The tulip mania

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• The tulip mania
• rise of tulip bulb prices in 1637 to the level of
  average house
• increase by a factor of 20 within a month, the
  market
• collapsed back within the next 3 months.
• South Sea Co. 1720 at the London Stock, Sir
  Isaac Newton "I can calculate the motions of the
  heavenly bodies, but not the madness of people."

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• global macroscopic'' (and often
  "catastrophic") economic phenomena
• - generated by simple buy and sell
  microscopic'' operations.
• the simulation of spatial and temporal
  localization of the sales.

• -      Sudden death - the total and almost
  immediate disappearance of a product (due to the
  introduction of a new generation product or to
  the lack of demand).
• -      Wave-fronts - the geographical spreading
  of new products through the markets by spatially
  and temporally localized waves (Bettelheim and
  Lehmann1999).
• -      The larger profit /survival rate of the
  second producer of a new product after the
  failure (or limited success) of the first
  producer to introduce it (see Goldenberg et
  al.1999).

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lattices real "geographic" space or a network
of interacting markets or individuals.
reactants the product itself, the instruments
to buy it or the knowledge on the product
existence, etc. reactions economic processes
in which valuables are transformed, lost or
created. diffusion the transfer of these
valuables from one location or business entity to
another.
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The "Tamagotchi '' model Washington Post
(Sullivan 1997) TOKYO, Jan. 24 -- By dawn
today, a line of almost 2,000 people stretched a
quarter of a mile through the Ginza shopping
district. Hundreds of them had spent the night
camped out on the sidewalk in the numbing
midwinter cold. When you want a toy chicken badly
enough, you will endure anything. (Ohbuchi
1999) TOKYO - Bandai Co. Ltd. said Thursday
that it will post a 16 billion yen special loss
for 1998/99 due to operations restructuring. The
company also revised its parent net forecast to a
loss of 14.5 billion yen (about US121.4 million)
from an expected profit of 3.5 billion yen (about
29 million). This is partly due to losses caused
by excessive inventory of unsold Tamagotchi,
which can now be found for 10 in US toy stores.
So much for the US virtual-pet craze, eh?
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"Tamagotchi '' (egg watch in Japanese) 1997 a
very abrupt wave of Tamagotchi sales swept across
most of the world and died within months.
Millions were touched at one time by the "
Tamagotchi mania". Various countries were
reached by the wave at slightly different times,
but overall duration of the sales at each
location did not exceed a few months.
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Tamagotchi story clean laboratory for marketing
models obtaining the macroscopic phenomena from
the microscopic properties. The microscopic
properties at the product level are

•  
• -      nobody really needs a Tamagotchi .
• -      people want a Tamagotchi only upon
  actually seeing one.
• -      the price is relatively small/ readily
  affordable.
• -      usually people are satisfied with only one
  Tamagotchi.
• -      in fact people get bored with it after a
  while.
• -      the cost of transporting a Tamagotchi
  between production and selling locations is
  small.
• -      The product is always with the individual
  owning it.

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Observed behavior at variance with the usual
simple diffusion market theory that would lead
to

•  
•           diffuse boundaries between the regions
  where the new product dominates and the virgin
  regions.
•           the expansion of the product territory
  with the square root of time.
•           a long lasting dominance of the
  product in the already dominated area.
• In reality the situation is very different
•           the spread of the product is defined
  by sharp boundaries.
•           the distance the front advances is
  proportional to time.
•           the initial selling rate is diminished
  greatly inside the territory traversed already by
  the wave.

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• O Obtain the macroscopic features as collective
  properties of a multitude of individual
  interactions which reflect the above microscopic
  properties of the Tamagotchi product.
• Consequently, the elementary microscopic
  objects to be included in the MS are
• -  A's which represent sold product units
  (Tamagotchi '').
• -  B's representing the knowledge or conceptual
  awareness of the product.
• - C's representing the a priori availability of
  money to be allocated for the purpose of buying
  A's.

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• The elementary objects A, B and C are placed on a
  lattice whose sites represent spatial locations/
  customers. The elementary reactions
• -      If a B and a C are placed on the same
  lattice site (i.e. there exists on the same site
  both the awareness of Tamagotchi and the money
  available to buy it), then there is a certain
  probability rate for generating an A and a B on
  that site. In this case the C will disappear. The
  interpretation is that a product A is bought at
  that site and the awareness B is increased. The
  money C is consumed by the transaction.
• -      The second reaction creates a B on a
  lattice site if an A is already present on that
  lattice site. This reaction represents the
  influence that the Tamagotchi presence has in
  making the environment more aware of the
  Tamagotchi (people in the neighborhood of a
  Tamagochi can see it, hear reports from its
  owner, be involved in discussions about its
  health etc).
• - The third reaction is the disappearance of
  A's with a certain probability rate. It
  represents the loss of Tamagotchi due to wear and
  tear or by just being discarded by their owners.

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• -       
• -      The fourth reaction is the disappearance
  of B's (with certain probability rate). It
  represents the fact that the Tamagotchi's can
  eventually be forgotten.
• -      The fifth reaction is the spontaneous
  appearance of C's on any site (with a certain
  probability rate). This represents the continuous
  influx of money due to salaries, allowances, and
  other incomes.
• -      The sixth reaction is the disappearance of
  C with a certain probability rate. It represents
  the spending of money on products other than
  Tamagotchi or just financial losses.
• -      B can spread from one site to a
  neighboring one. This corresponds to learning of
  Tamagotchi by hearing of it from a neighbor.

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Tamagotchi Selling Waves -- macroscopic long
lasting wave-fronts of high A concentration
moving across the simulation space. --dynamical
explanation auto-catalytic character of the
Tamagotchi sales.
positive feedback loop Sales of Tamaguchi -gt
Visibility -gt Awareness -gt Demand -gt Sales
-gt -gt
-gt -gt -gt
self-organizing waves.
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Figure 6.1 Contemporary snapshots of A, B and
respectively C distributions
A
B
C

• the front of Tamagotchi sales (the black front in
  Fig. 6.1.A)
• - preceded and followed by a region of high
  Tamagotchi awareness (the black strip with
  similar shape in Fig. 6.1.B). - leaves behind a
  region in which the resources are depleted (the
  white region in Fig. 6.1.C)

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dynamics of the waves - dominated by the
first individual sales penetrating a new region
and - not by the diffusion in the region of a
macroscopic number of B's. Indeed, the
statistical marketing methods (polls conducted
on the ground) are sensitive to - macroscopic
amounts of sales and awareness (B), while - the
real dynamics is triggered at the level of
the first individual sales and
the first individuals in that area
aware of the product.
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product propagation --- in waves ---
linear in time rather than
--- normal diffusion --- square root of time
different time scales for emergence and decline
of markets gt planning marketing campaigns
production and
investment. avoid over-stocking and/or
to exploit in time the imminent emergence of
market demands. By the time the polls discover
it, it is too late
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optimal place and time for starting a marketing
campaign, whether to be the first to start the
marketing of a new product or to wait for the
competition to invest in the creation of market
awareness (B's). One possible strategy to make
this model useful for practitioners is to study
the space-time evolution of past sales in order
to establish the connectivity of the various
market locations and their capacity in terms of C
distribution. This would represent a
quantitative microscopic encoding of the market
conditions, receptivity and capacity. Once the
correct microscopic "map" of the market is
obtained from past data, it can be used for new
products. One can then study the effects of a
second product (pre-existing or newly
introduced), the effect of introducing a cheaper/
more flashy product, or the effect of an
economic/political crisis in parts of the map.