Reasoning about Dependence, Preference and Coalitional Power

TL;DR

This paper introduces a new logical framework for reasoning about dependence, preferences, and coalitional power, providing axiomatizations, decidability results, and applications to cooperative game theory.

Contribution

It develops the logic of preference and dependence (LPFD) and its hybrid extension (HLPFD), unifying various game-theoretic concepts and connecting with existing logics.

Findings

LPFD is sound, strongly complete, and decidable.

The framework models Nash equilibrium, Pareto optimality, and the core.

Connections with other logics like coalition logic are established.

Abstract

This paper presents a logic of preference and functional dependence (LPFD) and its hybrid extension (HLPFD), both of whose sound and strongly complete axiomatization are provided. The decidability of LPFD is also proved. The application of LPFD and HLPFD to modelling cooperative games in strategic and coalitional forms is explored. The resulted framework provides a unified view on Nash equilibrium, Pareto optimality and the core. The philosophical relevance of these game-theoretical notions to discussions of collective agency is made explicit. Some key connections with other logics are also revealed, for example, the coalition logic, the logic functional dependence and the logic of ceteris paribus preference.