This paper provides a micro foundation for the behavior assumptions as well as outcomes in noisy rational expectations equilibrium models. If there are gains from trade, and all agents are rational and can acquire costly information, then equilibria in double auction markets may have the following properties. (i) Ex ante identically informed agents evolve endogenously to noise traders, speculat...

Processing of the certain information, especially inferences based on certain information. Is based on classical two-valued logic. Due to strict and complete logical foundation (classical logic), making inference levels. Thus, it is natural and necessary to attempt to establish some rational logic system as the logical foundation for uncertain information processing. It is evident that this kin...

In this paper I show that Proclus is an adherent of the Classical Model of Science as set out elsewhere in this issue, and that he adjusts certain conditions of the Model to his Neoplatonic epistemology and metaphysics. In order to show this, I develop a case study concerning philosophy of nature, which, despite its unstable subject matter, Proclus considers to be a science. To give this scienc...

and Parkes used the " string-theoretic " principle of mirror symmetry to predict the numbers of rational curves of any degree on a quintic threefold [7]. This prediction took mathematicians by surprise, as the best results at the time only counted rational curves of degree three or less. Since then, exciting new developments have led to mathematical proofs of these predictions and many other re...

Rational proofs, introduced by Azar and Micali (STOC 2012) are a variant of interactive proofs in which the prover is neither honest nor malicious, but rather rational. The advantage of rational proofs over their classical counterparts is that they allow for extremely low communication and verification time. In recent work, Guo et al. (ITCS 2014) demonstrated their relevance to delegation of co...

We give a necessary and sufficient condition for an algebraic ODE to have a rational type general solution. For a first order autonomous ODE F = 0, we give an exact degree bound for its rational solutions, based on the connection between rational solutions of F = 0 and rational parameterizations of the plane algebraic curve defined by F = 0. For a first order autonomous ODE, we further give a p...

Recommender systems assist and augment this natural social process. In a typical recommender system people provide recommendations as inputs, which the system then aggregates and directs to appropriate recipients. In some cases the primary transformation is in the aggregation; in others the system’s value lies in its ability to make good matches between the recommenders and those seeking recomm...

A decision maker is characterized by two binary relations. The first reflects decisions that are rational in an “objective” sense: the decision maker can convince others that she is right in making them. The second relation models decisions that are rational in a “subjective” sense: the decision maker cannot be convinced that she is wrong in making them. We impose axioms on these relations that...