1) There are three firms: firm 1, firm 2 and firm 3. Each firm i chooses the level of production

qi. The market price is determined by market demand: p = 24 - q1- q2 - q3. And the

marginal cost of production is zero.

(a) Suppose firm 1 moves first, then firm 2 moves and finally firm 3 moves. Each firm can

observe the previous firms' production strategies. Find all the subgame perfect equilibria

(b) Suppose firm 1 moves first, and then firm 2 and 3 move simultaneously. Find all the

subgame perfect equilibria.

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2) 5 pirates on the Black Pearl: Captain Jack Sparrow, Master Gibbs, William Turner, Crew

A and Crew B find 100 gold coins on an island. They plan to split the coins by the following

rule. At first Captain Jack Sparrow will make a proposal about how to split the coins.

the proposal is passed, then an agreement will be reached immediately. And if the proposal

is rejected, Jack will be thrown into the sea and it is Gibbs's turn to make a proposal

Similarly, if the proposal is passed, then an agreement will be reached among the remaining

four pirates immediately and if it is rejected, Master Gibbs will be thrown into the sea and

it is Turner's turn to propose. If it is rejected, then Turner will be thrown into the sea and

Crew A proposes and if the proposal by A is rejected again, A will be thrown into the sea

and then B will get all the gold coins. Once a pirate proposes, all the pirates include himself

choose to accept or not. If more than or equal to half of the pirates choose to accept, then

the proposal is passed; Otherwise, it is rejected. Suppose there is no discounting in this

game. Find the maximum number of coins Jack Sparrow can get in the subgame perfect

equilibrium.