, Volume 78, Issue 1, pp 183-200,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 25 Nov 2011

Deontic Logic for Strategic Games

Abstract

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.