Game Theory

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Jason 101 Feb 25, 2005 at 14:25

Game Theory it’s nothing but a way of understanding people choices while “playing a game”. More generally understanding as Game any situation where one or several “agents” took action, being this agents the players. In game theory the main analysis is set on the “strategies” that are nothing but the players choices.
Games are usually divided into Cooperative and Non Cooperative, referring to players cooperation, chess would be a classic example of a Non Cooperative one because both players are of contrary sides while monopoly could be Cooperative anytime people decided to help each other to defeat the rest of the players having more tosses of the dice, money and properties.

Another classification that it’s usually taken into account it’s refers to the Information the players have while playing. Another basic definitions are:
Dominant Strategy: a strategy it’s said to dominate another if and only if disregarding the other players choices the use of this strategy give him better payoffs. Therefore a strategy it’s said to be dominated if exists a strategy that dominate it.
Payoff: Players are suppose to receive a either positive or negative payoff in any position of the game. a payoff it’s a number that reflects the desirebility or not of a strategy according to the other player ones
Rationality: A player it’s said to be rational if he plays with the objetive of maxime his payoffs.
Zero Sum Games: An n players game it’s said to be a zero sum if in each play the sum of the players payoffs it’s zero, in a two player game that would lead to two opposite players, their payoffs are always the same in magnitude but of different signs.
Nash Equilibria: It’s a list of strategies, one for each player with the property that non player can change his own strategy and receive a better payoff.
Finite Game: A game it’s said to be finite if every player have a finite number of strategies.

Non Cooperative Games are described in two classic ways:
Strategical or Normal Form and the Extensive Form. In the Normal one the game it’s described by a triplet of two sets and an order relation:
J : the set of all players
Si : the set of strategies for the i player
>i : preference relations asociated to each player(a,b belongs to Si, a it’s prefered to b if and only if a>b ). And the game it’s printed in a payoff matrix that reflects the payoffs every player receive. For example there’s a classic game called the Prisoner Dilemma, where two suspects are arrested without proofs and they are interrogated if they both cooperate and declare themselves guilty they receive a payoff 6, if one of them cooperate and the other one defect they receive 0 and 9 respectively while defecting give them a payoff 1. Here the payoffs are referred as months in prison, so the wise rational desition would be to minimize their’s payoff. An strategical representation of this game would be:
J={1,2}
S1={C(Cooperate),D(Defect)}
S2={C(Cooperate),D(Defect)}
<i being described by the payoff matrix(notice it’s < because this game aim it’s to minimize the payoffs instead of maximize it)
And the Game matrix:
I II C D
C 6 6 0 9
D 9 0 1 1
It’s a non-zero sum finite game since both players number of strategies it’s 2 whose payoffs doesn’t sum zero.

While in the Extensive form the Game it’s represented as a Tree Game. Every position of the game it’s put as node of the tree. This is to give a better idea of a time-depending game because it focus on all the possible desitions to be taken and all the possible responses to it making explicit the time.

This it’s nothing but a too brief description of game theory, that could be really useful for game developers by giving you algorithms for achieving Nash Equilibria, so if anyone feels interested for Game Theory I have many really good papers on GT. I’m particullarly interested in applying Genetic Algos to solve Games. If there’s either anyone interested on GT who wants me to help him/her or if anyone to help me with the Genetic Algorithms-Game Theory connection that I need I will gladfully answer :excl: /thank for it!!!!!!!! :D

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EvilSmile 101 Feb 26, 2005 at 07:37

Sounds interesting mate. Why don’t you paste a few links here?

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Jason 101 Feb 28, 2005 at 13:53

@EvilSmile

Sounds interesting mate. Why don’t you paste a few links here? [snapback]16260[/snapback]

I’ll soon put out some of my thesis on Game Theory EvilSmile, I promess I will!!!! :excl: and I’ll attach some bibliography :D

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scanmaster_k 101 May 04, 2005 at 15:27

The thing with the choices is gameplay, game theory (Ludology), is to me the science of games which of course include gameplay because that is what defines a game.

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irinacristescu 101 Oct 10, 2005 at 19:35

Hi, my name is Irina Cristescu and i am a student in the 4th year of study at the Faculty of Psychology. This year i must elaborate a final diploma paper, and i have decided to study Game Theory in Psychology, especially in the domain of Organizational Psychology. I couldn’t find any books on Game Theory in my country, except a few in Economics and Mathematics, but i need very much a psychological approach. The internet ressources are very vague and not very helpful if i don’t have a more scientific information.
I hope that someone could help me, I don’t even know if i posted the message in the right place. I would be very grateful if somebody could recommend me a few directions about a psychological/organizational approach on game theory, i really need help.
Thank you very much
With respect
Irina

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corey 101 Oct 10, 2005 at 19:55

@irinacristescu

I couldn’t find any books on Game Theory in my country, except a few in Economics and Mathematics, but i need very much a psychological approach.

http://print.google.com/print?q=game+theory&btnG=Search+Print should help.

corey

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Hodge 101 Oct 11, 2005 at 00:51

This was a good read, thanks jason.

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corey 101 Oct 11, 2005 at 17:22

@irinacristescu

Hi, my name is Irina Cristescu and i am a student in the 4th year of study at the Faculty of Psychology. This year i must elaborate a final diploma paper, and i have decided to study Game Theory in Psychology, especially in the domain of Organizational Psychology.

I thought this article might be an interesting read and has a book reference: http://www.businessweek.com/bwdaily/dnflash/oct2005/nf20051011_3028_db084.htm?campaign_id=rss_daily

corey

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irinacristescu 101 Oct 11, 2005 at 23:20

Thank you very much Corey for your kindness to help me and for the information you have provided. I havn’t studied Game Theory in school, maybe this is the reason why i’m having a little difficulty in finding information about psychologycal approach on game theory. In my country this domain is not yet very developped, so I have found little if not no books at all in the library of my faculty:wallbash: . So, not having acces to books, i tried the ressources on the internet, and i have found that a new theory has been developed in Game Theory: Psychological or Behavioral Game Theory. The ortodox Game Theory sustains that the decident is rational, and he takes the decisions on the basis of rational calculus. But here comes psychology and says that decidents are not emotional geniuses, and that they are not always rational, because of the interference of psychological variables. This is the lead i tend to follow. Unfortunately book refferences do not help me much if can’t find them in my country, and the internet ressources i have consulted are poor in experimental studies on Psychological Game Theory. But the article you have recommended to me was very useful because i’ve found out, for example, that Daniel Kahneman and Vernon L. Smith won the nobel prize for for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty. I will follow this lead and hope to find a few experimental studies in this area. Thank you very much again, your information is very helpful to me.
Have a nice day
Irina
ps: sorry for the grammar errors, my english is not exactely accurate