Consider a game in which there is $4 to be divided, and the first mover is only permitted to make one of three proposals: (a) $3 for the first mover and $1 for the second mover. (b) $2 for each player and (c) $1 for the first mover and $3 for the second mover. The second mover is shown the proposal and can either accept, in which case the proposal is implemented, or reject in which case both players earn 0.

a. Construct an extensive form representation of the game.

b. Identify the subgame perfect Nash equilibrium for the game.

c. There are other Nash equilibria that are not subgame perfect. Identify them. Explain why you might expect to observe them behaviorally.