# 9.* Consider the following game in extensive form : N = ( 1 , 2, 31 . 4 1 . 2 \3 12. 2.2 5, 6 , 1\ 2 , 4 , 7\ 4, 3 , 6\ 6 , 7 , 3 of 3. 7. 4 4, 2, 6

(a)  Write down the set of pure strategies of players 1, 2, and 3.

S1 = { ae, af, be, bf } S2 = { ck, cl, cm, dk, dl, dm} S3 = { g, h}

(b)  How many subgames does the game have? What are they?

The game has three Subgame which are circled in three blue rectangulars. The initial node (1.1) initiates a subgame, because the entire game is itself a subgame. Node 1.2 also initiates a subgame, because it begins with an information set containing only single decision node. Moreover, node 2.2 also initiates a subgame, because it begins with an information set containing a single decision node. However, Node 2.1 does not initiates a subgame, because one of its successors (node 3) is in the same information set as a node that is not one of its successors. (node 3 follows node 1.1)9.* Consider the following game in extensive form : N = ( 1 , 2, 31 .41 . 2\312.2.25, 6 , 1\2 , 4 , 7\4, 3 , 6\6 , 7 , 3of3. 7. 44, 2, 66 , 3 , 1( a ) Write down the set of pure strategies of players 1 , 2 , and 3.( b ) How many subgames does the game have ? What are they ?( C ) Determine the set of pure – strategy subgame perfect equilibria ( SPE ) . Explain your steps carefully .What is ( are ) the SPF path ( s ) and the SPE payoffs ?&quot;NOTE : Make sure your answer is based on the logic of SPE .]

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