Synthesising Full-Information Protocols

TL;DR

This paper introduces a model for games with explicit communication actions revealing full information, providing a strategy synthesis procedure and analyzing the complexity and expressiveness hierarchy based on the number of observers.

Contribution

It presents a generic reduction from imperfect to perfect information games and constructs a framework for full-information protocols with complexity analysis.

Findings

Number of observers affects expressiveness and complexity hierarchically.

Strategy synthesis is (n+1)-EXPTIME-complete for n observers.

Full-information protocols can express relations not possible with fewer observers.

Abstract

We lay out a model of games with imperfect information that features explicit communication actions, by which the entire observation history of a player is revealed to another player. Such full-information protocols are common in asynchronous distributed systems; here, we consider a synchronous setting with a single active player who may communicate with multiple passive observers in an indeterminate environment. We present a procedure for solving the basic strategy-synthesis problem under regular winning conditions. We present our solution in an abstract framework of games with imperfect information and we split the proof in two conceptual parts: (i) a generic reduction schema from imperfect-information to perfect-information games, and (ii) a specific construction for full-information protocols that satisfies the requirement of the reduction schema. Furthermore we show that the number of passive observers induces a strict hierarchy, both in terms of expressiveness and complexity: with n observers, a full-information protocol can express indistinguishability relations (defining imperfect information for the player in the protocol) that are not expressible with n-1 observers, and the strategy-synthesis problem is (n+1)-EXPTIME-complete.