Best-Effort Strategies for Losing States

TL;DR

This paper investigates strategies in finite graph games where Player 1 aims to produce winning traces, focusing on states where Player 1 cannot guarantee a win, and introduces criteria and algorithms for optimal play.

Contribution

It provides a characterization of admissible strategies and shows the equivalence between positional winning and subgame perfect strategies.

Findings

Characterization of admissible strategies

Algorithm for computing admissible strategies

Equivalence between positional winning and subgame perfect strategies

Abstract

We consider games played on finite graphs, whose goal is to obtain a trace belonging to a given set of winning traces. We focus on those states from which Player 1 cannot force a win. We explore and compare several criteria for establishing what is the preferable behavior of Player 1 from those states. Along the way, we prove several results of theoretical and practical interest, such as a characterization of admissible strategies, which also provides a simple algorithm for computing such strategies for various common goals, and the equivalence between the existence of positional winning strategies and the existence of positional subgame perfect strategies.