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."

- 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 Lehmann[1999]).

•-      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]).

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.

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 US$121.4 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?

"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.

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.

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.

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.

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.

-       •-      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.

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 -> Visibility -> Awareness -> Demand -> Sales -> -> -> -> -> self-organizing waves.

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)

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.

product propagation --- in waves --- linear in time rather than --- normal diffusion --- square root of time

different time scales for emergence and decline of markets => 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

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.