Question

For each of the following short statements, explain whether it is True or False. If it’s...

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.

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: