The Game Theory

The game theory was created back in the 1940's as way to scientifically calculate the possible outcomes in game play taking into consideration the moves of the other participants. Since its development it has been used in a wide range of applications, including economics, philosophy, and political science, to name a few. The idea behind the game theory is that one can choose the best possible outcome for himself, taking into consideration the decisions that his opponents might make. Using the game theory in economics one can create a payoff matrix, which consists of creating a table of outcomes based on different possible outcomes that would result from each decision made. From this matrix all possible outcomes would be displayed so that the "player" can make the best possible decision based on the best possible decisions that his opponent could make. Given this information one can see the best possible solution that his or her opponent can make and then they can be ready to decide the best possble solution given what his oppenent will do.
When two or more parties decide to work together for the best interests of those involved they may decided to "collude" with each other, thus forming a cartel. Each party would then decide how to divide and share the benefits of working together. However each party involved may decide not to stick to the agreement. In that decision they may use the payoff matrix to show the possible outcomes given that the other parties may not decide to stick to the agreement. With this information given, it makes me wonder though, why they would decide to work together if, according to economists, that the parties involved will just end breaching the agreement anyway?