Maximin Strategy
This strategy is based on the fact that sometimes it is more prudent to maximize the minimum gains achievable in a gaming situation. Let's take the Meat and Potatoes example to appreciate this strategy. In this example, Businessman M loves selling Meat, and Businessman P loves selling potatoes. As a consequence, let's assume they have the following payoff matrix (the number before the comma is the payoff in dollars for Businessman M and the number after the comma is the payoff in dollars for Businessman P):
As you can see, businessman M has a dominant strategy of selling meat. Why? Because irrespective of what P sells, M comes out ahead by selling meat. If M sells potatoes, he can make either $130,000 or $110,000. Both these amounts are less than $150,000 (and $200,000) which M can make by selling M. However, P does not have a dominant strategy; his fortunes are tied to what M does.
Let's first consider the Nash Equilibrium for this game. If P assumes that M is rational and will maximize his profits by pursuing the dominant strategy of selling meat, P will respond by selling potatoes. So the top right-hand quadrant is the Nash Equilibrium here; both M and P maximize their profits. M can make $200,000 and P can make $120,000.
The whole concept of Nash Equilibrium is based on the fact that both M and P behave rationally. However, can P always count on M being rational? Suppose M starts following a Guru, who convinces M that he should not only give up eating meat, but he should stop selling it as well. Even though not rational, if M starts selling potatoes; if P has the strategy of selling potatoes, it can be extremely costly for P. Why? Because M will make $110,000; where as P will make only $20,000. Let's further assume that P lives in a nice home and makes a mortgage payment of $3000 per month. With $20,000 yearly profit, P can't pay that mortgage, and will be foreclosed. So, CAN P TAKE THE RISK OF SELLING POTATOES, IF HE IS CONSERVATIVE AND AFRAID THAT M MAY NOT BEHAVE RATIONALLY? No.
So, what does P do? P will sell meat, for he is assured of making at least $80,000. In this scenario, P is pursuing a Maximin Strategy of maximizing the minimum gains that can be earned. Please note that even though it is not a profit-maximizing strategy, the maximin strategy ensures that P will not be on the streets!
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