The core of the games with fractional linear utility functions

TL;DR

This paper studies cooperative production games with fractional linear utility functions, transforming them into linear programs to analyze core stability and stable outcomes in multiobjective and exchange economy settings.

Contribution

It introduces a method to analyze the core of fractional linear utility games using linear programming duality, extending to multiobjective and exchange economy scenarios.

Findings

Proves the non-emptiness of the core for these games.

Characterizes stable outcomes in multiobjective cases.

Analyzes cooperative games in exchange economies.

Abstract

We consider fractional linear programming production games for the single-objective and multiobjective cases. We use the method of Chakraborty and Gupta (2002) in order to transform the fractional linear programming problems into linear programming problems. A cooperative game is attached and we prove the non-emptiness of the core by using the duality theory from the linear programming. In the multiobjective case, we give a characterization of the Stable outcome of the associate cooperative game, which is balanced. We also consider the cooperative game associated to an exchange economy with a finite number of agents.