On an overcast morning, deciding whether to carry your umbrella can be viewed as a game between
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Question:
Weather
Rain No Rain
You Carry umbrella Stay dry Lug umbrella
Leave it home Get wet Hands free
Lets assume that you are willing to assign the following numerical payoffs to these out comes, and that you are also willing to make decisions on the basis of expected values (that is , average payoffs):
(Carry umbrella, rain) = -2
(Carry umbrella, no rain) = -1
(Leave it home, rain) = -5
(Leave it home, no rain) = 3
Solve
a) If the weather forecast says there is a 50% chance of rain, should you carry your umbrella or not? What if you believe there is a 75% chance of rain?
b) If you are conservative and wish to protect against the worst case, what pure strategy should you pick?
c) If you are rather paranoid and believe that nature will pick an optimal strategy in this two-person zero-sum game, then what strategy should you choose?
d) Another approach to this decision problem is to assign payoffs to represent what your regret will be after you know natures decision. In this case, each such payoff is the best payoff you could have received under that state of nature, minus the corresponding payoff in the previous table:
Weather
Rain No Rain
You Carry umbrella 0 = (-2) - (-2) 4 = 3 - (-1)
Leave it home 3 = (-2) - (-5) 0 = 3 - 3
What strategy should you select if you wish to minimize your maximum possible regret?
Related Book For
Foundations of Financial Management
ISBN: 978-1259024979
10th Canadian edition
Authors: Stanley Block, Geoffrey Hirt, Bartley Danielsen, Doug Short, Michael Perretta
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