Game Theory: the sexiest part of math

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

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22 thoughts on “Game Theory: the sexiest part of math

  1. What an interesting post. There is one other variable that will affect the choice the two criminals will make. Which invalidates the math which was obviously prepared by a non criminal mind. They figure out ahead of time what the possibilities are in case they are caught and know exactly what the other will do even if separated with no communication. They know the alternatives offered and have planned for this possibility. Sicilian code of silence. Accepting any plea bargain will get you killed anyway. omerta – code of silence and loyalty.

    • Thank you Sir 😀 well, I take preparation for any possibilities as a kind of cooperative agents in game theory. In real case, we may hope that the police agents has another game to led betrayal between/among suspected agents 😛

    • Good article but I also seen the flaws, if the two had been involved in a criminal act it was most likely preplanned with contingencies for a uniform story. I also grew up in a disorganized crime family… You kept your mouth shut & waited for an attorney to show up, that’s it. This also speaks to people in power, they get ahead by “having a plan” they are very calculating, that is how they succeed. Plus a lot of politicians have legal experience. Maybe they should’ve tried this on the Wall Street CEO’s :~)

      Still an excellent read! You have a brilliant mind.

  2. Very interesting read! I remember it well when I studied economics – it was the only interesting area I liked in a very boring course.

    Of course what you do if you’re a corrupt politician being interrogated by the cops is to threaten the cops with your power and say that they’ll get fired or demoted unless they let you go.

    Nobody wants corrupt politicians to go to jail – that’s a big problem for other politicians because then they have to be even more careful and people say that they’re all corrupt.

    So what happens is that the big politician makes a phone call to the chief of police and the thing gets taken care of quietly.

    Lessoon is; if you’re in a room with the cops keep your mouth shut! 😉

    • The real theory in math is much more complicated, just like the reality , well, it’s about politician, what if the coos get corrupt …. now, I am really getting confused

      • I think there should be a new one – the cop’s dilemma.

        There are 2 corrupt politicians in the police station who say that if the cop decides to prosecute them then they will use their influence and power to destroy his career. But if the cop does not prosecute them, then he might also be accused of doing the wrong thing and have his career destroyed.

        What does the cop do?????

        So you could have 2 games – the prisoner’s dilemma and the cop’s dilemma happening at the same time with the same people.

      • Well, it just a matter of name..whether is it prisoner’s dilemma, politician’s dilemma or cop’s dilemma, we still talking about cooperative and non-cooperative interaction between/among them. Nash didn’t give that name, I don’t know who give it name, prisoner’s dilemma

  3. “Politicians also appreciate this theory because it shows how “rational” personal interest can hurt everyone” is the scariest part, for me. I liked that the criminals in your example were politicians. Interesting stuff!

  4. this post is so cool, i will share this with my 14 year old who is so cool with math. we will now receive email when you post something new. also you can follow us at our blog:
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    and LIKE us or FOLLOW us and make us smile like now by leaving us a Comment. Thanks and we will read more in your blog. We would like to repost, please with links back to you. Enjoy your weekend.
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  5. I heard about the “Tit for Tat” programs first on Radio Lab and was very excited to see it here and read it out again. Sometimes math can be cool (or atleast accessible to normal people) 🙂
    On a side note: Love the name of your blog; its pretty much the reason i stopped by, but i’m glad i did

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