Name

1. Labor Day, Again This is another look at the Principal - Agent game.  In this game there is no monitoring of the work effort made by Agent; nodes 4 and 5 are tied together and belong to the same information set.  In this new version of the game Principal earns 11 if 'nature' looks in a kindly way upon the enterprise, regardless of the effort made by Agent.  Notice that Agent is paid more for producing more revenue for Principal, regardless of the effort made by Agent.

a. What is Agent's expected payoff from a Hi effort?

b. What is Agent's expected payoff from a Lo effort?

c. At node 3 what effort should be made by Agent?  Hi  Lo

d. What is Principal's expected payoff from a Hi effort made by Agent?

e. What is Principal's expected payoff from a Lo effort make by Agent?

f. At node 2 should Agent accept the job offer? Yes, accept offer.  No

g. At node 1 should Principal make a contract offer? Yes, make offer  

2. Subgame Perfection In the following game there are two players: One and Two.  Player One goes first and must choose between A and B.  Player Two moves next, and knows what One has done in her initial move at node 1.  When One makes his next move he remembers what he has done at node 1, but nodes 4 and 5 belong to the same information set and nodes 6 and 7 belong to another information set.  That is, One knows that Two has played at either node 2 or node 3, but doesn't know the action two has actually chosen.

a. How many subgames are there?

b. What is the solution to the subgame that begins at node 2? < G, C > < G, D > < H, C > < H, D >

c. What is the solution to the subgame that begins at node 3? < K, E > < K, F > < L, E > < L, F >

d. Given your answers to b. and c., what should One do at node 1? Play A  Play B

e. As One contemplates the normal form of this game, how many strategic plans does he have?

f. As Two contemplates the normal from of this game, how many strategic plans does she have?

g. What is the strategic plans for One and Two of the subgame perfect equilibrium in the extensive form of the game? Player One A, G, K A, H, K A, G, L A, H, L B, G, K B, H, K B, G, L B, H, L   Player Two C, E D, E C, F D, F