Question

Consider the same football situation as in the previous question, but now suppose the payoffs (probabilities of winning) are as given in the following normal form:

		Defense
		Defend Pass	Defend Run
Offense	Pass	0.2, 0.8	0.3, 0.7
	Run	0.5, 0.5	0.4, 0.6

Do any of the teams (the one playing defense or the one playing offense) has a dominant strategy? Which one? Explain why.

Answer 1

OFFENSE/DEFENSE	DEFEND PASS	DEFEND RUN
PASS	0.2 , 0.8	0.3 , 0.7
RUN	0.5 , 0.5	0.4 , 0.6

If the player Offense plays strategy Pass, then player Defense will choose strategy Defend Pass as he gets a higher pay-off of 0.8 as compared to 0.7.

If the player Offense plays strategy Run, then Player Defense will choose strategy Defend Run as he gets a higher pay-off of 0.6 as compared to 0.5.

If the player playing Defense chooses strategy Defend Pass, then player Offense will choose strategy Run as he gets a higher pay-off of 0.5 as compared to 0.2.

If the player playing Defense chooses strategy Defend Run, then player Offense will choose strategy Run as he gets a higher pay-ff or his probability of winning is higher in this case that is 0.4 as compared to 0.3.

So, player playing Offense has a clear dominant strategy of playing Run because no matter what the Defense player is choosing, he chooses strategy Run only.