  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.
