Collaborative Research: Interactive Beliefs, Strategic Uncertainty and Solution Concepts

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What must an analyst hypothesize about the information of agents in order to characterize their behavior in strategic situations? Traditional analysis focused on hierarchies of belief. Recent developments in the theory of games with incomplete information reveals that hierarchies of belief are only part of the answer.This project develops a methodology for describing strategic uncertainty in a primitive, model-independent language and to use that language to investigate the foundations of the standard model for games of incomplete information: Harsanyi type spaces coupled with traditional solution concepts. One a product of this characterization is a new understanding of what properties of information, beyond traditional belief-hierarchies, are sufficient and necessary for various commonly-employed solution concepts.Building on this foundation, the project investigates further the structure of type spaces in order to flesh out the connection between similarity of behavior as captured by toplogical notions to the more familiar and intuitive concept of common p-belief. The project identifies the regular hierarchies at which behavior is "robust" in all games. The remaining hierarchies are "critical types." It is shown that critical types are exactly those types for which some non-trivial common p-belief statement holds. As a consequence of this fact, two extreme results are established. First, all types considered in applied analysis are critical types. On the other hand, almost all hierarchies are regular. Broader ImpactsA clear understanding of non-cooperative solution concepts is crucial for the field of game theory. While it has become indispensable in applied economics, there remain some significant gaps in the foundations of game theory, especially in the context of incomplete information. Most economists apply the Harsanyi methodology without fully understanding its meaning. Indeed, few textbooks even at the graduate level include a careful introduction to the fundamentals of incomplete information and the reduced-form role of the Harysanyi model. A broader goal of this project is to clarify and extend our understanding of the translation between fundamental assumptions and the reduced-form models used to capture them. This will empower applied economists to bring more transparency to the assumptions about interactive beliefs that play an operational role in their models. The art of transforming such fundamental assumptions into tractable but transparent models will eventually become standard material in graduate textbooks.