1Static game question

Imagine an airline traveler andTSAareplayingasimultaneousstaticgame. The airline traveler has to decide first whether to bring small liquids in their carry-on or not.If the traveler brings small liquids, they then have to decide whether to take their small liquids out of their bag at the security checkpoint.TSA also has three options.TSA can conduct a light search for small liquids, a thorough search for small liquids, or not search at all.

If the traveler does not bring any small liquids, they always make their flight and will geta utility of 8.TSA will get a utility of 8 if they conduct a light search verifying the lack of liquids without much effort, TSA will get a utility of 6 if they conduct no search at all since it's less work but also they feel less secure, and TSA will get a utility of 5 if they conduct a thorough search since they worked hard and found nothing.

If the traveler brings their liquids and takes the liquids out of their bag, regardless of what TSA does, the traveler will make their flight with their liquids on-hand and will get utility of 9.In this case, TSA will get 9 utility if they conduct a light search verifying the liquids without much effort.TSA will get a utility of 6 if they conduct no search at all since it's less work but also they feel less secure, and TSA will get a utility of 5 if they conduct a thorough search since they worked hard and found nothing.

If the traveler brings their liquids and does not take their liquids out of their bag, and TSA conducts any type of search (light or thorough), TSA will find the liquids, the traveler will need to stay for extra scanning, and they will miss their flight.They will then get a utility of 5. If the traveler brings their liquidsanddoesnottaketheirliquidsoutoftheirbag, and TSA does not search their bag,they will make their flight with their liquids and the leastamountofeffortandwillgetautilityof10.Inthesecases,TSAwillgetautility of 6 if they conduct no search at all since it's less work but also they feel less secure, they will get a utility of 10 if they conduct a light search since they will feel good about finding the traveler's liquid with minimal effort, and they will get a utility of 5 if they conduct a thorough search since they will find the liquid but they will have to do the greatest amount of work.

A.Draw the payoff matrix for this game, including the players, their possible actions, and the payoffs for each combination of actions.

The payoff matrix

B. Does the traveler have a dominant strategy?If yes, what is it?If no, why not?

C. Does the TSA have a dominant strategy?If yes, what is it?If no, why not?

D. What is the Nash equilibrium of this game?

E. Is this a prisoners' dilemma?