Chapter 10.4, Problem 1MP

Suppose that the investor in Example 1 wishes to invest $\$10,000$ in long- and short-term bonds, as well as in gold, and he is concerned about inflation. After some analysis, he estimates that the return (in thousands of dollars) at the end of a year will be as indicated in the following payoff matrix:

$\begin{array}{l}\text{ Inflation (fate)}\\ \begin{array}{cc}\text{Up }3\%& \text{Down 3\%}\end{array}\\ \begin{array}{c}\text{Gold}\\ \text{long-term bonds}\\ \text{Short-term bonds}\end{array}\left[\begin{array}{rr}\hfill 3& \hfill -3\\ \hfill -3& \hfill 2\\ \hfill -1& \hfill 1\end{array}\right]\end{array}$

Again, assume that fate is a very good player that will attempt to reduce the investor's return as much as possible. Find the optimal strategies for both the investor and for fate. What is the value of the game?