Eco514-Game Theory ecture 6: Interactive Epistemology(1) Marciano siniscalchi October 5. 1999 Introduction This lecture focuses on the interpretation of solution concepts for normal-form games. You will recall that, when we introduced Nash equilibrium and rationalizability, we mentioned numerous reasons why these solution concepts could be regarded as yielding plausible restric- tions on rational play, or perhaps providing a consistency check for our predictions about However, in doing so, we had to appeal to intuition, by and large. Even a simple assump- tion such as "Player 1 believes that Player 2 is rational" involves objects that are not part of the standard description of a game with complete information. In particular, recall that Bayesian rationality is a condition which relates behavior and beliefs: a player is "rational if and only if she chooses an action which is a best reply given her beliefs. But then, to say that Player 1 believes that Player 2 is rational implies that Player 1 holds a conjecture on oth Player 2's actions and her beliefs The standard model for games with complete information does not contain enough ure for us to formalize this sort of assumption. Players'beliefs are probability distributions n their opponents'action profiles But, of course, the model we have developed(following Harsanyi)for games with payoff uncertainty does allow us to generate beliefs about beliefs, and indeed infinite hierarchies of mutual beliefs The objective of this lecture is to present a model of interactive beliefs based on Harsanyi's ideas, with minimal modifications to our setting for games with payoff uncertainty. We shall then begin our investigation of "interactive epistemology"in normal-form games by looking at correlated equilibriumEco514—Game Theory Lecture 6: Interactive Epistemology (1) Marciano Siniscalchi October 5, 1999 Introduction This lecture focuses on the interpretation of solution concepts for normal-form games. You will recall that, when we introduced Nash equilibrium and Rationalizability, we mentioned numerous reasons why these solution concepts could be regarded as yielding plausible restric￾tions on rational play, or perhaps providing a consistency check for our predictions about it. However, in doing so, we had to appeal to intuition, by and large. Even a simple assump￾tion such as “Player 1 believes that Player 2 is rational” involves objects that are not part of the standard description of a game with complete information. In particular, recall that Bayesian rationality is a condition which relates behavior and beliefs: a player is “rational” if and only if she chooses an action which is a best reply given her beliefs. But then, to say that Player 1 believes that Player 2 is rational implies that Player 1 holds a conjecture on both Player 2’s actions and her beliefs. The standard model for games with complete information does not contain enough struc￾ture for us to formalize this sort of assumption. Players’ beliefs are probability distributions on their opponents’ action profiles. But, of course, the model we have developed (following Harsanyi) for games with payoff uncertainty does allow us to generate beliefs about beliefs, and indeed infinite hierarchies of mutual beliefs. The objective of this lecture is to present a model of interactive beliefs based on Harsanyi’s ideas, with minimal modifications to our setting for games with payoff uncertainty. We shall then begin our investigation of “interactive epistemology” in normal-form games by looking at correlated equilibrium. 1