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We analyze the problem of agents' interactions in a given population. The purpose of this paper is twofold. Starting from a scheme proposed by Galam [Physica A 320, 571 (2003)], which is based on a majority rule to treat the individuals' interactions, we first study some of its relevant properties. Then, we introduce special individuals, called opinion leaders, who play a key role in information spreading in several practical applications. Opinion leaders have the special feature of strongly interfering with the process based on the majority rule, speeding up the diffusion. We consider a model describing agents' interactions, which encompasses Galam's proposal, where opinion leaders are included as special agents. Then we study its specific properties which significantly recast and extend some conclusions drawn for the models given by Galam and Ellero, Fasano, and Sorato [Physica A 388, 3901 (2009)]. Finally, we provide theoretical and numerical results concerning the dynamics of our model, showing that a small percentage of opinion leaders may both accelerate and/or even reverse the overall consensus among all the agents.

This paper describes a parametric family of utility functions for decision analysis. The parameterization embeds the HARA class in a four-parameter representation for the risk aversion function. The resulting utility functions can have only four shapes: concave, convex, S-shaped, and reverse S-shaped. This makes the family suited for both expected utility and prospect theory. The paper also describes an alternative technique to estimate the four parameters from elicited utilities, which is simpler than standard fitting by minimization of the mean quadratic error.

We propose a variety of models to represent the joint effect of several advertising media on the demand for a product in a homogeneous market, and discuss the associated profit maximization problems. An advertising productivity function represents the combination of several media and, together with demand and advertising cost functions, determines the features of the associated profit problem. We distinguish between additive and nonadditive advertising productivity functions, then between smooth and nonsmooth ones.The demand function may either be linear or not. We observe how different models may exhibit either synergy or interference effects. In some cases we obtain explicit optimal solutions

Abstract.In this paper we analyze some issues related to the general problem of information spreading among individuals, where suitable assumptions on the information exchange are considered. In particular, starting from the scheme proposed in [5], which is based on a majority rule to treat the individuals' interaction, we define and introduce special individuals who play a key role in the information spreading. The latter will be addressed as opinion leaders, and have the special feature of strongly interfering with the process based on the majority rule. We consider a new model, where opinion leaders are introduced as special agents, and study its specific properties which significantly recast some conclusions worth for the model in [5]. Finally, we provide some results cocerning the dynamics of the model.