Some choices are dominated by others and can be

Some choices are dominated by others and can be eliminated: A will not choose A3 since either
A1 or A2 will produce a better result, no matter what B chooses; B will not choose B3 since
some mixtures of B1 and B2 will produce a better result, no matter what A chooses.
B chooses B1B chooses B2 B chooses B3
A chooses A1 +3 −2 +2
A chooses A2 −1 0 +4
A chooses A3 −4 −3 +1

A can avoid having to make an expected payment of more than 1/3 by choosing A1 with
probability 1/6 and A2 with probability 5/6, no matter what B chooses. B can ensure an expected
gain of at least 1/3 by using a randomized strategy of choosing B1 with probability 1/3 and B2
with probability 2/3, no matter what A chooses. These mixed minimax strategies are now stable
and cannot be improved.
b)
Brandenburger and Nalebuff discuss how game theory works and how companies can use the
principles to make decisions. The authors state that managers can use the principles to create new
strategies for competing where the chances for success are much higher than they would be if
they continued to compete under the same rules. A classic example used in the article is the case
of General Motors. The automobile industry was facing many expenses due to the incentives that
were being used at the retailers. General Motors responded by issuing a new credit card where
the cardholders could apply a portion of their charges towards purchasing a GM car. GM even
went so far as to allow cardholders to use a smaller portion of their charges towards purchasing a
Ford car, allowing both companies to be able to raise their prices and increase long term profits.
This action by GM created a new system where both GM and Ford could be better off, unlike the
traditional competitive model where one company must profit at the expense of another.
The authors state that while the traditional win-lose strategy may sometimes be appropriate, but
that the win-win system can be ideal in many circumstances. One advantage to win-win
strategies is that since they have not been used much, they can yield many previously
unidentified opportunities. Another major advantage is that since other companies have the
opportunity to come out ahead as well, they are less likely to show resistance. The last advantage
is that when other companies imitate the move the initial company benefits as well, in contrast to
the initial company losing ground as they would in a win-lose situation.
The authors also state that there are five elements to competition that can be changed to provide
a more optimal outcome. These elements are: the players (or companies competing), added
values brought by each competitor, the rules under which competition takes place, the tactics
used, and the scope or boundaries that are established. By understanding these factors,
companies can apply different strategies to increase their own odds of success.