Game theory is a branch of applied math, it is a study of mathematical models of conflict and cooperation between intelligent rational decision makers and mainly used in economics, political science, psychology as well as logic and biology. This theory can explain a paradox inside society, in which people can work together in a society where each of them tend to be a winner. This paradox complicate Darwin in construct his evolution theory.
Classical game theory has been done by many mathematicians but the modern game theory was studied by John von Neumann and developed by John Forbes Nash. At that time, Game theory was known as the sexiest mathematical field. Not only known for his work in applied math, Nash also known for his work in pure math for his work in Riemann manifold abstraction. Nash has proved that Riemann manifold abstraction can be regarded as an isometric manifold of euclidean space. He also contributed in the development of non-linear differential equation theory for partial parabolic. He is a typical of people who would rather to work alone, not in a team …(it’s so ME ya 😀 )
His work in game theory was widely appreciated by the economists because this theory can explained mathematically why the invisible hand (submitted by Adam Smith) could fail to provide goods to public. Nash showed the difference between cooperative where each agent is bound to cooperate with each other and non-cooperative game, where there is no force from outside the game that can enforce a set of rules that have been predetermined.
In cooperative game, if all agents expectations are fulfilled, they won’t change the strategy because they won’t to loose themselves and an equilibrium resulted. This equilibrium is called as Nash equilibrium. Finally, this theory brought Nash to won Economic Nobel. His work can explain and forecast business decisions in competitive market, macroeconomic theory for policy, foreign trade theory, information economy and etc. Politicians also appreciate this theory because it shows how “rational” personal interest can hurt everyone.
Prisoner’s dilemma is a canonical example of a game analyzed in a game theory that shows why 2 agents might not cooperate, even if it appears that it is in their best interest to do so. This is very exciting to be applied in white-collar crime. Let make a basic scenario of white-collar crime. Two politicians are known yo have committed corruption. However, police suspect that they have committed bribery also. Both of them were places in separate cells and each of them were give an offer:
1. Politician who testified against other politician associated with bribery crime would be released, while other inmates are imprisoned for 13 years. This is called a “sucker’s payoff”
2. If they deny, or testify against each other, then both will get a 5 year prison.
3. When both are silent, then each will undergo 3-year prison sentence.
Here, the two politicians basically have two choices: to cooperate (in this scenario, remain silent) or for treason. Collaboration means that the prisoner concerned could be languishing in jail for 5 or 3 years. But when a traitor, so he can undergo 0n 3 or a 5-year prison , depending on the recognition of other politicans.
Because each of the politician did not know what choice the other politician was taken (both are in separate cells and can not communicate with each other), rational choice, according to the Darwinian rule of survival is the most favorable option (remember the rules of survival of the fittest ). In this case is to maximize the best possible (zero years in prison) and minimize the worst possible time (3 or 5 years in prison).
In the 1980s, a computer programming competition held to find the best solution for the prisoners’ dilemma. A simulation program called Tit-for-tat came out as winners. As indicated by its name (which literally means a blow returned one hit), this program worked first-round pick, and then imitate whatever the opponent in the next rounds.
In this case, work together to bring positive results, while the traitor will eventually get in return (if you betray me, the next round you will betray me). Conversely, if we work together, no matter what other people do, the result is “suckers payoff.” Other people have no incentive to cooperate with us, and consequently we will always be a loser.
But it is only a simulation. In the real world, the fine could have been lost, and the traitor could get lucky, and sometimes indeed the case. The appearance can be triggered when one of the main cooperation between the following conditions exist: the ‘politicians’ meet each other many times, they know each other, they remember the previous meeting. But there are also other factors that also need to be taken into account, ranging from the possibility of a meeting between politicians, the errors (when a call untukk work precisely regarded as treason), to the possibility of forming behavioral genetics inherited from generation to generation. Thus, the tit-for tat may be too ideal to be difficult to apply in the real world.
The solution is to add the element of error, which may simply be caused human tendency to make mistakes. Tit-for-tat strategy is not the greatest, because it does not have a forgiving nature: once two players tit-for-tat began to betray each other, they will continue to do so. By adding a little element of uncertainty, each player can develop new strategies. Addition of a small element of randomness in the behavior of the program allows the emergence of “forgiveness”, and the opportunity to test the behavior of other players.
One strategy that uses a forgiving nature is the “tit-for-tat kind” (generous tit-for-tat), which added an element of randomness to break the vicious circle of mutual betrayal. Another strategy is more successful, given the name Pavlov, can be described by the phrase “If it is not broke, do not get repaired (and if you lose, change strategy).” However, uncertainty was possible collaboration, and optimistic message in a model of tit- for-tat remain valid.
In short, what is shown by the prisoner’s dilemma can also occur in the personal level as well as evolutionary: If I work with you, then you most likely will also cooperate with me (strategy of tit-for-tat) and we will obtain the same score in the “game life “***. Conversely, if we betray each other, then we both lose and end up “game over”.
***real life, not refer to another mathematical theory called game of life
PS: Just like any other bad popular science articles, the real theory is more complicated and mathematically.
see more in : proceeding of national academy of science USA
example for the application in politic: liberty university law review