We introduce α-synchronous relations for a rational number α. We show that if a rational relation is both αand α-synchronous for two different numbers α and α, then it is recognizable. We give a synchronization algorithm for α-synchronous transducers. We also prove the closure under boolean operations and composition of α-synchronous relations.

We consider general economies in which rational agents interact locally. The local aspect of the interactions is designed to capture in a simple abstract way social interactions, that is, socio-economic environments in which markets do not mediate all of agents’ choices, and each agent’s choice might be in part determined, for instance, by family, peer group, or ethnic group effects. We study s...

This paper offers an alternative explanation for what is typically referred to as an asset pricing bubble. We develop a model that formalizes the Cochrane (2002) convenience yield theory of technology company stocks to explain why a rational agent would buy an “overpriced” security. Agents have a desire to trade but short-sale restrictions and other frictions limit their trading strategies and ...

An elliptic divisibility sequence, generated by a point in the image of a rational isogeny, is shown to possess a uniformly bounded number of prime terms. This result applies over the rational numbers, assuming Lang’s conjecture, and over the rational function field, unconditionally. In the latter case, a uniform bound is obtained on the index of a prime term. Sharpened versions of these techni...

We analyse scenarios in which individually rational agents negotiate with each other in order to agree on deals to exchange resources. We consider two variants of the framework, one where agents can use money to compensate other agents for disadvantageous deals, and another one where this is not possible. In both cases, we analyse what types of deals are necessary and sufficient to guarantee an...

In the classic AGM belief revision theory, beliefs are static and do not change their own shape. For instance, if p is accepted by a rational agent, it will remain p to the agent. But such rarely happens to us. Often, when we accept some information p, what is actually accepted is not the whole p, but only a portion of it; not necessarily because we select the portion but because p must be perc...

This paper analyzes “In‡uence Peddling”with interaction between human capital transfer and collusion-building aspects in a model, in which each government o¢ cial regulates multiple …rms simultaneously. We show that (i) there exists an “optimal” division rule for collusion between a sequence of “quali…ed”regulators and a …rm; (ii) as the regulators increasingly bene…t from the collusion, they s...

In this paper we present a model for coalition formation and payo distribution in general environments. We focus on a reduced complexity kernel-oriented coalition formation model, and provide a detailed algorithm for the activity of the single rational agent. The model is partitioned into a social level and a strategic level, to distinguish between regulations that must be agreed upon and are f...

Despite the development of many modeling formalisms and model solution methods, most tool implementations support only a single formalism. Furthermore, models expressed in a chosen formalism cannot be combined to interact with models expressed in other formalisms. This chapter provides an overview of selected performance/dependability modeling tools motivating the need for multi-formalism and m...

We state a simple condition on a rational subset X of a free monoid B for the existence of a sequential function that is a one-to-one mapping of some free monoid A onto X. As a by-product we obtain new sequential bijections of a free monoid onto another.