On two solution concepts in a class of multicriteria games

TL;DR

This paper compares two solution concepts in multicriteria zero-sum matrix games, highlighting their differences and common roots through characterization and properties, extending classical single-criterion insights.

Contribution

It introduces new consistency properties for characterizing minimax and Pareto-optimal security payoffs in multicriteria games, clarifying their distinctions.

Findings

Minimax and Pareto-optimal security payoffs differ in multicriteria games.

Properties used in single-criterion cases are extended with new consistency conditions.

The paper explains the intrinsic differences and common roots of the two solution concepts.

Abstract

In this paper we compare two solution concepts for general multicriteria zero-sum matrix games: minimax and Pareto-optimal security payoff vectors. We characterize the two criteria based on properties similar to the ones that have been used in the corresponding counterparts in the single criterion case, although they need to be complemented with two new consistency properties. Whereas in standard single criterion games minimax and optimal security payffs coincide, whenever we have multiple criteria these two solution concepts differ. We provide explanations for the common roots of these two concepts and highlight the intrinsic differences between them.