Bridging the Gap Between Single and Multi Objective Games

TL;DR

This paper establishes a theoretical connection between single and multi-objective games, enabling the transfer of algorithms and insights between these models, and introduces a new fictitious play algorithm for multi-objective games.

Contribution

It provides a formal transformation between single and multi-objective games, ensuring equivalence of Nash equilibria, and demonstrates its utility with a new algorithm for multi-objective games.

Findings

Game transformation guarantees equivalence of Nash equilibria.

The mapping allows applying algorithms across game types.

A fictitious play algorithm for multi-objective games is introduced.

Abstract

A classic model to study strategic decision making in multi-agent systems is the normal-form game. This model can be generalised to allow for an infinite number of pure strategies leading to continuous games. Multi-objective normal-form games are another generalisation that model settings where players receive separate payoffs in more than one objective. We bridge the gap between the two models by providing a theoretical guarantee that a game from one setting can always be transformed to a game in the other. We extend the theoretical results to include guaranteed equivalence of Nash equilibria. The mapping makes it possible to apply algorithms from one field to the other. We demonstrate this by introducing a fictitious play algorithm for multi-objective games and subsequently applying it to two well-known continuous games. We believe the equivalence relation will lend itself to new insights by translating the theoretical guarantees from one formalism to another. Moreover, it may lead to new computational approaches for continuous games when a problem is more naturally solved in the succinct format of multi-objective games.