In: Economics
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.
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.