Static Game Question.

Imagine an airline traveler and TSA are playing a simultaneous static game. The airline traveler decides first whether to bring liquids in their carry-on or not. If the traveler brings liquids, they then have to decide whether to take their small liquids out of their bag at the security checkpoint. TSA has three options for searching the liquids: thorough, light, or none.

Utility of the traveler not bringing any liquids: 8

TSA Utility: thorough search - 5; light search - 8; no search - 6

Utility of the traveler bringing liquids and taking it out of bag: 9

TSA Utility: thorough search - 5; light search - 9; no search - 6

Utility of the traveler bringing liquids and not taking it out of bag: 5 (in the case of TSA thorough or light search); 10 (in the case of no search)

TSA Utility: thorough search - 5; light search - 10; no search - 6

1. Draw the playoff matrix for this game, including the players, their possible actions, and the payoffs for each combination of actions.
2. Does the traveler have a dominant strategy? If yes, what is it? If no, why not?
3. Does the TSA have a dominant strategy? If yes, what is it? If no, why not?
4. What is the Nash equilibrium of this game?
5. Is this a prisoners' dilemma?