Deontic Logic for Strategic Games

We develop a multi-agent deontic action logic to study the logical behaviour of two types of deontic conditionals: (1) conditional obligations, having the form "If group were to perform action , then, in group interest, group ought to perform action " and (2) conditional permissions, having the form "If group were to perform action , then, in group interest, group may perform action ". First, we define a formal language for multi-agent deontic action logic and a class of consequentialist models to interpret the formulas of the language. Second, we define a transformation that converts any strategic game into a consequentialist model. Third, we show that an outcome is a Nash equilibrium of a strategic game if and only if a conjunction of certain conditional permissions is true in the consequentialist model that results from the transformation of that strategic game.