Darth Vader meets his Jedi Master from another life, Obi-Wan Kenobi, on the Death Star. Darth Vader has been waiting a long time for another rematch and the two immediately begin a light saber duel.

At the start of the light saber battle, Darth Vader has 1,000 hit points and Obi-Wan Kenobi has 200 hit points. The two force wielders can use only a full attack or a defensive attack in their light saber battle. After each swing, both inflict damage on the other based on the payout described below. The game will repeat until one of the combatants runs out of hit points.

If both full attack, Darth Vader reduces Obi Wan's hit points by 50 damage and Obi-Wan reduces Darth Vader's hit points by 10 damage. If both are defensive attack, Darth Vader reduces Obi Wan's hit points by 20 and Obi-Wan reduces Darth Vader's hit points by 10. If Obi-Wan full attacks and Darth Vader is defensive attack, then Obi-Wan reduces Darth Vader's hit points by 15 and Darth Vader does not reduce Obi Wan's hit points. If Darth Vader full attacks and Obi-Wan defensive attacks, Darth Vader reduces Obi Wan's hit points by 30 damage and Obi-Wan does not reduce Darth Vader's hit points. [After each swing (i.e., repetition of the game), you will need to reduce the hit points by the damage from each swing].

Part 1 : Draw the payout matrix for the light saber battle.

Part 2 : (a) Does Darth Vader have a dominant strategy? If so, what is the dominant strategy? (b) Does Obi-Wan have a dominant strategy? If so, what is the dominant strategy?

Part 3 : Is there a Nash equilibrium? If so, identify the Nash equilibrium.

Part 3 : (a) Who will win the light saber battle? (b) How many swings (i.e., repetitions of the game) will the light saber battle last?

Part 4 : Is this a finitely or indefinitely repeated game? Explain your reasoning