Game Theory and Social Choice
Distinguished Professor Rohit Parikh
Game theory has become important as a central tool in our understanding of the workings of society. And epistemic logic, pursued by computer scientists, and game theory have led to fruitful collaborations. As for social choice theory, in this year of the big election, it is important as a tool to understand how elections work. We will discuss the classical work going back to von Neumann, Morgenstern, John Nash, as well as the work of Kenneth Arrow and Amartya Sen.
This course will provide an introduction to both game theory and social choice with emphasis on topics like the Nash equilibrium, bargaining, the Arrow theorems, Gibbard Satterthwaite theorem and epistemic logic.
List of topics
The topics may include but are not limited to:
Choice and utility, cardinal and ordinal
Mixed strategies and Nash equilibrium
Dominance and Rationalizable strategies
Bargaining. Results of Nash and Kalai-Smorodinsky Auctions
Social choice and elections
Theorems of Arrow and Gibbard Satterthwaite
Aumann’s agreeing to disagree theorem and contributions arising from it including work from CUNY
Epistemic Logic and epistemic game theory
Students will learn the main results in game theory, be able to solve simple games and be able to come up with algorithms where relevant. Another requirement will be to be able explain (and sketch the proof of) major results in social choice like the Arrow theorem.
Homeworks will be assigned each week and graded. There will be a final and (probably) a midterm examination as well. Students who do exceptionally well in the midterm examination will have the option to write a paper in lieu of the final.