Entropy-Norm space for geometric selection of strict Nash equilibria in n-person games

TL;DR

This paper introduces an entropy-norm based geometric criterion for selecting strict Nash equilibria in n-person games, aiming to balance utility maximization and inequality aversion, supported by experimental comparison.

Contribution

It proposes a novel entropy-norm space mapping for Nash equilibrium selection that considers both utility and fairness, extending existing equilibrium analysis methods.

Findings

The entropy-norm criterion effectively orders Nash equilibria considering equality and utility.

Application to group decision making shows the criterion's practical relevance.

Limitations are discussed for certain exceptional cases.

Abstract

Motivated by empirical evidence that individuals within group decision making simultaneously aspire to maximize utility and avoid inequality we propose a criterion based on the entropy-norm pair for geometric selection of strict Nash equilibria in n-person games. For this, we introduce a mapping of an n-person set of Nash equilibrium utilities in an Entropy-Norm space. We suggest that the most suitable group choice is the equilibrium closest to the largest entropy-norm pair of a rescaled Entropy-Norm space. Successive application of this criterion permits an ordering of the possible Nash equilibria in an n-person game accounting simultaneously equality and utility of players payoffs. Limitations of this approach for certain exceptional cases are discussed. In addition, the criterion proposed is applied and compared with the results of a group decision making experiment.