arXiv subjects

Fariba Hashemi

Publications and source records attributed to Fariba Hashemi.

4 recordsLinked to original sources

arXiv2024

Nonlinear Economic State Equilibria via van der Waals Modeling

The renowned van der Waals (VDW) state equation quantifies the equilibrium relationship between pressure $P$, volume $V$ and temperature $k_{B}T$ of a real gas. We assign new variable interpretations adapted to the economic context: $P \rightarrow Y$, representing price; $V \rightarrow X$, representing demand; and $k_{B}T \rightarrow κ$, representing income, to describe an economic state equilibrium. With this reinterpretation, the price elasticity of demand (PED) and the income elasticity of demand (YED) are non-constant factors and may exhibit a singularity of the cusp-catastrophe type. Within this economic framework, the counterpart of VDW liquid-gas phase transition illustrates a substitution mechanism where one product or service is replaced by an alternative substitute. The conceptual relevance of this reinterpretation is discussed qualitatively and quantitatively via several illustrations ranging from transport (carpooling), medical context (generic versus original medication) and empirical data drawn from the electricity market in Germany.

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arXiv2019

Imitation, proximity, and growth -- A collective swarm dynamics approach

This paper is based on the premise that economic growth is driven by an interplay between innovation and imitation in an economy composed of interacting firms operating in a stochastic environment. A novel approach to modeling imitation is presented, based on range-dependent processes that describe how firms consider proximity when imitating peers who are found in a given neighborhood in terms of productivity. Using a particularly tractable approach, we are able to analyze how drastically different economic growth scenarios emerge from different imitation strategies. These emerging scenarios range from diffusive growth where the variance of productivity grows indefinitely, to balanced growth described by a traveling wave with fixed variance. The latter scenario is sustained only when imitation strength among firms exceeds a critical bifurcation threshold.

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arXiv2019

Opinion formation dynamics -- Swift collective disillusionment triggered by unmet expectations

We propose a microscopic model to describe how individual opinions shared between interacting agents initiate excessive collective expectations about a new idea or an innovation, followed by a swift collapse towards a dramatic collective disillusionment. The basic assumption which underlies the dynamics is that the information gathering process is not instantaneous but requires maturation. Agents steadily refine and update their personal opinion via a recurrent consultation of a public pool which stores information tokens (ITs). The expectation for the innovative idea is monitored in real-time by counting the number of stored ITs. The flow dynamics of ITs is assimilated to a single node queuing system (QS) with feedback loop. It incorporates the information pool (the waiting room), an IT inflow, and a service outflow that stylizes the information gathering process. Contrary to basic queuing theory, here the ITs roaming the QS are endowed with time-dependent internal variables. This additional dynamic information is used to construct the information maturation process. Such a maturation of the information introduces response delays into the dynamics, which ultimately generates the collective disillusionment trough. We illustrate the introduced generic modeling framework by considering in details the hype cycle dynamics, a key managerial topic when dealing with diffusion of innovation. In a second part of the paper, we introduce a stylized framework to detect, as soon as possible, the onset of the collective disillusionment phase, while minimizing the frequency of false alarms.

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arXiv2011

Spatio-Temporal Patterns for a Generalized Innovation Diffusion Model

We construct a model of innovation diffusion that incorporates a spatial component into a classical imitation-innovation dynamics first introduced by F. Bass. Relevant for situations where the imitation process explicitly depends on the spatial proximity between agents, the resulting nonlinear field dynamics is exactly solvable. As expected for nonlinear collective dynamics, the imitation mechanism generates spatio-temporal patterns, possessing here the remarkable feature that they can be explicitly and analytically discussed. The simplicity of the model, its intimate connection with the original Bass' modeling framework and the exact transient solutions offer a rather unique theoretical stylized framework to describe how innovation jointly develops in space and time.

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