Games between Diversely Sophisticated Players

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Conventional equilibrium analysis of games presumes that all players are rational decision makers with full understanding of the game and the equilibrium behaviour of their opponents. Yet part of what makes strategic interactions interesting is players' limited, often asymmetric ability to understand the game's regularities. Conventional game theory is silent over this important dimension. The last twenty years saw a few attempts to model limited strategic sophistication, in the form of novel "equilibrium concepts" that depart from conventional Nash equilibrium, capturing phenomena such as limited depth of reasoning in one-shot interactions, or naive extrapolation from small, selective or coarse-grained samples drawn from the equilibrium distribution of play. This state of affairs, in which aspects of "boundedly rational expectations" in games are captured by distinct equilibrium concepts, is unsatisfactory. First, it turns modeling bounded rationality in games into a collection of seemingly ad-hoc tools, thus inhibiting economic applications. Second, these aspects should not be viewed as mutually exclusive. They are often artifacts of the feedback players receive when learning the equilibrium, just as conventional informational constraints are not intrinsic personal characteristics but vary from one situation to another. My objective in this project is to formulate a general game-theoretic model that can accommodate many forms of limited strategic sophistication, drawing inspiration from the textbook theory of "games with incomplete information" due to Harsanyi (1967-8). I plan to demonstrate the usefulness of this model with a number of economic applications. If successful, the project can give a major boost to theoretical and applied work on strategic interactions between players with diverse strategic sophistication.