---veblen05.nlogo

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@#$#@#$#@
WHAT IS IT?
-----------
Veblen Rev 3.4, September 05, 2004, by Ralph Abraham

This is the second draft of a NetLogo model for conspicuous consumption.
Further background may be found at www.vismath.org/research/landscapedyn.

HOW IT WORKS
------------
The turtles are consumers. Each consumer is shown as a triangle
on the state space. They have different colors just for the visual effect.
When several consumers are on the same patch (discretized interval
of the strategy space) only the top one can be seen in entirety,
but the x position is a floating point number, so parts of lower
turtles may be seen.

The strategy space is shown as five horizontal rows in the center of the display.
These are to be regarded as superimposed layers on a single interval.
It represents a unit interval corresponding to the choice of strategy, x.
All consumers have the same income, 1, but choose variously how much to spend
on ordinary consumption, x, and how much to spend on conspicuous consumption,
1-x. Thus x = 0 represents 100% conspicuouos consumption, such as diamond rings, and x = 1 represents 100% inconspicuous consumption, such as food.

A chosen number of consumers begin at initial positions in the state space.
The initial distribution is important to the outcome of a run.
This model is arranged so that the initial distribution is the sum
of an arbitrary number of square waves. Thus the operator may approximate an arbitary initial distribution. Interesting choices include a single square wave or herd, two herds, a tent shape or heap, two heaps, and so on. In any case, the operator begins by adding square waves, or sub-herds, until a desired initial distribution is obtaied. Each addition of a sub-herd is called a "puff".

At the start, and after each step of the run, the density of consumers, F ("rho" in F2001), in the strategy space, is in color on a horizontal line
below the state space. The density, F, is also shown as a histogram in the plot window,
showing the total number of turtles on each patch. Patches are roughly discretized.

The distribution, D (integral of F), of consumers in the strategy space is shown
in color below the F color bar. Black for zero, white for one. This function always
increases monotnically from zero to one.

A constant "amp" in the definition of the payoff function ("c" in F2001)
may be set with a slider. The stepsize may also be set
with a slider. Using the Euler algorithm, each turtle moves
uphill by an increment: stepsize * slope.

The slope of the landscape, or gradient of phi, phi-sub-x,
is shown in SPECTRAL COLORS, below the red display.
Here is the color code: cyan for positive slopes (move to the right),
magenta for negative slopes (move to the left) and yellow for a narrow zone
around zero.

HOW TO USE IT
-------------
STEP #1: THE INITIAL HERD

(1a) Set the "population" slider to determine the number of consumers
in the initial sub-herd.

(1b) Set the 'center" slider to the center of the initial sub-herd of turtles
(that is, the first puff into the distribution of consumers).

(1c) Set the "width" slider to the width of the initial sub-herd,
as a percentage of the total width of the window.

(1d) Press the "setup" button to create the initial distribution
of consumers on the choice interval. The initial histogram shows
a narrow herd of turtles around your chosen center, on row 1.
The histogram duplicates the information shown by the green
color strip.

(1e) Choose a layer with the "puff-row" drop-down choice list. 
Then repeat (1a), (1b), and (1c), and press the "puff" button.
A second square-wave sub-herd joins the herd on the chosen row.
The total population is now indicated by the "totalpop" counter.
Repeat as required to create the initial distribution desired.

STEP #2: ACTION

(2a) Press the "step" button to activate a single step in the
consumption game. Every turtle will take one step, proportional
to the slope of the landscape at its current position (the value
of phi-sub-x at its current x). You will see the turtles move,
and then the histogram will be redrawn.

(2b) Adjust the "stepsize" slider so that the herd moves very
slowly, to avoid numerical artifacts, such as gaps.

(2c) Press "step" several times to judge the stepsize choice.

(2d) Press "go" to trigger a rapid sequence of steps.
Press "go" again to halt the action.

THINGS TO NOTICE
----------------
Try to predict what will occur in the long run.


THINGS TO TRY
-------------
Try different numbers of turtles, and change the value
of the payoff constant with the  amp slider. Most instructively,
move the center around.


CREDITS AND REFERENCES
----------------------
Many thanks to Uri Wilensky for his cleverness and industry,
and to the NSF for support.
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NetLogo 2.0.0
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