PLEASE GIVE LONG ANSWERS AND DRAW DIAGRAMS

Q.2 It is given that two men are engaged in a duel. They each have two choices: shoot straight (to try to kill the other) or duck (to try to avoid being killed). If they both shoot straight, they both die; if they both duck, they live, but both lose some "face". If one ducks and one shoots straight, they both live, but the one who shoots earns "honor" and "respect" from his peers, while the one who ducks loses "face" and is ridiculed as a coward. Therefore, shooting and living gives a higher reward than ducking and living, regardless of what the other person does. [Total Marks: 30]

a) For the context above, set up a game (in normal form). There are many numbers you may choose, as long as you maintain the ordinal ranking between the payoffs. Make sure to label all necessary elements of the game when you set it up.

b) Do each player in your model have a dominant strategy? Make sure to include all of your working to back your answer.

c) Using the best response method, does the game have a Nash Equilibrium/Equilibria? Is this Nash Equilibrium also a Dominant Strategy Equilibrium, briefly state why or why not?