Econ 790. Game Theory and Applications
Description. This course covers basic game theory and applications. Topics covered include strategic games with complete information, Bayesian games (with incomplete information), extensive games with perfect information, and extensive games with imperfect information. Equilibrium concepts covered include Nash equilibrium, mixed-strategy Nash equilibrium, rationalizability, Bayesian Nash equilibrium, subgame perfect Nash equilibrium, and sequential equilibrium. Depending on availability of time, additional topics may include strictly competitive games and repeated games. The course may include diverse applications such as in business strategy, auctions, voting, international trade, military conflicts, contracts, regulation, and industrial organization. Prerequisites: Math 127 and Math 526, or equivalent.
Econ 901. Monotone Games
Description. Socio-economic situations involve interdependent decision-making in which individual decisions affect the decisions of others and thereby affect the collective outcome. The behavior of participants in these situations and their collective impact can be predicted with mathematical models from game theory.
This course is about monotone games – those situations in which participants have incentives to take decisions in particular directions, that is, either decisions that are coordinated with those of others, or decisions that are opposed to those of others, or a combination of the two. The first type of decision exhibits strategic complements, the second type exhibits strategic substitutes, and the third type is a combination of the two, sometimes termed strategic heterogeneity. Collectively, incentives in these cases fall under the category of monotone interdependent incentives or monotone incentives and occur in a large number of situations in a variety of disciplines, including biology, business, computer science, economics, mathematics, medicine, philosophy, political science, psychology, and others.
Monotone games study the pattern of rational and decentralized decision-making by participants facing monotone incentives and their collective equilibrium impact when all participants are simultaneously trying to do the best for themselves and there is no tendency for change.
A novel feature here is that the theory of monotone games is developed in a unified manner and many applications are presented. This includes both the established work on games with strategic complements and the new work on strategic substitutes and strategic heterogeneity, the latter cases being available only in professional journals. We shall focus on identifying unifying threads across different cases, and showing how newer results are similar to or different from the standard results, and how students may understand better all these cases under the unifying umbrella of monotone games.
Prerequisites: This is a self-contained course. It is helpful if students know some basic game theory, but this is not required. It is important that students are familiar with formal mathematical reasoning; for example, as covered in PhD core courses in economics. For math students, it is sufficient to have taken Math 500 or its higher equivalents. If you are unsure about your readiness, please contact the instructor.