Exam 21: Game Theory

250 750 500 300 -250 1200 500 500 600 If the probabilities of d1, d2, and d3 are 0.2, 0.5, and 0.3, respectively, then what decision should be made under expected value?

In order to attract listeners, a radio station gives away money if listeners correctly identify the amount of money found by a "treasure hunter". A contestant would guess the amount on the air, and the disc jockey would then play a tape in which the "treasure hunter" said how much he had found. If the caller guessed correctly, they won the amount of money found by the treasure hunter. If they guessed incorrectly, they received nothing. Suppose that the treasure hunter either found $50 or $100. The payoff matrix represents this game: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { Treasure Hunter Finds: } \\ \begin{array} { l r r c } & & \$ 50 & \$ 100 \\ \hline \text { Caller Guesses } & \$ 50 & \$ 50 & \$ 0 \\ & \$ 100 & \$ 0 & \$ 100 \end{array} If the station plans on running the game every day for 10 days, how much will they pay out?

In order to attract listeners, a radio station gives away money if listeners correctly identify the amount of money found by a "treasure hunter". A contestant would guess the amount on the air, and the disc jockey would then play a tape in which the "treasure hunter" said how much he had found. If the caller guessed correctly, they won the amount of money found by the treasure hunter. If they guessed incorrectly, they received nothing. Suppose that the treasure hunter either found $50 or $100. The payoff matrix represents this game: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { Treasure Hunter Finds: } \\ \begin{array} { l r r c } & & \$ 50 & \$ 100 \\ \hline \text { Caller Guesses } & \$ 50 & \$ 50 & \$ 0 \\ & \$ 100 & \$ 0 & \$ 100 \end{array} If the station plans on running the game every day for 10 days, how much will they pay out?

A strategy is a plan of action followed by a player.