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"Mathematics student enthusiastic about economics" - SOP for economic Ph.D. program

h_n_abadi 1 / 1  
Dec 18, 2010   #1
It might seem plausible that a mathematics student becomes enthusiastic about game theoretical approach in economics, but in chasing my interests, I have experienced a rather atypical perspective. The word ``plausible'' here refers to the widely accepted idea that mathematical tools critically have helped social scientists, especially economists, to pursue their analysis; however, to me, mathematics is not merely a tool, rather, patterns of argumentation which are the essence of consistent conclusions. Analyzing economics as a game among economic agents, one will be confronted by some original queries. How these agents interact and how they make their decisions? In what degree agents are limited in their decision making? Could they be contributed to any learning structure? Succinctly and beautifully is Ludwig Von Mises' statement: \textit {``Action is a display of potency and control that are limited. It is a manifestation of man who is restrained by the circumscribed powers of his mind, the physiological nature of his body, the vicissitudes of his environment, and the scarcity of external factors on which his welfare depends.''} An amazing coincidence of mathematics and economics occurred to me when I became beleaguered with such questions in a mathematical logic class. In fact, my perception of game theoretical features of economics and modeling agents' knowledge has specialized throughout my involvement in that class, which seems to be rather anomalous at the first glance. I am impressed by the fact that how mathematical logic got me engaged in game theory and, especially, modeling knowledge of economic agents.

My ardor for mathematical logic burgeoned in the foundations of mathematics class for the first time in the first year of my undergraduate, when I vehemently encountered with construction of mathematical reasoning, which other courses in mathematics had bereft. During my junior, this idea went to a much more sophisticated form in the logic class, where I found myself imbued with enthusiasm for a deep understanding of the natural deduction system and soundness-completeness theorems. I faced an alluring turning point then, the concept of epistemic logic. It was truly astonishing to know that these materials play an influential role in the economic issues pertaining to modeling knowledge. Indeed, the classic assumption of rational economic agents which have been predominant in the economic literature, have always been a challenging area and the matter of knowledge is a key point here, since agents if limited, are circumscribed in their knowledge, and these leads to the idea of modeling knowledge of agents who have constraints in their cognitive power.

I was elected for two consecutive years as a member of SAMCS\footnote{Scientific Association of Mathematics and Computer Science}. The organization's main purpose is to bring about some improvement in the perception of mathematics for the university's students. We organized some mathematics contests, including PMO\footnote{Preliminary Mathematics Olympiad}, to ennoble the mathematical competitive environment in the university. Although my membership in this association combined with my engagement in mentioned extra-curricular game theoretical concepts failed me to do perfectly as I could on some other courses in my undergraduate years, I never stopped to prosecute my real volition. In spite of all the reversals, I relied on my firm resolution to study just that which interested me and not that for which I was designated.

Studying game theory, especially modeling knowledge, got me familiar with the concept of bounded rationality which I shall say was my incipient inclination toward economics and led me to broaden my understanding of economics as a graduate student. I have pursued what I had been thrilled for throughout my graduate years. It might seem that I have done a good job as a graduate student compared to my undergraduate years, however, I strongly believe this is a result of the eagerness in my educational route. Being in the area of study in which I have been interested, game theory, I plausibly coped with the onerous fusion consisting tough academic curriculum, on the one hand, and zealousness to do my own researches on the other.

As a researcher in the area of game theory, I am interested in materials mostly associated with theoretical approaches. Indeed, the most exciting area of research to me is to extend the idea of bounded rationality inasmuch as to be applicable as a cogent substitute for rationality. Here, the purpose will be to weaken the assumption of rational agents' knowledge to the more acceptable ones, beliefs, which emerge inevitably from relaxing common knowledge assumption. As a project for the course Microeconomics II, I investigated the essence of the topic. Two key approaches regarding bounded rationality, the set theoretical and logical approach, as I had expected due to my previous acquaintance, had a telling conjunction with my mathematical background in logic and set theory and have kindled my passion to seek more. Although the term "seeking more" seems to be relatively obscure describing one's passion, it embodies that I am not relying categorically on what I just have got. Though I am preparing myself for a wider range of choices for my research, since nothing is totally predictable about the way to which my interests will lead me, I considerably anticipate that the mentioned area will be the theme of my research.

Besides this fundamental area of research, as a specific game theoretical implication to the economic situations, one of my classmates and I have started an investigation on oligopolies and have looked into a model of oligopoly consisting firms with capacity constraint in a Ph.D. game theory course. The idea of capacity constraint, which originally was professor Szidarovszky's\footnote{Ferenc Szidarovszky, Professor of Mathematics and Economics, Department of System and Industrial Engineering, University of Arizona, who taught game theory jointly with professor Farshad Fatemi.}, one of our game theory professors, was an alluring issue, since, in reality such an assumption is ineluctable for the firms. Though the work is still in progress, some mathematical modelings have been done, and the main purpose of the research is to explain that in what degree the result of such oligopoly could be different from the classic models. Although this research is leading me to an investigation in oligopolies, I find myself enthusiastic in variety of subjects in game theory, such as bargaining, repeated games, cooperative games and mostly decision theory. Indeed, the basic idea of game theory in describing a situation in which agents' well-being are affected by the others action -the common characteristics of all these subjects- is what has inclined me toward game theoretical economic analysis.

Following up on my interests, the problematic issue of making a decision for continuing my academic education emerges. Being resolute in my area of research in game theory, I am doing the laborious task of searching for graduate programs with appropriate concentration on this field of specialization. NYU's economics program stands as my top priority, and it is largely because of the outstanding faculty's researches and theoretical approach of game theory, especially in bounded rationality, which makes the NYU's economics program an unparalleled one. In the quest for suitable programs, I was thrilled to know that professors Ariel Rubnestein and David Pearce both are NYU's faculty members. Without reservation, professor Rubnestein's book, \textit{Modeling Bounded Rationality}, is what that impressed and led me to purse my education in economics. I have always been referred to another book of him, \textit{A Course in Game Theory}, which was one of the references of our game theory course, for any theoretical problems. These professors extensive work on the area of bounded rationality is what I consider the best chance for pursuing my intended field of study. Repeated games is an essentially important area of study in economics, since most of social games have the perennial nature, and professor Pearce research in this area is truly comprehensive. In addition, I have followed professors Efe Ok and Charles A. Wilson papers in the decision theory. In fact, the astonishing coherence of these professors academic works makes economics program at NUY to loom large in my mind. Undoubtedly, together these professors' proficiency in the forefront of game theory would make my work as a researcher at NYU full of motivation and enthusiasm.

EF_Kevin 8 / 13,324 129  
Dec 23, 2010   #2
How do these agents interact, and how do they make their decisions?

Specialized is the wrong word here:
In fact, my perception of game theoretical features of economics and modeling agents' knowledge has specialized throughout...
Oh, I know what to do:
In fact, my perception of game theoretical features of economics and modeling agents' knowledge has become specialized throughout during my involvement

I am impressed by the fact that how mathematical logic got me ...

This is a VERY well constructed sentence, very artfully constructed: Studying game theory, especially modeling knowledge, got me familiar ...

You need another apostrophe
Indeed, the basic idea of game theory in describing a situation in which agents' well-being are affected by the others' action

The essay seems to end abruptly. How about adding a conclusion paragraph that expresses the main theme of the essay. Also, as I look to the beginning of the essay I see no clear main idea for the essay either. Is there a perfect word or term for the reader to associate with your outlook? What word or term would you choose as your theme? Add it to the thesis statement in paragraph 1.

OP h_n_abadi 1 / 1  
Dec 23, 2010   #3
Thanx a lot, you were very helpful.

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