A corporate farm grows both wheat and rice. Rice does better in wetter years, and wheat does better in normal or drier years. Based on records over the past 20 years and current market prices, a consulting firm provides the farm managers with the following payoff matrix, where the entries are in millions of dollars:

For each year that the payoff matrix holds, the farm can split the planting between wheat and rice proportional to the size of entries in its optimal strategy matrix.

(A) Find the optimal strategies for the farm and the weather, and the value of the game.

(B) What is the expected value of the game for the farm if the weather (fate) chooses to play the pure strategy “wet” for many years, and the farm continues to play its optimal strategy?

(C) Answer part (B), replacing “wet” with “normal.”

(D) Answer part (B), replacing “wet” with “dry.”

Transcribed Image Text:

Corporate Wheat farm Rice Weather (fate) Wet Normal Dry -2 8 2 7 -3 3 ننا