Knowledge-Based Strategies for Multi-Agent Teams Playing Against Nature

TL;DR

This paper introduces a framework for multi-agent teams with imperfect information playing against Nature, focusing on higher-order knowledge and strategy synthesis without communication.

Contribution

It proposes the MKBSC extension for higher-order knowledge computation and strategy synthesis, linking explicit knowledge with finite memory strategies.

Findings

MKBSC computes higher-order knowledge iteratively.

Strategies can be transferred between original and transformed games.

Explicit and finite memory strategies are shown to be equivalent.

Abstract

We study teams of agents that play against Nature towards achieving a common objective. The agents are assumed to have imperfect information due to partial observability, and have no communication during the play of the game. We propose a natural notion of higher-order knowledge of agents. Based on this notion, we define a class of knowledge-based strategies, and consider the problem of synthesis of strategies of this class. We introduce a multi-agent extension, MKBSC, of the well-known Knowledge-Based Subset Construction applied to such games. Its iterative applications turn out to compute higher-order knowledge of the agents. We show how the MKBSC can be used for the design of knowledge-based strategy profiles and investigate the transfer of existence of such strategies between the original game and in the iterated applications of the MKBSC, under some natural assumptions. We also relate and compare the "intensional" view on knowledge-based strategies based on explicit knowledge representation and update, with the "extensional" view on finite memory strategies based on finite transducers and show that, in a certain sense, these are equivalent.