Reasoning in Games: Players as Programs

Much of the work in traditional game theory is focused on the analysis of solution concepts (typical examples include the Nash equilibrium and its refinements or the various notions of iterated dominance). A solution concept is intended to represent the "rational'' outcome of a strategic interactive situation. That is, it is what (ideally) rational players would do in the situation being modeled. This course will focus on a key foundational question: How do the (rational or not-so rational) players decide what to do in a strategic situation? This has both a normative component (What are the normative principles that guide the players' decision making?) and a descriptive component (Which psychological phenomena best explain discrepancies between predicted and observed behavior in game situations?). The main challenge is to find the balance between descriptive accuracy and normative relevance. While this is true for all theories of individual decision making and reasoning, focusing on game situations raises a number of compelling issues that many students at ESSLLI will find interesting. Robert Aumann and Jacques Dreze adeptly summarize one of the most pressing issues when they write: "the fundamental insight of game theory [is] that a rational player must take into account that the players reason about each other in deciding how to play''. Exactly how the players (should) incorporate the fact that they are interacting with other (actively reasoning) agents into their own decision making process is the subject of much debate.

The aim of this course is to cover some of the most successful and fruitful approaches to modeling players' reasoning and deliberations in games---from logic, artificial intelligence, cognitive science, and game theory---with an eye toward the possibility of unification. The course will draw on (recent) literature in game theory, behavioral economics, cognitive science, and artificial intelligence. Such an interdisciplinary perspective will appeal to many of the participants at ESSLLI. Students attending this course will understand how methods from the mathematical theory of evolution can provide a powerful tool to explain strategic interactions; be exposed to intriguing experimental results about how humans behave in strategic situations; and get hands-on experience using WebPPL probabilistic programs to represent agents in game situations.

The course will be of interest to students in logic, philosophy, computer science (especially multi-agent systems), linguistics (especially those interested in formal pragmatics) and cognitive science. It is an advanced course, but it will be self-contained. I will spend at least one day covering the theoretical background on game theory, Bayesian models and learning in games. An important component of the course is to use the WebPPL probabilistic programming language to represent agents in game situations. I will introduce this programming language (making use of the tutorials at probmods.org and agentmodels.org); however, the goal is not to provide a general introduction to probabilistic programming, but rather to develop enough understanding of the WebPPL language to model agents interacting in game situations. The main objective of the course is to develop useful models of reasoning in specific games and to compare and contrast existing approaches to models players' reasoning in games. I will start with an extended discussion of coordination games, discussing WebPPL programs for agents playing coordination games, Brian Skyrms's model of deliberation in coordination games, models of team reasoning, and the theory of focal points. I will conclude by discussing other games (e.g., the Prisoner's Dilemma, Battle of the Sexes, and the Traveler's Dilemma) and (time permitting) how to account for other psychological phenomena (e.g., risk aversion, guilt, framing effects).