Chapter 10.1, Problem 44E

Investment Suppose that you want to invest $\text{\$}10,000$ for a period of $5$ years. After getting financial advice, you come up with the following game matrix, where you $\left(R\right)$ are playing against the economy $\left(C\right)$. Each entry in the matrix is the expected payoff (in dollars) after $5$ years for an investment of $\text{\$}10,000$ in the corresponding row designation, with the state of the economy in the corresponding column designation. (The economy is regarded as a rational player who can make decisions against the investor in any case, the investor would like to do the best possible, irrespective of what happens to the economy.) Find saddle values and optima strategies for each player.

$\begin{array}{l}\text{ Economy }C\\ \begin{array}{ccc}\text{Fall}& \text{Nochange}& \text{Rise}\end{array}\\ \text{Investor }R\begin{array}{c}\text{5-Year }CD\\ \text{Blue-chipstock}\\ \text{Speculativestock}\end{array}\left[\begin{array}{ccc}5,870& 5,870& 5,870\\ -2,000& 4,000& 7,000\\ -5,000& 2,000& 10,000\end{array}\right]\end{array}$