Game theory is an applied mathematics theory used for understand and explain the mechanisms that are used when people make decisions.
The theory was systematized by mathematician John von Neumann and economist Oskar Morgenstern in 1944.
The theory seeks to understand the functioning of the logic of strategic interaction and the interdependent relationships between people. Whether in competitive or cooperative situations, decisions have results and affect others involved. This is the study center for Game Theory.
The theory has many applications and can be used in simple fields like strategy games, or complex ones. as in administration, political science, economics and even in intelligence research artificial.
the mathematician john nash contributed a lot to the evolution of the theory. The initial researches studied the mathematical explanation (mathematical function) for the competition and cooperation relationship between players. The mathematician managed to discover the equilibrium point of this relationship, which came to be called Nash's balance.
In economics and administration theory can be used mainly in strategic decision making. It can be an analysis tool to classify needs and situations to decide with strategy and achieve the desired results. It is also efficient for analyzing the strategies of competing companies.
prisoner's dilemma
Prisoner's Dilemma is the classic example of the application of game theory. In this dilemma, it is assumed that each one of those involved wants to have the maximum advantage in the situation, without taking into account the consequences for the others involved. The dilemma deals with the decision between cooperation and betrayal.
The prisoner's dilemma works like this: two suspects in a crime are arrested and there is not enough evidence to convict them both. They receive a separate proposal:
- if one of the prisoners confesses to the crime and the other does not, whoever confesses will not be sentenced and whoever has remained silent will be sentenced for 6 years;
- if the two do not confess, they may be sentenced to 1 year in prison each;
- if the two confess and betray their partner, they will be sentenced for 3 years each.
Possible hypotheses can be graphically organized in the payoff matrix. The matrix is the representation of all possible outcomes in the situation or game, which will be consequences of the decisions of those involved.
The big issue in the prisoner's dilemma is that each must make their own decision independently and without knowing the other's decision and the possible consequences.
In this case, it is clear that individual choice (betrayal) does not represent the best result for both, but it can be the best possible result regardless of the other's decision. In game theory, betrayal is called dominant strategy.
