Settled Equilibria


September 26, 2013


When people recurrently interact in familiar settings, social conventions may develop so that people tend to disregard alternatives outside the conventional norm. For rational players to usually restrict attention to a block of conventional strategies, no player should prefer to deviate from the block when others are likely to act rationally and conventionally inside it. We explore concepts that formalize this idea for finite normal-form games. Settled equilibria are Nash equilibria with support in minimal blocks that can be conventionally accepted in such a sense. This refinement has substantial cutting power in many games. It excludes some equilibria that meet other stringent refinements, for instance mixed equilibria of simple coordination games. We provide a psychological micro model for our approach and show that it implies a form of properness. We prove the general existence of settled equilibria. Since these are proper, they induce sequential equilibria in all extensive-form games with the given normal form. Thus, settled equilibrium is also a refinement of sequential equilibrium.


Roger Myerson

Roger Myerson is the Glen A. Lloyd Distinguished Service Professor of Economics at the University of Chicago. Professor Myerson has made seminal contributions to the fields of economics and political science. In game theory, he introduced refinements of Nash’s equilibrium concept, and he developed techniques to characterize the effects of communication when individuals have different information. His analysis of incentive constraints in economic communication introduced some of the fundamental ideas in mechanism design theory, including the revelation principle and the revenue-equivalence theorem in auctions and bargaining. Professor Myerson has also applied game-theoretic tools to political science, analyzing how political incentives can be affected by different electoral systems and constitutional structures. Myerson is the author of Game Theory: Analysis of Conflict (1991) and Probability Models for Economic Decisions (2005). He also has published numerous articles in Econometrica, the Journal of Economic Theory, Games and Decisions, and the International Journal of Game Theory, for which he served as an editorial board member for 10 years. Professor Myerson has a PhD from Harvard University and taught for 25 years in the Kellogg School of Management at Northwestern University before coming to the University of Chicago in 2001. He is a member of the American Academy of Arts and Sciences and of the National Academy of Sciences. In 2007, he was awarded the 2007 Nobel Memorial Prize in Economic Sciences in recognition of his contributions to mechanism design theory. – See more at: