A comparison of the notions of optimality in soft constraints and graphical games

TL;DR

This paper explores the relationship between optimality concepts in soft constraints and graphical games, showing that many optimal solutions in soft constraints align with Nash equilibria and Pareto efficiency in graphical games.

Contribution

It establishes a formal connection between optimality in soft constraint satisfaction problems and equilibrium concepts in graphical games, broadening understanding across both fields.

Findings

Optimal solutions in weighted SCSPs correspond to Nash equilibria.

Many optimal solutions are also Pareto efficient strategies.

The connection applies to a large class of soft constraints.

Abstract

The notion of optimality naturally arises in many areas of applied mathematics and computer science concerned with decision making. Here we consider this notion in the context of two formalisms used for different purposes and in different research areas: graphical games and soft constraints. We relate the notion of optimality used in the area of soft constraint satisfaction problems (SCSPs) to that used in graphical games, showing that for a large class of SCSPs that includes weighted constraints every optimal solution corresponds to a Nash equilibrium that is also a Pareto efficient joint strategy.