What is game theory?

Game Theory is a well known way of analysis used in many fields
to determine what people would do, when each of their actions affects the others and neither is
aware of what the other is going to do. This dilemma of sorts results in decisions made by all
the players that lead to their gaining less than what they could have
otherwise.

For example, let's analyze two firms A and B, competing
with each other to sell a TV that is similar in every way. Now, before Christmas, they have to
decide whether they should offer a 10% discount to customers who buy the TV from them. The
profits each of them can make if neither offers a discount is $5 million. If A offers a discount
and B doesn't, A makes profits of $4 million and B make profits of $3 million. If B offers a
discount and A doesn't the payoff is reversed. In case both offer a discount each of them only
makes profits of $3.5 million. Now what would the two do.

As each of
the firms wants to maximize its gains, neither of them should offer a discount and make profits
of $5 million each. But none is aware of what the other will do which could reduce their profits
to $3 million. So, both of them are forced to offer a discount. Though this results in total
profits of only $7 million instead of $10 million, this is the decision we find them taking using
Game Theory as the tool of analysis.