Chapter 10.4, Problem 12E

Tour agency A tour agency organizes standard and luxury tours for the following year. Once the agency has committed to these tours, the schedule cannot be changed. The state of the economy during the following year has a direct effect on tour sales. From past records the agency has established the following payoff matrix (in millions of dollars):

$\begin{array}{l}\text{ Economy (fate)}\\ \begin{array}{ccc}\text{Down}& \text{Nochange}& \text{Up}\end{array}\\ \begin{array}{c}\text{standard}\\ \text{Luxury}\end{array}\left[\begin{array}{c}1\\ 0\end{array}\begin{array}{c}2\\ 1\end{array}\begin{array}{c}0\\ 3\end{array}\right]\end{array}$

(A) Find optimal strategies for both the agency and fate (the economy). What is the value of the game?

(B) What proportion of each type of tour should be arranged for in advance in order for the agency to maximize its return irrespective of what the economy does the following year?

(C) What is the expected value of the game to the agency if they organize only luxury tours and fate plays the strategy “down”? If the agency plays its optimal strategy and fate plays the strategy “no change”? Discuss these and other possible scenarios.