Discrete Choices under Social Influence: Generic Properties

We consider a model of socially interacting individuals that make a binary choice in a context of positive additive endogenous externalities. It encompasses as particular cases several models from the sociology and economics literature. We extend previous results to the case of a general distribution of idiosyncratic preferences, called here Idiosyncratic Willingnesses to Pay (IWP). Positive additive externalities yield a family of inverse demand curves that include the classical downward sloping ones but also new ones with non constant convexity. When j, the ratio of the social influence strength to the standard deviation of the IWP distribution, is small enough, the inverse demand is a classical monotonic (decreasing) function of the adoption rate. Even if the IWP distribution is mono-modal, there is a critical value of j above which the inverse demand is non monotonic, decreasing for small and high adoption rates, but increasing within some intermediate range. Depending on the price there are thus either one or two equilibria. Beyond this first result, we exhibit the generic properties of the boundaries limiting the regions where the system presents different types of equilibria (unique or multiple). These properties are shown to depend only on qualitative features of the IWP distribution: modality (number of maxima), smoothness and type of support (compact or infinite). The main results are summarized as phase diagrams in the space of the model parameters, on which the regions of multiple equilibria are precisely delimited.Comment: 42 pages, 15 figure

Order-of-Magnitude Influence Diagrams

In this paper, we develop a qualitative theory of influence diagrams that can be used to model and solve sequential decision making tasks when only qualitative (or imprecise) information is available. Our approach is based on an order-of-magnitude approximation of both probabilities and utilities and allows for specifying partially ordered preferences via sets of utility values. We also propose a dedicated variable elimination algorithm that can be applied for solving order-of-magnitude influence diagrams

Collective states in social systems with interacting learning agents

We consider a social system of interacting heterogeneous agents with learning abilities, a model close to Random Field Ising Models, where the random field corresponds to the idiosyncratic willingness to pay. Given a fixed price, agents decide repeatedly whether to buy or not a unit of a good, so as to maximize their expected utilities. We show that the equilibrium reached by the system depends on the nature of the information agents use to estimate their expected utilities.Comment: 18 pages, 26 figure

Development Strategies for Pythia version 7

This document describes the strategies for the development of the Pythia7 program. Both the internal and external structure of the program is discussed. Some comments on relationship to other software is given as well as some comments on coding conventions and other technical details.Comment: 27 pages, 3 eps figure

The Long Wavelength Array Software Library

The Long Wavelength Array Software Library (LSL) is a Python module that provides a collection of utilities to analyze and export data collected at the first station of the Long Wavelength Array, LWA1. Due to the nature of the data format and large-N ($\gtrsim$100 inputs) challenges faced by the LWA, currently available software packages are not suited to process the data. Using tools provided by LSL, observers can read in the raw LWA1 data, synthesize a filter bank, and apply incoherent de-dispersion to the data. The extensible nature of LSL also makes it an ideal tool for building data analysis pipelines and applying the methods to other low frequency arrays.Comment: accepted to the Journal of Astronomical Instrumentation; 24 pages, 4 figure

ASSESSING FARMERS' ATTITUDES TOWARD RISK USING THE "CLOSING-IN" METHOD

The 1996 Farm Bill and low commodity prices have regenerated interest in the impact of risk and farmers' risk attitudes on production agriculture. Previous research has used expected utility theory (EUT) and direct elicitation of utility functions (DEU) for eliciting risk attitudes. To overcome the criticism of EUT and DEU, a recently developed technique called the "closing in" method is adapted for eliciting farmers' risk attitudes. This method is applied to Illinois farmers by using a computerized decision procedure, and is validated by comparing the results to the farmers' self-assessment of their risk attitudes and score to a risk attitudinal scale.Risk and Uncertainty,