Deontic Logic for Strategic Games
Allard Tamminga · Erkenntnis · 2011
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 $${\mathcal{H}}$$ were to perform action $$\alpha_{\mathcal{H}}$$ , then, in group $${\mathcal{F}}\hbox{'s}$$ interest, group $${\mathcal{G}}$$ ought to perform action $$\alpha_{\mathcal{G}}$$ ” and (2) conditional permissions, having the form “If group $${\mathcal{H}}$$ were to perform action $${\alpha_{\mathcal{H}}}$$ , then, in group $${\mathcal{F}}\hbox{'s}$$ interest, group $${\mathcal{G}}$$ may perform action $$\alpha_{\mathcal{G}}$$ ”. 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 $$ a^{\ast} $$ 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.