Impact of Social Interactions on Demand Curves for Innovative Products

Maciejowska, Katarzyna; Jędrzejewski, Arkadiusz; Kowalska-Pyzalska, Anna; Weron, Rafał

doi:10.12693/aphyspola.129.1045

Cited by 9 publications

(7 citation statements)

References 16 publications

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“…Therefore, the q-voter model with anticonformity is insensitive to switching between types of disorder, in contrast to the model with independence. The phase diagrams for this quenched disorder are presented in Figure 1c and in Figure 2b (9) and (13). Even so, Figure 3 shows that the trajectories in a phase space are different for these cases.…”

Section: Model A: Anticonformity + Conformitymentioning

confidence: 96%

Person-Situation Debate Revisited: Phase Transitions with Quenched and Annealed Disorders

Jędrzejewski

Sznajd-Weron

2017

Entropy

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Abstract:We study the q-voter model driven by stochastic noise arising from one out of two types of nonconformity: anticonformity or independence. We compare two approaches that were inspired by the famous psychological controversy known as the person-situation debate. We relate the person approach with the quenched disorder and the situation approach with the annealed disorder, and investigate how these two approaches influence order-disorder phase transitions observed in the q-voter model with noise. We show that under a quenched disorder, differences between models with independence and anticonformity are weaker and only quantitative. In contrast, annealing has a much more profound impact on the system and leads to qualitative differences between models on a macroscopic level. Furthermore, only under an annealed disorder may the discontinuous phase transitions appear. It seems that freezing the agents' behavior at the beginning of simulation-introducing quenched disorder-supports second-order phase transitions, whereas allowing agents to reverse their attitude in time-incorporating annealed disorder-supports discontinuous ones. We show that anticonformity is insensitive to the type of disorder, and in all cases it gives the same result. We precede our study with a short insight from statistical physics into annealed vs. quenched disorder and a brief review of these two approaches in models of opinion dynamics.

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Section: Model A: Anticonformity + Conformitymentioning

confidence: 96%

Person-Situation Debate Revisited: Phase Transitions with Quenched and Annealed Disorders

Jędrzejewski

Sznajd-Weron

2017

Entropy

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“…As is common in the literature, for the macroscopic quantity that describes the state of the system at time t we choose the public opinion (alternatively interpreted as the ratio of adopted [30] or the market penetration rate [31, 49]): Two cliques can interact with each other through cross links between them. The number of cross links is equal to LN 2 , where the fraction of cross links L ∈ [0, 1] is a parameter of the model, see Fig 1.…”

Section: Methodsmentioning

confidence: 99%

The Hunt Opinion Model—An Agent Based Approach to Recurring Fashion Cycles

et al. 2016

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We study a simple agent-based model of the recurring fashion cycles in the society that consists of two interacting communities: “snobs” and “followers” (or “opinion hunters”, hence the name of the model). Followers conform to all other individuals, whereas snobs conform only to their own group and anticonform to the other. The model allows to examine the role of the social structure, i.e. the influence of the number of inter-links between the two communities, as well as the role of the stability of links. The latter is accomplished by considering two versions of the same model—quenched (parameterized by fraction L of fixed inter-links) and annealed (parameterized by probability p that a given inter-link exists). Using Monte Carlo simulations and analytical treatment (the latter only for the annealed model), we show that there is a critical fraction of inter-links, above which recurring cycles occur. For p ≤ 0.5 we derive a relation between parameters L and p that allows to compare both models and show that the critical value of inter-connections, p*, is the same for both versions of the model (annealed and quenched) but the period of a fashion cycle is shorter for the quenched model. Near the critical point, the cycles are irregular and a change of fashion is difficult to predict. For the annealed model we also provide a deeper theoretical analysis. We conjecture on topological grounds that the so-called saddle node heteroclinic bifurcation appears at p*. For p ≥ 0.5 we show analytically the existence of the second critical value of p, for which the system undergoes Hopf’s bifurcation.

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“…Such an approach allows for analytical treatment, which is particularly useful at an initial stage, when we want to identify the role of each of the model parameters. Extended studies, also for real Facebook and Google+ social networks are presented in [10].…”

Section: The Modelmentioning

confidence: 99%

“…The key question that we ask here is: What mechanism on the microscopic level can hamper innovation diffusion? Secondly, by introducing the concept of the reservation price, we make a first step towards investigating the demand curve for this product, which is one of the fundamental issues in the economy and is studied in [10].…”

Section: Introductionmentioning

confidence: 99%

Linking Consumer Opinions with Reservation Prices in an Agent-Based Model of Innovation Diffusion

et al. 2016

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We extend a recently developed agent-based model of innovation diffusion by linking the opinions of potential consumers with their market behavior via the concept of reservation prices. Through a dynamic mechanism that takes into account social influence, the agents in our model can both increase or decrease their product appraisal. Considering complete graph network structures and using mean-field treatment we find that the model can exhibit a plethora of scenarios, observed empirically but not attainable within the classical Bass model. We also show the existence of a critical market price above which the innovation cannot diffuse.

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Impact of Social Interactions on Demand Curves for Innovative Products

Cited by 9 publications

References 16 publications

Person-Situation Debate Revisited: Phase Transitions with Quenched and Annealed Disorders

Person-Situation Debate Revisited: Phase Transitions with Quenched and Annealed Disorders

The Hunt Opinion Model—An Agent Based Approach to Recurring Fashion Cycles

Linking Consumer Opinions with Reservation Prices in an Agent-Based Model of Innovation Diffusion

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