Games with a Weak Adversary

TL;DR

This paper investigates multi-player graph games with partial observation, establishing decidability and complexity bounds for certain coalition configurations, and revealing the complexity of strategies needed in different informational settings.

Contribution

It presents new decidability results and tight complexity bounds for partial-observation games with specific coalitions, especially when one player is weaker due to limited information.

Findings

Decidability for certain coalition configurations with partial observation.

2-EXPTIME-completeness for parity objectives when player 1 is less informed.

Memory of non-elementary size needed for some cases with perfect observation.

Abstract

We consider multi-player graph games with partial-observation and parity objective. While the decision problem for three-player games with a coalition of the first and second players against the third player is undecidable, we present a decidability result for partial-observation games where the first and third player are in a coalition against the second player, thus where the second player is adversarial but weaker due to partial-observation. We establish tight complexity bounds in the case where player 1 is less informed than player 2, namely 2-EXPTIME-completeness for parity objectives. The symmetric case of player 1 more informed than player 2 is much more complicated, and we show that already in the case where player 1 has perfect observation, memory of size non-elementary is necessary in general for reachability objectives, and the problem is decidable for safety and reachability objectives. Our results have tight connections with partial-observation stochastic games for which we derive new complexity results.