On Satisficing in Quantitative Games

TL;DR

This paper explores the satisficing problem in two-player discounted-sum graph games, proposing automata-based methods that outperform traditional numerical approaches when the discount factor is an integer.

Contribution

It introduces a novel automata-based approach for satisficing in discounted-sum games, showing improved efficiency over numerical methods for integer discount factors.

Findings

Automata-based method is more efficient for integer discount factors.

Satisficing offers broader applicability than optimization in game analysis.

Numerical methods are less compelling compared to automata-based approaches.

Abstract

Several problems in planning and reactive synthesis can be reduced to the analysis of two-player quantitative graph games. {\em Optimization} is one form of analysis. We argue that in many cases it may be better to replace the optimization problem with the {\em satisficing problem}, where instead of searching for optimal solutions, the goal is to search for solutions that adhere to a given threshold bound. This work defines and investigates the satisficing problem on a two-player graph game with the discounted-sum cost model. We show that while the satisficing problem can be solved using numerical methods just like the optimization problem, this approach does not render compelling benefits over optimization. When the discount factor is, however, an integer, we present another approach to satisficing, which is purely based on automata methods. We show that this approach is algorithmically more performant -- both theoretically and empirically -- and demonstrates the broader applicability of satisficing overoptimization.