To introduce the notation used in game theory, let us consider a simple game. Suppose there are
only two lighting fixture stores, X and Y, in Urbana, Illinois. (This is called a duopoly.) The
respective market shares have been stable up until now, but the situation may change. The
daughter of the owner of store X has just completed her MBA and has developed two distinct
advertising strategies, one using radio spots and the other newspaper ads. Upon hearing this, the
owner of store Y also proceeds to prepare radio and newspaper ads.
The payoff matrix in Table M4.1 shows what will happen to current market shares if
both stores begin advertising. By convention, payoffs are shown only for the first game player, X
in this case. Y’s payoffs will just be the negative of each number. For this game, there are only
two strategies being used by each player. If store Y had a third strategy, we would be dealing
with a payoff matrix.