Problem:
There are two players, called Row and Column, who play a game that can last two periods. In the first period they simultaneously choose actions F or C. If they both choose F, then the game continues, and they move to the second period. If at least one player chooses C the game ends and they get the payoffs in the table below:
After playing (F, F) in the first period, the players again simultaneously choose F or C in the second period and get the payoffs below. (The game cannot continue beyond the second period.)
(a) Find all the Nash equilibria of the game that is played in period 2 (after (F, F) is played in the first period).
(b) Find all the subgame perfect equilibria of the entire game.
(c) Describe the players' strategies at Nash equilibrium of this game that is not a subgame perfect equilibrium.
(d) Now suppose that the game that is played in the second period is the game
And if (F, F) is played in the second period then the strategic form
is played in the third period.
Draw the extensive form for this game. Describe how you think your answers to the questions above will change, but do not calculate all the equilibria. Will the players benefit from this increased number of periods and why?
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