According to Bob, the payoffs of the several outcomes are as follows:
a. If it is sunny and he is not carrying and umbrella, 10
b. If it is sunny and he is carrying an umbrella, 8
c. If it is rainy and he is not carrying an umbrella, 2
d. If it is rainy and he is carrying an umbrella, 6
Draw the game matrix of this one-person game (vs. Nature). What should the probability of rain (P) be for Bob to take an umbrella with him?© BrainMass Inc. brainmass.com June 4, 2020, 5:02 am ad1c9bdddf
Payoff matrix: Bob vs. Nature
(Numbers show Bob's payoff) Nature's strategy
Bob's strategy Umbrella 8 6
No umbrella 10 2
Let Pr = the probability of ...
This solution shows how to use game theory to determine whether Bob should take his umbrella with him. Detailed calculations and a complete payoff matrix are given.