Abstract: We discuss two issues regarding group knowledge.
How can we tell by the behavior of agents in a group what their beliefs are or at least what they are not? For instance someone going out without an umbrella reveals the fact that she does not know (believe) it is raining. She does not need to tell us, we can infer what she believes from what she does. We deal not only with beliefs of agents about the world but also with their beliefs about the beliefs of other agents and so on.
A principal tool used is the notion of rationalizable strategy, defined by Bernheim and Pearce in Econometrica 1984 but generalized to take into account the different states of knowledge of the agents. The tools developed apply not only to agents who are competent users of language but also animals and children and agents who have reason to deceive.
How can we influence the behavior of agents by influencing what they know or what they believe? We give a theoretical account of this and also show that for any state of knowledge described by a finite Kripke structure, there is an n-tuple of signals that can be sent, one to each agent which will create precisely that state of knowledge. We distinguish between cautious and aggressive agents and point out that given the same choice situation, the two kinds of agents may act differently. Thus knowing the temperament of the agent helps us to predict its behavior.
The work in 1) is work under progress. Work in 2) is joint with Cagil Tasdemir, a recent doctorate from CUNY, and Andreas Witzel, now working at Google in New York.