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ECON 3301 – Game Theory and Strategic Thinking

Semester 2 2022

Tutorial 6 - Week 10

1.    Consider a game with two players, who can choose sequentially to move up or down. The game is represented by the following tree:

1.1. Find the subgame perfect equilibria of this game in pure strategies.

1.2. Find the subgame perfect equilibria of this game in mixed strategies.

1.3. Now suppose that the game is modified to become a simultaneous move game. Draw a game tree to represent this new game.

1.4. Find the subgame perfect equilibria of this game in pure strategies.

1.5. Find the subgame perfect equilibria of this game in mixed strategies.

2.    Suppose that two people play the same stage game twice. At each stage, payoffs are:

Find  a  subgame  perfect  Nash  equilibrium  such  that  in  the  first  period  players  do  not  use strategies that would be a Nash equilibrium in the stage game.