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Two television stations compete with each other for viewing audience. Local programming options for the $5$:$00$ P$.$M$.$ weekday time slot include a sitcom rerun, an

early news program, or a home improvement show. Each station has the same programming options and must make its preseason program selection before

knowing what the other television station will do$.$ The viewing audience gains in thousands of viewers for Station A are shown in

Determine the optimal strategy for each station.

The optimal strategy for Station A is to implement strategy $a_1$ with probability

$,$ implement strategy $a_2$ with probability

$,$ and

implement strategy $a_3$ with probability

implement strategy $b_2$ with probability

$.$ The optimal strategy for Station B is to implement strategy $b_1$ with probability

$,$ and implement strategy $b_3$ with probability

What is the value of the game?

The expected value of the game is

$.$ This is an expected increase of

viewers for Station A$.$