Question

7. Consider a setting where player 1 and player 2 can each take on of two action: put a coin in player 3’s box or not. Player 3 then can either open the box or not. Consider the following variants of the game:

a. Player 1 moves first, player 2 sees player 1’s choice and moves second, player 3 sees both choices then acts. Write down the extensive form of this setting. (You can ignore payoffs)

b. Player 1 and player 2 move simultaneously. Player 3 observes their choices then acts. Write down the extensive form of this setting. (You can ignore payoffs)

c. Player 1 and player 2 move simultaneously. Player 3 does not observe their choices when he acts. Write down the extensive form of this setting. (You can ignore payoffs)

d. Player 1 and player 2 move simultaneously. Player 3 observes only if the box is empty or not (he can shake it and hear if something is inside), then acts. Write down the extensive form of this setting. (You can ignore payoffs)

e. Player 1 and player 2 move simultaneously. Player 3 observes how many coins are in the box (not who put them there), then acts. Write down the extensive form of this setting. (You can ignore payoffs)

Answer 1