Tuesday, April 04, 2017

Bholenath and Game theory (Prof. SD's diary I)

Note: The piece below is a part of my next novel. It's the first diary entry of an Economics professor who is a pioneer in game theory. Any comments will be surely appreciated.
Bholenath is the greatest game theorist. He looks at every interconnection present in this world. We can never fully understand these interconnections. We are endogenous to it. Any idea we throw in will in effect change us. The concept of endogeneity thwarts any human mind to generalize a concept or a theorem without assumptions. That is why I never disbelieved in Bholenath. There has to be an exogenous observer who sees things but does not change. It remains in question how much he can influence what’s going around. It would be great writing a research paper with him.

He not only observes but maintains the equilibrium present on earth. There are innumerable interactions among humans present at any given time. There are so many games at play at once. The boundary for each game may be limited, but their subtle interactions cannot be ignored.
Sometimes solutions don’t seem plausible. We can never find an equilibrium to a given set up. But it is important to look at the boundaries and not assume that there is no solution. Maybe we have not taken that crucial element into consideration, maybe we have left it out, even though one must admit that extending the boundaries not only brings in a new perspective but also more questions. That is where the art of a modeller lies. He should know what to bring in and what to leave out of the boundary. He should be ready to question the certain and believe in the improbable. It looks as if I have to do the best modelling of my life to find a solution to this problem I have been facing for so many days now. The boundaries are hazy and nothing is clear. Parameters keep changing regularly. Someone is inside my head and I know for sure it is not me.
Solving for equilibrium looks so simple once you get a solution. A reader can read two-three pages and understand it. It is getting to the solution which is painful. At times when nothing makes sense, a trick of the trade move or discovery of the fallacy in the solution can bring in a ray of hope to the problem solver. What it simply means is that every problem is solvable, anybody with enough patience can solve a problem, and that no problem should be left unsolved. We must reach a solution by working to create the little pinhole in the dark room through which the ray of light can enter. In a separate problem sent to me by my good friend from Cornell University who won the Nobel Prize two years back, a small fallacy had created the issue. Once you clarify it, the path to the solution was as smooth as butter. While these kinds of problems can be solved by simplifying the assumptions and then working towards the solution, my real life problem does not seem to simplify at all. It seems I have laughed after so many days today. How do I suddenly end up hearing sounds after reaching the age of 60? Nobody seems to have an answer, not even game theory.

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