In the following extensive form sequential game there are two players, the Bad G

Question

In the following extensive form sequential game there are two players, the Bad Guy and the Father. The Bad Guy moves first and decides whether to kidnap the child or not. If the Bad Guy docs not kidnap the child, the game is over. If the Bad Guy kidnaps the child, the father can choose to pay the ransom or not The Bad Guy then gets a second play, in which he can choose to kill or release the child. Find the Nash equilibrium. BadGuy Don'tKidna Kidnap 3,5 Father Pay Ranson on't PayRansom BadGuy BadGuy Kill Release Kill Release 4, 1 5,3 2,2 1,4

Explanation / Answer

Start solving the game using backward induction.

Looking at the lowest node, Bad guy has to decide between Kill and release. He has two nodes: left and right.

In the left node, he will choose Release (as 5 > 4) and in the right node he will choose Kill (as 2 > 1)

Now, the turn for Father comes. He has to choose between Pay Ransom (5,3) and Don’t pay Ransom (2,2)

He will chose Pay ransom (as 3 > 2)

Now, the game shortens to Bad guy deciding between Don’t Kidnap (3,5) and Kidnap (5,3)

He will thus chose Kidnap (as 5 > 3)

Thus, Nash equilibrium: (Kidnap ; Pay ransom ; Release)

(Note: In payoffs, the first one is for Bad guy and second is for father)

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