Good day, everyone. I'm Professor N (no, not Nash), and I'm here to present to you a case study on Game Theory. This is a 3 person game, and by nature, it is zero sum. First things first, lets understand a couple of things: (definitions courtesy wiki. too lazy to type. copy paste rules)
1. Game Theory - A branch of applied mathematics that attempts to mathematically capture behavior in strategic situations, in which an individual's success in making choices depends on the choices of others.
2. Zero Sum Game - A situation in which a participant's gain or loss is exactly balanced by the losses or gains of the other participant(s). If the total gains of the participants are added up, and the total losses are subtracted, they will sum to zero.
Yes so now you have what you need for the moment.
Let us consider 3 participants in this game; X, Y and Z. It must be understood that X and Y are involved in a game of their own. Due to unavailability of data, I cannot tell you what the sum of their game is. It can be noted, however, that the unavailability of data can be attributed to the game under study.
X and Y had a great deal of interaction between them, independent of each one's interaction with Z, with varying degrees (not of freedom). This, by nature poses the possibility of two separate games influencing the aforementioned two separate games, making in all, 4. This implies, ceteris paribus, that the degrees (yes, of freedom) must therefore be, 3. Since that has no reference to this case, we shall abandon these said degrees of freedom, spurning them as we would spurn a rabid dog.
The existence of these separate games is of great significance. To understand, let us see the chain of events, starting, ever so obviously, from the beginning. X and Z also had a great deal of interaction between them, starting with the first time these two variables (read participants) came into contact on the same plane (Cartesian, to avoid confusion). However, since we know that the Butterfly Effect holds true in most cases, especially where it should not, certain small changes in the initial system involving X and Z caused their system to be non-robust, and hence, collapse. Although here, interestingly, what was affected was only the correlation and not the regression. Thus far, X and Z had been positively correlated. After and due to the system falling apart from the top, X and Z became negatively correlated. However, due to unavailability of data, and very honestly, fateful cockup, the regression equation never changed.
This means that apart from their negative correlation, the two mentioned variables possess covariance, thereby rendering them not completely independent of each other. Now let us let this be, and examine X and Y.
X and Y, as mentioned before, displayed characteristics of adhesion. The two variables were perfectly correlated. Again, fateful cockup and Edward Lorenz (through the butterfly effect) intervened, and their system lost credibility, though not robustness. The two variables remained suspended within the dynamics of their own cartesian plane. Interestingly and unexpectedly, Y wandered into the plane Z was on and interacted with said Z. Y and Z interacted mostly with decreasing degrees of freedom, since their plane merged and overlapped (merging and overlapping independently, of course) with the plane of X.
As is common with most assumptions, they are proved wrong. X and Y assumed their independance, but not counting on their covariance proved to be the undoing. X and Y found their balance, and their system was restored, eliminating the errors of the previous state. Utimately, X and Y became so closely correlated that their correlation went beyond perfect. The net result of this was that the system Y and Z had been in fell apart completely.
This leaves us with only two systems now, the debris of the aforementioned four. As can easily be seen, this is a zero sum game.
Now you have seen the case. IF you see a problem, give me the solution. Man I love professorial work :D
Jigsaw
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6 comments:
"However, since we know that the Butterfly Effect holds true in most cases, especially where it should not, certain small changes in the initial system involving X and Z caused their system to be non-robust, and hence, collapse."
The whole problem with some of our professors is that they assume that the students are not listening. HOWEVER. They are.
Getting back to the point, just because the "butterfly effect" holds in "most cases", doesnt mean you can use it. One because "most cases" is a probabilistic term, so your hypothesis is henceforth only probably true (hoping that the rest of what you wrote is fine). Of course, the bigger problem for you, professore is that "butterfly effect" is itself very probabilistic. A flutter of a butterfly wing MAY cause rain in Beijing.
So now, like any good student of the sciences, I shall not read the rest of your post, much like I wont listen to a professor ("N") who doesnt know his probabilities. Hmph.
lol....i appreciate your comment, but you again forget that the same probability works both ways
because a) it may....never says will not.....and since the probabilistic value of the application in my system cannot be i) ignored ii) denied iii) calculated, you can go take a running jump....
second of all, i saw this happen first hand, and i know the initial changes that affected the final system.....and witnessed the collapse....therefore, i used it not assuming that the effect might fit here, i used it knowing that it already has.....
again remember, case studies are constructed by people who already know the answers to that particular case....
QED
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interestingly, the butterfly effect should've been called the seagull effect, since that was the bird Lorenz used to first describe his findings....in later speeches and presentations, he used the more "poetic" butterfly
I sense that you are talking about some love triangle business with certain amount of cross fertilization. And I cant but wonder, which one of your subjects will follow this train of thought, or will try to follow this train of thought.
My dear student, either you are
a) stupid,
b) demented, or
c) you recently saw rab ne bana di jodi and have suffered brain damage
This is not a love triangle, but hat is all I can say. when your system changes in a similar fashion, you will understand it in all its poetic splendour. either that, or a seagull will poop on you
Tcha. you mean to say i have to read with more attention aa?
aiyo rama. ok.
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