Beyond Nash Equilibrium in Open Spectrum Sharing: Lorenz Equilibrium in Discrete Games

TL;DR

This paper introduces the Lorenz equilibrium, a new solution concept for open spectrum sharing in cognitive radio environments, addressing limitations of Nash and Pareto solutions by promoting fairness and higher payoffs.

Contribution

The paper proposes the Lorenz equilibrium as a novel solution concept that improves fairness and efficiency in spectrum sharing games, serving as an effective selection criterion among Nash equilibria.

Findings

Lorenz equilibrium ensures higher payoffs than Nash equilibrium.

LE promotes equitable and Pareto efficient solutions.

LE can serve as a selection criterion in multi-player discrete games.

Abstract

A new game theoretical solution concept for open spectrum sharing in cognitive radio (CR) environments is presented, the Lorenz equilibrium (LE). Both Nash and Pareto solution concepts have limitations when applied to real world problems. Nash equilibrium (NE) rarely ensures maximal payoff and it is frequently Pareto inefficient. The Pareto set is usually a large set of solutions, often too hard to process. The Lorenz equilibrium is a subset of Pareto efficient solutions that are equitable for all players and ensures a higher payoff than the Nash equilibrium. LE induces a selection criterion of NE, when several are present in a game (e.g. many-player discrete games) and when fairness is an issue. Besides being an effective NE selection criterion, the LE is an interesting game theoretical situation per se, useful for CR interaction analysis.