Question: Model the following strategic interaction as a sequential game and find its subgame perfect Nash equilibrium. Ali and zeynep evaluate their options about attending an

Model the following strategic interaction as a sequential game and find its subgame perfect Nash equilibrium.

Ali and zeynep evaluate their options about attending an event together in a sequential game. They have two options: Ballet or Soccer.

First, Ali either(I) buys 2 tickets for a ballet show; or (II) buys 2 tickets for a soccer gamer (III) doesn't buy any ticket. Zeynep observes Ali's action. If Ali bought 2 tickets for one of the events, then Zeynep can choose between 2 options: (I)she can veto Ali's suggestion so that they will not go anywhere together; or (II) she can accept Ali's suggestion so that they will go to the event for which the tickets are bought.

Furthermore, if Ali did not buy any ticket, then Ali will stay at home for sure, buy Zeynep can buy a ticket for either event for herself and attend that event individually, or she can also choose to stay at home. If Ali bought two tickets but Zeynep chose to veto, then Zeynep will stay at home for sure, but Ali will individually go to the event for which the tickets are already bought.

Here are some necessary info:

Each ticket costs a utility of 2

Ali collects a utility of 9 from Soccer, a utility of 5 from staying at home, and a utility of 1 from Ballet

Zeynep collects a utility of 9 from Ballet, a utility of 5 from staying at home, and a utility of 1 from Soccer.

The utilities above are for attending the respective events individually.

Each person collects an additional utility of 3 if they attend an event together

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3. What is my goal?

2. I try to be as logical as possible

1. To understand the prerequisites for personal communication mastery.