Common knowledge of payoff uncertainty in games

Abstract

Using epistemic logic, we provide a non-probabilistic way to formalise payoff uncertainty, that is, statements such as 'player i has approximate knowledge about the utility functions of player j. ' We show that on the basis of this formalisation common knowledge of payoff uncertainty and rationality (in the sense of excluding weakly dominated strategies, due to Dekel and Fudenberg (1990)) characterises a new solution concept we have called 'mixed iterated strict weak dominance.'

Common Knowledge of Rationality in Extensive Games

“…Although a full answer cannot be given at this stage, we have shown elsewhere that several well-known, normal form game characterization theorems can be treated in our framework (De Bruin [17]). Furthermore, in a paper criticizing a characterization result due to Dekel and Fudenberg [21] we have proved a new characterization result for normal form games (De Bruin [18]). This shows the framework to be fruitful and flexible.…”

“…Ranging over an (if you wish, finite) set of real numbers including the correct utilities (that is, including the set {x|u i (k, l) = x for some k, l, i}), the antecedent u i (k, l) = r turns out true for the utility r that i assigns to O(k, l), while the consequent says that i knows he so assigns utility. In fact, in a critique of the epistemic characterization of the solution concept studied by Dekel and Fudenberg [21] we have formalized common knowledge of the fact that players are approximately correctly informed about their opponents' utility functions (de Bruin [18]).…”