Results 1 
9 of
9
Speculative trade under unawareness  The infinite case, mimeo
, 2009
"... We generalize the “Notrade ” theorem for finite unawareness belief structures in Heifetz, Meier, and Schipper (2009) to the infinite case. ..."
Abstract

Cited by 10 (7 self)
 Add to MetaCart
We generalize the “Notrade ” theorem for finite unawareness belief structures in Heifetz, Meier, and Schipper (2009) to the infinite case.
Agreement theorems in dynamicepistemic logic
 J. Philosophical Logic
"... In this paper we study Aumann’s Agreement Theorem in dynamicepistemic logic. We show that common belief of posteriors is sufficient for agreements in “epistemicplausibility models”, under common and wellfounded priors, from which the usual form of agreement results follows, using common knowled ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
(Show Context)
In this paper we study Aumann’s Agreement Theorem in dynamicepistemic logic. We show that common belief of posteriors is sufficient for agreements in “epistemicplausibility models”, under common and wellfounded priors, from which the usual form of agreement results follows, using common knowledge. We do not restrict ourselves to the finite case, and show that in countable structures such results hold if and only if the underlying “plausibility ordering ” is wellfounded. We look at these results from a syntactic point of view, showing that neither wellfoundedness nor common priors are expressible in a commonly used language, but that the static agreement result is finitely derivable in an extended modal logic. We finally consider “dynamic ” agreement results, show they have a counterpart in epistemicplausibility models, and provide a new form of agreements via “public announcements”. Comparison of the two types of dynamic agreement reveals that they can indeed be different. 1
Unawareness, Beliefs, and Speculative Trade
, 2009
"... We define a generalized statespace model with interactive unawareness and probabilistic beliefs. Such models are desirable for potential applications of asymmetric unawareness. We compare unawareness with probability zero belief. Applying our unawareness belief structures, we show that the common p ..."
Abstract

Cited by 7 (4 self)
 Add to MetaCart
We define a generalized statespace model with interactive unawareness and probabilistic beliefs. Such models are desirable for potential applications of asymmetric unawareness. We compare unawareness with probability zero belief. Applying our unawareness belief structures, we show that the common prior assumption is too weak to rule out speculative trade in all states. Yet, we prove a generalized “Notrade” theorem according to which there can not be common certainty of strict preference to trade. Moreover, we show a generalization of the “Noagreeingtodisagree” theorem.
Awareness
, 2014
"... Unawareness refers to the lack of conception rather than the lack of information. This chapter discusses various epistemic approaches to modeling (un)awareness from computer science and economics that have been developed over the last 25 years. While the focus is on axiomatizations of structures cap ..."
Abstract
 Add to MetaCart
Unawareness refers to the lack of conception rather than the lack of information. This chapter discusses various epistemic approaches to modeling (un)awareness from computer science and economics that have been developed over the last 25 years. While the focus is on axiomatizations of structures capable of modeling knowledge and propositionally determined awareness, we also discuss structures for modeling probabilistic beliefs and awareness as well as structures for awareness of unawareness. Further topics, such as dynamic awareness, games with unawareness, decision theory under unawareness, and applications are just
Agreeing to agree and Dutch books *
"... Abstract We say that agreeing to agree is possible for an event E if there exist posterior beliefs of the agents with a common prior such that it is common knowledge that the agents' posteriors for E coincide. We propose a notion called Dutch book which is a profile of interim contracts betwee ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract We say that agreeing to agree is possible for an event E if there exist posterior beliefs of the agents with a common prior such that it is common knowledge that the agents' posteriors for E coincide. We propose a notion called Dutch book which is a profile of interim contracts between an outsider and the agents based on the occurrence of E, such that the outsider makes positive profit in all states. We show that in a finite state space, when the agents cannot tell whether E occurred or not, agreeing to agree is possible for E if and only if there is no Dutch book on E. This characterization also holds in countable state spaces with two agents. We weaken the notion of Dutch book to characterize agreeing to agree in a countable state space with multiple agents, when each set in each agent's information partition is finite.
THE REVIEW OF SYMBOLIC LOGIC, Page 1 of 35 PEOPLE WITH COMMON PRIORS CAN AGREE TO DISAGREE
"... Abstract. Robert Aumann presents his Agreement Theorem as the key conditional: “if two people have the same priors and their posteriors for an event A are common knowledge, then these posteriors are equal ” (Aumann, 1976, p. 1236). This paper focuses on four assumptions which are used in Aumann’s p ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. Robert Aumann presents his Agreement Theorem as the key conditional: “if two people have the same priors and their posteriors for an event A are common knowledge, then these posteriors are equal ” (Aumann, 1976, p. 1236). This paper focuses on four assumptions which are used in Aumann’s proof but are not explicit in the key conditional: (1) that agents commonly know, of some prior μ, that it is the common prior; (2) that agents commonly know that each of them updates on the prior by conditionalization; (3) that agents commonly know that if an agent knows a proposition, she knows that she knows that proposition (the “K K ” principle); (4) that agents commonly know that they each update only on true propositions. It is shown that natural weakenings of any one of these strong assumptions can lead to countermodels to Aumann’s key conditional. Examples are given in which agents who have a common prior and commonly know what probability they each assign to a proposition nevertheless assign that proposition unequal probabilities. To alter Aumann’s famous slogan: people can “agree to disagree”, even if they share a common prior. The epistemological significance of these examples is presented in terms of their role in a defense of the Uniqueness Thesis: If an agent whose total evidence is E is fully rational in taking doxastic attitude D to P, then necessarily, any subject with total evidence E who takes a different attitude to