Question

For each of the following short statements, explain whether it is True or False. If it’s true, explain why. If it’s false, give a counter-examples or explain why it’s false. (a) (b) (c)

(5 points) Suppose in a game a player has three decision nodes, with three possible actions at each node: A,B and C. The player has fewer strategies in a version of the game where C end the game, than in another version of the game where C does not.

(5 points) You can construct an example of a game where a strategy A is weakly dominant, but is also weakly dominated by another strategy B.

(5 points) Because backwards induction always chooses the best option at every decision node, there is always a unique SPNE if a game has any SPNEs.

Answer 1

a) Suppose in a game a player has three decision nodes, with three possible actions at each node: A,B and C. The player has fewer strategies in a version of the game where C end the game, than in another version of the game where C does not.

FALSE. The number of strategies remain the same if C ends the game or any other action. Number of strategies

b) You can construct an example of a game where a strategy A is weakly dominant, but is also weakly dominated by another strategy B.

TRUE.

c) Because backwards induction always chooses the best option at every decision node, there is always a unique SPNE if a game has any SPNEs.

FALSE.

Using backward induction, we can find a unique SRNE i .e sequentially rational nash equilibrium. There can be a game which has two SPNE like the following: