A Percolation-Based Model Explaining Delayed Take-Off in New-Product Diffusion

A model of new-product diffusion is proposed in which a site-percolation dynamics represents socially-driven diffusion of knowledge about the product's characteristics in a population of potential buyers. A consumer buys the new product if her valuation of it is not below the price of the product announced by the firm in a given period. Our model attributes the empirical finding of a delayed ``take-off'' of a new product to a drift of the percolation dynamics from a non-percolating regime to a percolating regime. This drift is caused by learning-effects lowering the price of the product, or by network-effects increasing its valuation by consumers, with an increasing number of buyers.new-product diffusion, innovation adoption, spatial stochastic processes, percolation

A percolation model of the product lifecycle

The product lifecycle model can be understood as a three-stage model of technological development associated with a particular product technology. In the explorative stage many different designs are developed, in the development stage products become standardized into a dominant design, and in the mature stage only incremental changes occur within the dominant design. Although the product lifecycle model is widely accepted and often applied in empirical research, innovation scholars have failed to develop systematic theoretical models that explain the different stages of technological development along the lifecycle. In this study, an attempt is made to contribute to product lifecycle theory by developing a theoretical model based on percolation dynamics. The model combines the concept of increasing returns to adoption with information diffusion among consumers within social networks. The main contribution of the model is that it replicates the three stages of the product lifecycle as an outcome of a single elementary process. The model also replicates the S-shaped diffusion curve and the occurrence of an industry shakeout.mathematical models, percolation model, diffusion, social networks, product lifecycle, dominant design

Entanglement generation in a quantum network at distance-independent rate

We develop a protocol for entanglement generation in the quantum internet that allows a repeater node to use $n$-qubit Greenberger-Horne-Zeilinger (GHZ) projective measurements that can fuse $n$ successfully-entangled {\em links}, i.e., two-qubit entangled Bell pairs shared across $n$ network edges, incident at that node. Implementing $n$-fusion, for $n \ge 3$, is in principle not much harder than $2$-fusions (Bell-basis measurements) in solid-state qubit memories. If we allow even $3$-fusions at the nodes, we find---by developing a connection to a modified version of the site-bond percolation problem---that despite lossy (hence probabilistic) link-level entanglement generation, and probabilistic success of the fusion measurements at nodes, one can generate entanglement between end parties Alice and Bob at a rate that stays constant as the distance between them increases. We prove that this powerful network property is not possible to attain with any quantum networking protocol built with Bell measurements and multiplexing alone. We also design a two-party quantum key distribution protocol that converts the entangled states shared between two nodes into a shared secret, at a key generation rate that is independent of the distance between the two parties

Levy distribution and long correlation times in supermarket sales

Sales data in a commodity market (supermarket sales to consumers) has been analysed by studying the fluctuation spectrum and noise correlations. Three related products (ketchup, mayonnaise and curry sauce) have been analysed. Most noise in sales is caused by promotions, but here we focus on the fluctuations in baseline sales. These characterise the dynamics of the market. Four hitherto unnoticed effects have been found that are difficult to explain from simple econometric models. These effects are: (1) the noise level in baseline sales is much higher than can be expected for uncorrelated sales events; (2) weekly baseline sales differences are distributed according to a broad non-Gaussian function with fat tails; (3) these fluctuations follow a Levy distribution of exponent alpha = 1.4, similar to financial exchange markets and in stock markets; and (4) this noise is correlated over a period of 10 to 11 weeks, or shows an apparent power law spectrum. The similarity to stock markets suggests that models developed to describe these markets may be applied to describe the collective behaviour of consumers.Comment: 19 pages, 7 figures, accepted for publication in Physica

A percolation model of eco-innovation diffusion: the relationship between diffusion, learning economies and subsidies

An obstacle to the widespread adoption of environmentally friendly energy technologies such as stationary and mobile fuel cells is their high upfront costs. While much lower prices seem to be attainable in the future due to learning curve cost reductions that increase rapidly with the scale of diffusion of the technology, there is a chicken and egg problem, even when some consumers may be willing to pay more for green technologies. Drawing on recent percolation models of diffusion by Solomon et al. [7], Frenken et al. [8] and Höhnisch et al. [9], we develop a network model of new technology diffusion that combines contagion among consumers with heterogeneity of agent characteristics. Agents adopt when the price falls below their random reservation price drawn from a lognormal distribution, but only when one of their neighbors has already adopted. Combining with a learning curve for the price as a function of the cumulative number of adopters, this may lead to delayed adoption for a certain range of initial conditions. Using agent-based simulations we explore when a limited subsidy policy can trigger diffusion that would otherwise not happen. The introduction of a subsidy policy seems to be highly effective for a given high initial price level only for learning economies in a certain range. Outside this range, the diffusion of a new technology either never takes off despite the subsidies, or the subsidies are unnecessary. Perhaps not coincidentally, this range seems to correspond to the values observed for many successful innovations.Innovation diffusion, learning economies, percolation, networks, heterogeneous agents, technology subsidies, environmental technologies

A Percolation Model of the Product Lifecycle

The product lifecycle model can be understood as a three-stage model of technological development associated with a particular product technology. In the explorative stage many different designs are developed, in the development stage products become standardized into a dominant design, and in the mature stage only incremental changes occur within the dominant design. Although the product lifecycle model is widely accepted and often applied in empirical research, innovation scholars have failed to develop systematic theoretical models that explain the different stages of technological development along the lifecycle. In this study, an attempt is made to contribute to product lifecycle theory by developing a theoretical model based on percolation dynamics. The model combines the concept of increasing returns to adoption with information diffusion among consumers within social networks. The main contribution of the model is that it replicates the three stages of the product lifecycle as an outcome of a single elementary process. The model also replicates the S-shaped diffusion curve and the occurrence of an industry shakeout.Percolation; diffusion; social networks; product lifecycle; dominant design

Diffusion of shared goods in consumer coalitions. An agent-based model

This paper focuses on the process of coalition formation conditioning the common decision to adopt a shared good, which cannot be afforded by an average single consumer and whose use cannot be exhausted by any single consumer. An agent based model is developed to study the interplay between these two processes: coalition formation and diffusion of shared goods. Coalition formation is modelled in an evolutionary game theoretic setting, while adoption uses elements from both the Bass and the threshold models. Coalitions formation sets the conditions for adoption, while diffusion influences the consequent formation of coalitions. Results show that both coalitions and diffusion are subject to network effects and have an impact on the information flow though the population of consumers. Large coalitions are preferred over small ones since individual cost is lower, although it increases if higher quantities are purchased collectively. The paper concludes by connecting the model conceptualisation to the on-going discussion of diffusion of sustainable goods, discussing related policy implications