Physica A: Statistical Mechanics and its Applications
Social percolation models
Introduction
Methods borrowed from physics have been recently applied to a wide range of subjects [1], [2], [3], [4], [5], [6], [7]. In particular, very simple models were adopted as mathematical metaphors for generic classes of collective phenomena in social systems.
We are proposing here to answer the following set of questions:
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“Why does one observe either hits or failures in certain markets such as toys, gadgets, cinema industries [8], but also in the adoption of technological changes [9], of political and economical measures [10], and in the political arena, rather than a featureless distribution of partial successes ?”
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A possible answer to the first question being percolation, the next question is “since economic agents are adaptive and profit seeking, should we observe some meta-dynamics driving the market either close to the percolation threshold or away from it?”
The general explanation for the extremely bi-modal distribution of market shares in certain commodities markets is often discussed in evolutionary economics in terms of bounded rationality [9], [11], [12]: in those cases, decisions are not taken upon complete a priori information, but rather, decision makers are submitted to social influence of earlier adopters. The resulting dynamics is a dynamics of propagation across a social network. But apart from a seminal paper by Föllmer [11], most economics literature about propagation of ideas, or adoption of new products and new techniques is inspired from epidemiology and only considers single traits that propagate like viruses infecting new people on the occasion of random binary encounters in otherwise homogeneous populations [9], [12].
In the present study, we wish to take into account the fact that possible adoption of new ideas, products, or technologies concern agents, whose tastes and interests vary across the population and whose mutual influence is a priori pre-determined in a sparse network of social interactions. In terms of physics, the social network of influences is more like a disordered network rather than a well stirred vessel of homogeneous material. A further important notion, often neglected by economists, is the importance of the diversity of economics actors; as suggested by Kirman [13], this notion departs from the standard notion of a “representative” agent.
Section snippets
The static case of fixed customer preferences and product quality
We here present the simplest model (to our knowledge) which relates the emergence of collective social/economic phenomena to the existence of a self-organized percolation transition. We use the cinema language of deciding to go and see a given film, but the model can be used for other binary economic, technological or political choices.
Our basic assumption is the existence of a social network which supports information transfer in those cases when not all information is public. Our knowledge of
The model
Since we are considering human economic agents, further interesting elements, missing in traditional percolation theory are introduced: the natural evolution of the tastes of the viewers and the business interest of the film makers, might keep this system close to criticality. Indeed,
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after opportunities during which they went to the cinema, the agents will be more demanding and typically increase their preferences pi; on the opposite, those who preferred not to go, lower their expectations and
Acknowledgements
This work was funded in part by NSERC and in part by the Commission of the European Communities, Agriculture and Fisheries (FAIR) Specific RTD programme, CT96-2092, “Improving Agri-Environmental Policies: A Simulation Approach to the Role of the Cognitive Properties of Farmers and Institutions”. The Laboratoire de Physique Statistique is associated to CNRS (URA 1306) and Universités Paris 6 and Paris 7. SS thanks the Université of Paris 7 for supporting his stay in Paris and DS thanks the
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