哥伦比亚大学经济金融科研项目

Columbia University Economic and Financial Research Project

科研主题

以下领域内的相关课题，具体课题根据学生的基础，导师面试后确定。

game theory 【博弈论】

Design of mechanism and method  【机制与方法设计】

Decision theory  【决策理论】

Behavioral economics   【行为经济学】

Information Acquisition and Mechanism Method Design【信息获取与机制方法设计】

Mathematics【数学】

科研课题（参考课题）

Goals

How do/should individuals make decisions in this interactive world? Through this research program, students are introduced to the game theoretic perspective of social and economic activities. More importantly, students will learn to read papers in the frontier of economics and appreciate their strengths and weaknesses. Toward the end of the program, students will be guided to initiate their own research on a topic of their choice. Hopefully the research is continued in the future and turned into a paper.

The tentative plan is to:

1. Lay the mathematical foundation for modern game theory - so you can speak jargon and think about games abstractly;

2. Discuss numerous games encountered in the real world - so you get a sense of how economists \simplify" complex situations into a compact game-form;

3. Study in-depth the existing literature of selected subareas of game theory –so you develop the knowledge of what has/has not been done and acquire the skills to replicate a paper as well as write your own;

4. Formulate an interesting question and probe its answer via guided research - so you take away first-hand experience of how research actually goes and discover for yourself whether it is exciting or excruciating.

Whether you are in the process of applying for graduate school or just considering that as an option, this research program will give you new insights on the life of an academic. Even if you have no intention of pursuing academia, knowing game theory may provide you with a different angle to approach strategic decisions. To be a bit practical, many financial trading firms are taking advantage of game theoretic models to make millions of profits nowadays. No wonder game theory has become a mandatory course in business schools, and the topic often pops up in job interviews.

Last but not least, many results in game theory are cool and even surprising. In learning these results, you will also get to know such great names (including 10 Nobel laureates) as John von Neumann, Harold Kuhn, David Blackwell, John Nash, Rein-hard Selten, John Harsanyi, Robert Aumann, Thomas Schelling, Eric Maskin, Roger Myerson, David Gale, Lloyd Shapley, Alvin Roth, Drew Fudenberg and Jean Tirole. I hope you will be fascinated and inspired by their talents as well as by their lives.

Prerequisites

As the program will be mostly self-contained, it is not necessary to have previous expo-sure to game theory or any other subfield of economics. However, some advanced mathematical knowledge is indispensable to understanding the materials and ultimately proving theorems of your own. The detailed requirements are listed below:

You should be comfortable with algebraic manipulations such as solving systems of (linear) equations. Knowing some basic calculus (how to take derivatives) and/or probability (what expectation means) is a definite plus. Better still is decent famil-iarity with real analysis, point-set topology, linear algebra and probability theory. Anability to read and write proofs will be highly beneficial. But most importantly, you should be willing to look things up and not let confusion slip through。