Game Theory II   

Justin Fox is a truely brilliant professor – connecting the math and formal theory to the games that play out in real life, stimulating participation and discussion, and always ready to help. — participant from Russia

Whereas decision theory explores how a single individual makes a decision, game theory explores situations in which multiple individuals must make decisions and uses mathematical models to analyze choices, where the wellbeing of any one individual depends not only upon their own choice, but also upon the choices of others. It has proven to be an extremely useful tool for refining our understanding of a wide variety of phenomena of interest to economists, political scientists, sociologists, anthropologists, and others. In addition, it has helped social scientists to unpack empirical puzzles and motivate further empirical scholarship and is used by governments and companies to inform a wide variety of business and policy decisions.

This one-week course is the second part of a two-course sequence (cf. Game Theory I) and covers more advanced topics in game theory. It covers the techniques game theorists use to analyze ‘imperfect information’ settings in which individuals may be uncertain of the motivations of others. In addition, participants study settings where there are long-run relationships, which is useful for understanding when cooperation among self-interested parties can be sustained.


Dates

This course was offered in 2017.


Instructor

Justin E. Fox (picture), Washington University in St. Louis


Detailed Description

Upon reviewing basic game theoretical concepts, this one-week course quickly moves on to more advanced topics. The first section focuses on scenarios where individuals may be uncertain of the motivations, preferences, or abilities of others. These forms of uncertainty are frequently encountered in in the real word, e.g., where citizens are uncertain of the motivations and capabilities of political leaders or where CEOs are uncertain of the motivations and goals of other business leaders. This part introduces the weak sequential equilibrium, a solution concept that is tailored for games of incomplete information and a refinement of subgame perfection (cf. Game Theory I). We analyze a class of game-theoretic models that allow us to study the formation and maintenance of reputation. For instance, we explore how leaders' desire to cultivate a reputation for having the 'correct' policy preferences can lead them to pursue policies that are not in the public's best interest and under what conditions an individual's advice and recommendations can be trusted by others.

For the second and final part of the course, we turn to analyzing settings where individuals have long-run relations with each other. This allows us to study cooperation, e.g., among individuals or nations.

Key topics covered by this course include:

  • Simultaneous move games and sequential move games under conditions of imperfect information

  • Key solution concepts for games of imperfect information (e.g., Bayesian equilibrium and perfect Bayesian equilibrium)

  • The conditions under which individuals are able to credibly convey their private information (such as their motivations and intentions) to others, with a focus on cheap-talk and signaling games

  • Reputation formation and maintenance

  • The conditions under which cooperation can arise in long-run relationships, with a focus on repeated games, including the repeated prisoner's dilemma


Class meetings focus on both theory and application and consist of a combination of traditional lectures and hands-on exercises, where problem sets reinforce the lecture material. Examples of phenomena that will be covered include policymaking in the shadow of elections, human capital accumulation and job-market signaling, and the role of institutions in fostering cooperation among individuals and nations.


Prerequisites

We strongly encourage participants to combine this course with the introductory Game Theory I. Alternatively, participants should be familiar with the concepts of Nash and subgame perfect equilibrium.


Requirements

Participants are expected to bring a WiFi-enabled laptop computer. Access to data, temporary licenses for the course software, and installation support will be provided by the Methods School.


Core Readings

Osborne, Martin J. 2004. An Introduction to Game Theory. Oxford: Oxford University Press.


Suggested Readings

Gibbons, Robert. 1997. An Introduction to Applicable Game Theory. Journal of Economic Perspectives 11: 127-149.

Fox, Justin, and Lawrence Rothenberg. 2011. Influence without Bribes: A Non-Contracting Model of Campaign Giving and Policymaking. Political Analysis 19: 325-341.

Gerson, Jacob E., and Matthew C. Stephenson. 2014. Over-Accountability. Journal of Legal Analysis 6: 185-243.


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