Consider the following two statements: A strictly dominated strategy of the stage game can never be played in a subgame perfect Nash equilibrium of an infinitely repeated game with discounting. An infinitely repeated game always has a subgame perfect Nash equilibrium. Which of the following is correct? a. Only statement 1 is true. b. Only statement 2 is true. c. Both statements are true. d. Neither statement is true.
Question
Consider the following two statements:
A strictly dominated strategy of the stage game can never be played in a subgame perfect Nash equilibrium of an infinitely repeated game with discounting. An infinitely repeated game always has a subgame perfect Nash equilibrium. Which of the following is correct?
a.
Only statement 1 is true.
b.
Only statement 2 is true.
c.
Both statements are true.
d.
Neither statement is true.
Solution
The correct answer is:
b.
Only statement 2 is true.
Explanation:
Statement 1 is not necessarily true. A strictly dominated strategy of the stage game can be played in a subgame perfect Nash equilibrium of an infinitely repeated game with discounting. This is because the threat of future punishment can make it rational for players to play strategies that are not best responses in the stage game.
Statement 2 is true. An infinitely repeated game always has a subgame perfect Nash equilibrium. This is a well-established result in game theory. The intuition is that the possibility of future play allows for the use of strategies that condition future play on past actions, which can support a wide range of outcomes as subgame perfect Nash equilibria.
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