Two companies are about to make a decision regarding an investment in a new promotional campaign. Company A will either advertise in all media or advertise in newspapers only. Company B will either run a sweepstake or run a big sale. The payoff matrix is shown below. $\begin{array} { l l c c } \hline && { \text { Company B } } \\&& \mathrm { B } _ { 1 } : \text { Run a } & \mathrm { B } _ { 2 } : \text { Run a } \\&& \text { sweepstakes } & \text { big sale } \\\hline & \begin{array} { l } \text { A1: Advertise } \\\text { in all media }\end{array} & 4 &-1 \\\text { Company A } & \begin{array} { l } \text { A2: Advertise } \\\text { in newspapers only }\end{array} & - 2 & 1 \\\hline\end{array}$
Determine the proportion of time that Company A should employ each strategy.

Question

Two companies are about to make a decision regarding an investment in a new promotional campaign. Company A will either advertise in all media or advertise in newspapers only. Company B will either run a sweepstake or run a big sale. The payoff matrix is shown below.

\begin{array} { l l c c } \hline && { \text { Company B } } \\&& \mathrm { B } _ { 1 } : \text { Run a } & \mathrm { B } _ { 2 } : \text { Run a } \\&& \text { sweepstakes } & \text { big sale } \\\hline & \begin{array} { l } \text { A1: Advertise } \\\text { in all media }\end{array} & 4 &-1 \\\text { Company A } & \begin{array} { l } \text { A2: Advertise } \\\text { in newspapers only }\end{array} & - 2 & 1 \\\hline\end{array}

Determine the proportion of time that Company A should employ each strategy.

Quizplus · Accepted Answer

To find the optimal mixed strategy for Company A, we set the expected payoffs of both strategies equal. Solving the equations, we find that Company A should employ A1 37.5% of the time and A2 62.5% of the time.

Two Companies Are About to Make a Decision Regarding an Investment