Chapter 10.2, Problem 51E

Investment You have inherited $\text{\$}10,000$ just prior to a presidential election and wish to invest it in solar energy and oil stocks. An investment advisor provides you with a payoff matrix that indicates your probable $4$ -year gains, depending on which party comes into office. How should you invest your money so that you would have the largest expected gain irrespective of how the election turns out?

$\begin{array}{l}\text{ Player }C\text{ (fate)}\\ \begin{array}{cc}\text{ Republican}& \text{ Democrat}\end{array}\\ \begin{array}{cc}\begin{array}{l}\text{Player}R\\ \text{(you)}\end{array}& \begin{array}{l}\text{Solar}\text{energy}\\ \text{Oil}\end{array}\end{array}\left[\begin{array}{c}\$1,000\\ \$5,000\end{array}\begin{array}{c}\$4,000\\ \$3,000\end{array}\right]\end{array}$

Note: For a one-time play (investment), you would split your investment proportional to the entries in your optimal strategy matrix. Assume that fate is a very clever player. Then if fate deviates from its optimal strategy, you know you will not do any worse than the value of the game, and you may do better.