Hierarchical Information and the Synthesis of Distributed Strategies

TL;DR

This paper explores conditions under which the complex problem of synthesizing strategies in infinite, imperfect information games becomes decidable, especially focusing on hierarchical information structures and their variations.

Contribution

It introduces new decidable classes of distributed synthesis problems by analyzing hierarchical information variations in synchronous games with perfect recall.

Findings

Decidability is maintained when the information hierarchy varies during the game.

Transient phases without hierarchical information are compatible with decidability.

The results have implications for designing distributed system architectures.

Abstract

Infinite games with imperfect information are known to be undecidable unless the information flow is severely restricted. One fundamental decidable case occurs when there is a total ordering among players, such that each player has access to all the information that the following ones receive. In this paper we consider variations of this hierarchy principle for synchronous games with perfect recall, and identify new decidable classes for which the distributed synthesis problem is solvable with finite-state strategies. In particular, we show that decidability is maintained when the information hierarchy may change along the play, or when transient phases without hierarchical information are allowed. Finally, we interpret our result in terms of distributed system architectures.