Aumann's seminal agreement theorem deals with the impossibility for agents to acknowledge their distinct posterior beliefs. It has also led to important economic implications, for example, in the context of speculation and trade. The reasoning of the agents gains in depth when also admitting...

We study the relationship between common knowledge and the sequence of iterated mutual knowledge from a topological point of view. It is shown that common knowledge is not equivalent to the limit of the sequence of iterated mutual knowledge. On that account the new epistemic operator limit...

We analyze the sequential structure of dynamic games with perfect information. A three-stage account is proposed, that species setup, reasoning and play stages. Accordingly, we define a player as a set of agents corresponding to these three stages. The notion of agent connectedness is introduced...

We conceive of a player in dynamic games as a set of agents, which are assigned the distinct tasks of reasoning and node-specific choices. The notion of agent connectedness measuring the sequential stability of a player over time is then modeled in an extended type-based epistemic framework....

The robustness of Aumann’s seminal agreement theorem with respect to the common prior assumption is considered. More precisely, we show by means of an example that two Bayesian agents with almost identical prior beliefs can agree to completely disagree on their posterior beliefs. Besides, a...

We introduce a framework for modeling pairwise interactive beliefs and provide an epistemic foundation for Nash equilibrium in terms of pairwise epistemic conditions locally imposed on only some pairs of players. Our main result considerably weakens not only the standard sufficient conditions by...