Question

2) A football team has the chance of scoring the game-winning touchdown on the last play of the game. It can either run or pass. The defense can play for the run or play for the pass. The following normal form lists the payoffs from the game made up by this last play. The payoffs are probabilities of winning the game.

		Defense
		Defend Pass	Defend Run
Offense	Pass	0, 1	1, 0
	Run	1, 0	0, 1

1. Does the team playing defense have a dominant strategy? Explain your answer.
   2. What is the Nash equilibrium or equilibria? Explain why.

Answer 1

Ans.(a) If offense plays pass, then it will be optimal for defense to play pass since then defense will achieve highest possible payoff.
If offense plays run, then it will be optimal for defense to play run since then defense will achieve highest possible payoff.
Since optimal strategy of defense is changing with the change in the strategy of offense there is no dominant strategy for defense.

Ans.(b)- There is no nash equilibrium in this game .
This is because,at each strategy ,there is an incentive for atleast one player to deviate to some other strategy.
e.g. at (PASS,DEFEND PASS), defense has incentive to switch from pass to run in order to achieve a higher payoff.

If you have any doubt,feel free to ask.