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

Consumers don't play dice, influence of social networks and advertisements

Empirical data of supermarket sales show stylised facts that are similar to stock markets, with a broad (truncated) Levy distribution of weekly sales differences in the baseline sales [R.D. Groot, Physica A 353 (2005) 501]. To investigate the cause of this, the influence of social interactions and advertisements are studied in an agent-based model of consumers in a social network. The influence of network topology was varied by using a small-world network, a random network and a Barabasi-Albert network. The degree to which consumers value the opinion of their peers was also varied. On a small-world and random network we find a phase-transition between an open market and a locked-in market that is similar to condensation in liquids. At the critical point, fluctuations become large and buying behaviour is strongly correlated. However, on the small world network the noise distribution at the critical point is Gaussian, and critical slowing down occurs which is not observed in supermarket sales. On a scale-free network, the model shows a transition between a gas-like phase and a glassy state, but at the transition point the noise amplitude is much larger than what is seen in supermarket sales. To explore the role of advertisements, a model is studied where imprints are placed on the minds of consumers that ripen when a decision for a product is made. The correct distribution of weekly sales returns follows naturally from this model, as well as the noise amplitude, the correlation time and cross-correlation of sales fluctuations. For particular parameter values, simulated sales correlation shows power law decay in time. The model predicts that social interaction helps to prevent aversion, and that products are viewed more positively when their consumption rate is higher.Comment: Accepted for publication in Physica

Real-time observation of ultrafast Rabi oscillations between excitons and plasmons in metal nanostructures with J-aggregates

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Community Structure and Market Outcomes: A Repeated Games in Networks Approach

Consider a large market with asymmetric information, in which sellers choose whether to cooperate or deviate and ‘cheat’ their buyers, and buyers decide whether to re-purchase from different sellers. We model active trade relationships as links in a buyer-seller network and suggest a framework for studying repeated games in such networks. In our framework, buyers and sellers have rich yet incomplete knowledge of the network structure; allowing us to derive meaningful conditions that determine whether a network is consistent with trade and cooperation between every buyer and seller that are connected. We show that three network features reduce the minimal discount factor necessary for sustaining cooperation: moderate competition, sparseness, and segregation. We find that the incentive constraints rule out networks that maximize the volume of trade and that the constrained trade maximizing networks are in between ‘old world’ segregated and sparse networks, and a ‘global market’

Localization landscape theory of disorder in semiconductors. II. Urbach tails of disordered quantum well layers

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