary and sufficient condition on & for (s, s) to be an SPE. A sufficiently
simplified inequality will do.
Transcribed Image Text:5. Two firms compete repeatedly in a market of homogeneous goods. Each year, the firms can choose to charge a low or high price. The following payoff table summarizes their payoffs each year. The competition goes on indefinitely. Let 5 E (0, 1) denote the discount factor for both firms. Firm 2 Low High Low 0, 0 5, 0 Firm 1 High 0, 5 4, 4 Consider an n-period punishment trigger strategy s: • Play "High price" in the first stage. • In stage t> 2, if some player deviated to "Low price" in the last period when he is supposed to play "High price", then play "Low price" for n periods and then restart the game. In other words, after playing "Low price" for n periods, play "High price" in the next stage as if it is the first stage of the game. Otherwise, play "High price". Find the necessary and sufficient condition on & for (s, s) to be an SPE. A sufficiently simplified inequality will do.
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