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Econ 102 – Fall 2021

Problem Set 3

5)   The following set of (extensive form) games represent two firms who are attempting to form a cartel. The firms are called “A” and “B” . The moves each can make are “Increase output” ( ↑ ) and “don’t increase output”(X).

The first game (shown below) represents their behavior in a single period where they act simultaneously, unaware of what their opponent is doing.

a.   (4 pts.) Solve the game by the Rollback (backward induction) method demonstrated in class by identifying the dominant strategies (the ones  that the players choose).  and circle the Nash Equilibrium (for the entire game) and write it above the starting node.

The second game (shown below) is a repeated game.  It represents their behavior in two successive periods. Within each period they act simultaneously, but recall what has happened previously.  In the second period, In the second period, the players acquire the same payoffs   they did in the first, while retaining the payoffs received in the first.  The figure below shows only two of the four possible subgames for the second period.

b.   (8 pts.) Solve the game by the Rollback method. Identify the dominant strategies and circle the Nash Equilibrium for each subgame and write it above its starting node.

c.   (2 pts) Has the player’s behavior changed significantly?  Why or why not?

The third game (shown below) is the same as the second, except that cheaters are penalized for their behavior in the previous period.  Those who expanded output during the first period loose everything they gained in that period.

d.   (8 pts.) Solve the game by the Rollback method. Identify the dominant strategies and circle the Nash Equilibrium for each subgame and write it above its starting node.

e.   (2 pts) How has the penalty changed the firm’s behavior?