Introduction to Game Theory

Transcription

1 Introduction to Game Theory ICPSR First Session, 2014 Scott Ainsworth, Instructor David Hughes, Assistant Bryan Daves, Assistant Course Purpose and Design: Strategic concerns underpin many social and political settings. As such, a basic understanding of strategic choices enhances one s understanding of social and political settings. This course introduces many of the fundamental concepts and tools for understanding basic game theory. The formal analysis inherent to game theoretic methods is deductively structured and logically based. However, no mathematical background beyond simple arithmetic is presumed for this course. Some set theory and calculus might be introduced. Those students with some familiarity with game theoretic tools will have a chance to refine those tools. The course has three goals. Our first goal is to become comfortable with the basics. Our second goal is to understand the application of game theoretic tools to various settings. Our third goal is to begin the development of our own applications of the tools and techniques discussed. The careful application of formal work will be a prominent concern throughout the course. Key Concepts Covered in the Course Include: At the broadest level: cooperative game theory, noncooperative game theory, equilibrium concepts associated with cooperative and noncooperative game theory At a more refined level: imputations, the core, pure and mixed strategies, complete and incomplete information, perfect and imperfect information, subgame perfection, beliefs Reading Material: The main text is Joel Watson s Strategy: An Introduction to Game Theory, 3 rd Edition. Other readings will be available electronically. Generally, the electronic articles apply game theoretic tools. Our discussion of the substance will be limited and I will not vouch for the meaningfulness of substantive applications. Instead, for the articles, we will focus on the development of the game theoretic model.

2 Lecture Style: I will use slides, but there is considerable board time. Grading: Grades are based on homework (@50%) and a final (@50%). Homework will be assigned toward the middle of the week (T, W, Th). T & W homework will be due on Friday. Th homework will be due on Monday. For those of you new to ICPSR, the pace is intensive for students, TAs, and instructors. Syllabus and Course Structure This course days. We will not meet on the 4 th of July. The final will be on the last day. We are left two-hour days. This syllabus is my best estimate of what we ll cover and when we ll cover it. Day 1: How do we understand people? Introduction, preferences, utility Watson Ch. 1 Recommended: Luce and Raiffa s Games and Decisions Ch. 2, Morrow s Game Theory for Political Scientists Ch. 2 Days 2: Cooperative Game Theory How to Share a Dollar Luce and Raiffa s Games and Decisions Ch. 8, 9 Ordeshook s Game Theory and Political Theory Ch. 7, 8, 9 Days 3 & 4: Bargaining The Nash Bargaining Solution Watson Ch. 18 Luce and Raiffa s Games and Decisions Ch. 6

3 Days 4 & 5: Applications of Cooperative Games Weingast A Rational Choice Perspective on Congressional Norms. American Journal of Political Science 23: Tsebelis Decision Making in Political Systems: Veto Players in Presidentialism, Parliamentarism,Multicameralism and Multipartyism. British Journal of Political Science 25: Days 5 & 6: What features of a social or political situation create a game? Extensive and Normal Form Game Forms Watson Ch. 2, 3 Recommended: Morrow s Game Theory for Political Scientists Ch. 3 Day 7: Normal Form Games Watson Ch. 4 & 5 Day 8: Strategies and Equilibrium Concepts Watson Ch. 6, 7 & 12 Day 9: Strategies and Equilibrium Concepts, cont.ed Watson Ch. 8, 9, 10 & 11 Days 10 & 11: Simple Games to Re-introduce Preferred to Sets and Win Sets Bonneau, Hammond, Maltzman, Wahlbeck Agenda Control, the Median Justice, and the Majority Opinion on the U.S. Supreme Court. American Journal of Political Science 51:

4 An Overview of Models of Legislatures Selections from Krehbiel Spatial Models of Legislative Choice. Legislative Studies Quarterly 13: Days 12 & 13: Subgame Perfection and Applications with Subgame Perfection Watson Ch. 14 & 15 Ferejohn and Shipan Congressional Influence on Bureaucracy. Journal of Law Economics and Organization 6:1-20. Proksch & Slapin Institutional Foundations of Legislative Speech. American Journal of Political Science 56: Thrower, Sharece. N.d. Presidential Action and the Supreme Court: The Case of Signing Statements. WP. University of Pittsburgh. Clark The Separation of Powers, Court Curbing, and Judicial Legitimacy. American Journal of Political Science 53: Day 14: Another look at bargaining Watson Ch. 19 Bohnet, Frey, Huck More Order with Less Law: On Contract Enforcement, Trust, and Crowding. American Political Science Review 95: Day 15: Repeated Games Axelrod The Emergence of Cooperation among Egoists. American Political Science Review 75: Watson Ch. 22 Recommended: Selections from John Maynard Smith. Evolution and the Theory of Games.

5 Day 16: Games of Incomplete Information Watson Ch. 24, 26 & 28 Day 17: Introducing Signals Appendix A in Bohnet, Frey, Huck More Order with Less Law: On Contract Enforcement, Trust, and Crowding. American Political Science Review 95: Schiemann Interrogational Torture. Political Research Quarterly 65:3-19. Ainsworth Regulating Lobbyists and Interest Group Influence. Journal of Politics 55: Farrell Cheap Talk, Coordination, and Entry. Rand Journal of Economics 18: Recommended: Cho and Kreps Signaling Games and Stable Equilibria. Quarterly Journal of Economics 102: Kreps Out of Equilibrium Beliefs and Out of Equilibrium Behavior in The Economics of Missing Markets, Information, and Games, ed. Frank Hahn. Oxford. Day 18: Wrap-up and Final By the end of this course, the following concepts and jargon will have been introduced. backward induction, Bayes theorem, beliefs, Cartesian product, cheap talk, complete information, cooperative game, core, coordination, directed graph, dominance, dominate, edge, extensive form game, focal point, imputation, incomplete information, information set, iterated dominance, intuitive criterion, mapping, mixed strategy, mixed strategy equilibrium, Nash Bargaining Solution (NBS), Nash equilibrium, nature, node (including initial & terminal), non-cooperative game, normal form game, pareto, perfect Bayes, player, pooling, preferred-to-sets, rationalizable, repeated game, separating, sequential rationality, strategic form game,

6 strategy, subgame, subgame perfection, tree, types, utility, v-set, yolk, win sets, zero sum There are many very good game theory references. The following is a woefully incomplete list of authors in alphabetical order. Austen-Smith and Banks have a two volume set. The first volume explores the connections between social choice theory and game theory, and the second focuses on game theory. Friedman is an economic historian who also studied duopoly theory and game theory. Fudenberg and Tirole Kreps has an extensive micro econ text that has excellent game theory presentations. McCarty and Meirowitz are political scientists who wrote a game theory text that is a notch more advanced than Watson s. This is one of the most recent game theory texts written for political scientists. Myerson wrote a very nice text back in the 1990s. Subsequently, he received a Nobel Prize for his work on mechanism design. Osborne has several game theory texts that are commonly used. They are a notch more advanced than Watson s.