globals
[
profit-min
profit-max
; failure-min
; failure-max
; num-investors
time-horizon
; sense-radius
; use-sense-radius?
; max-ticks
patch-color-mode ; 0 = profit, 1 = p-failure
g-mean-wealth
g-max-utility
]
turtles-own
[
wealth ; wealth, in dollars
current-utility
]
patches-own
[
profit ; annual profit (dollars)
p-failure ; annual probabilty of failure (0 to 1)
]
to setup
ca
initialize-globals
initialize-patches
crt num-investors
[
initialize-turtle
]
reset-ticks
end
to go
color-patches
ask turtles
[
move
]
ask turtles
[
update-wealth
]
set g-mean-wealth mean [wealth] of turtles
set g-max-utility max [expected-utility-of nobody] of patches
color-turtles
set-current-plot "Mean wealth"
set-current-plot-pen "mean"
plot mean-wealth
set-current-plot-pen "std. dev"
plot stdev-wealth
set-current-plot "Mean Current Utility"
plot mean-current-utility
tick
if ticks >= max-ticks
[
output-print (word "Total wealth: " precision total-wealth 2)
output-print (word "Mean wealth: " precision mean-wealth 2)
stop
]
end
;
; INITIALIZATION ROUTINES
;
;
to initialize-globals
; set num-investors 100
set profit-min 1000
set profit-max 10000
; set failure-min 0.02
; set failure-max 0.5
if failure-min > failure-max
[
set failure-max failure-min
]
set time-horizon 5 ; years
set g-mean-wealth 0
set g-max-utility (profit-max * time-horizon) * (1 - failure-min) ^ time-horizon
; set sense-radius 1
; set use-sense-radius? false
; set max-ticks 25
set-default-shape turtles "circle"
end
to initialize-patches
ask patches
[
set profit profit-min + random-float (profit-max - profit-min)
set p-failure failure-min + random-float (failure-max - failure-min)
set profit profit * profit-multiplier
set p-failure p-failure * risk-multiplier
]
color-patches
end
to initialize-turtle
move-to one-of patches with [ not any? turtles-here ]
set wealth 0
set size 0.8
color-turtle 1.0
end
;
; TURTLE PROCESSING
;
;
to update-wealth ; turtle procedure
set wealth wealth + profit
if random-float 1.0 < p-failure [ set wealth 0 ]
end
to move
; move-to find-best-patch
if expected-utility-growth < wealth-increase-threshold
[
let candidates neighbors with [not any? turtles-here ]
if any? candidates [ move-to one-of candidates ]
]
set current-utility expected-utility-growth
end
to-report expected-utility-growth
if wealth = 0 [set wealth 1.0]
let utility (wealth + (profit * time-horizon)) * (1 - p-failure) ^ time-horizon
let wealth-increase-rate (utility - wealth) / (wealth * time-horizon)
report wealth-increase-rate
end
to-report expected-utility-of [a-turtle]; patch reporter
ifelse a-turtle = nobody
[
; if no turtle is selected, report the utility for the wealth of the average turtle
report (g-mean-wealth + time-horizon * profit) * (1.0 - p-failure) ^ time-horizon
]
[
report ([wealth] of a-turtle + (time-horizon * profit)) * (1.0 - p-failure) ^ time-horizon
]
end
to-report find-best-patch ; turtle reporter
let candidates nobody
; if use-sense-radius?
ifelse vision-mode = "radius"
[
set candidates (patches in-radius sense-radius) with [ not any? turtles-here ]
set candidates (patch-set candidates patch-here)
] [
ifelse vision-mode = "neighbors"
[
set candidates neighbors with [ not any? turtles-here ]
set candidates (patch-set candidates patch-here)
]
[
; vision-mode should be either "radius" or "neighbors"
; If we get here, it was neither and something must be wrong.
error "Unknown vision-mode"
]
]
if not any? candidates
[
report patch-here
]
let best-candidate max-one-of candidates [ expected-utility-of myself]
report best-candidate
end
;
; OBSERVER REPORTERS
; Report statistics on wealth of all turtles
;
to-report total-wealth ; observer reporter
report sum [wealth] of turtles
end
to-report mean-wealth ; observer reporter
report mean [wealth] of turtles
end
to-report stdev-wealth ; observer reporter
report standard-deviation [wealth] of turtles
end
to-report mean-current-utility
report mean [current-utility] of turtles
end
;
;
; COLORING ROUTINES
;
;
to color-patches
;ifelse patch-color-mode = 1
ifelse color-patches-by = "profit"
[
ask patches
[
set pcolor scale-color blue profit profit-min profit-max
]
]
[
ifelse color-patches-by = "p-failure"
[
ask patches
[
ifelse (failure-min < failure-max) and (failure-min > 0)
[
set pcolor scale-color red (ln p-failure) (ln failure-max) (ln failure-min)
]
[
set pcolor scale-color red (p-failure) 1 0
]
]
]
[
ask patches
[
set pcolor scale-color magenta (expected-utility-of nobody) 0 g-max-utility
]
]
]
end
to color-turtle [max-wealth]
ifelse turtle-coloring-mode = "wealth"
[
ifelse wealth > 0.5 * max-wealth
[set color scale-color green wealth (0.5 * max-wealth) (1.5 * max-wealth)]
[set color scale-color red wealth (0.5 * max-wealth) (-0.5 * max-wealth)]
]
[
ifelse turtle-coloring-mode = "current utility"
[
let mcu max [current-utility] of turtles
if mcu = 0 [ set mcu 0.1]
ifelse current-utility > 0.5 * mcu
[set color scale-color green wealth (0.5 * mcu) (1.5 * mcu)]
[set color scale-color red wealth (0.5 * mcu) (-0.5 * mcu)]
]
[
ifelse turtle-coloring-mode = "satisfied?"
[
ifelse current-utility > wealth-increase-threshold
[ set color green]
[ set color red]
]
[
ifelse turtle-coloring-mode = "red"
[
set color red
]
[
error "Unknown turtle coloring mode"
]
]
]
]
end
to color-turtles
let max-wealth max [wealth] of turtles
ask turtles
[
color-turtle max-wealth
]
end
@#$#@#$#@
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@#$#@#$#@
# Business Investor Model
# A Business Investor Model
We demonstrate the sensing concept via a simple business model. In fields dealing with people and organizations, other terms such as "information acquisition" might be more intuitive than "sensing," but the concept is the same: when building an ABM we need to decide, and then program, exactly what information our agents have and where they get it.
This model simulates how people decide which business to invest in, when the alternative businesses they choose from differ in their annual profit and in their risk of failing such that the investors lose all their wealth. These business alternatives are modeled as NetLogo patches, a use of patches to represent something other than geographic space. In the first version, investors (modeled as turtles) are assumed to sense financial information only from neighbor patches; in a second version we will add links among turtles and simulate sensing through a network. As exercises, we will explore how different assumptions about sensing affect the results of this model. (In later chapters we will explore the effects of other assumptions, especially the way investors make trade-offs between profit and risk.)
## Purpose
The primary purpose of this model is to explore effects of "sensing"---what information agents have and how they obtain it---on emergent outcomes of a model in which agents make adaptive decisions using sensed information. The model uses investment decisions as an example, but is not intended to represent any real investment approach or business sector. (In fact, you will see by the end of Chapter 12 that models like this one that are designed mainly to explore the system-level effects of sensing and other concepts can produce very different results depending on exactly how those concepts are implemented. What can we learn from such models if their results depend on what seem like details? In part III of this course we will learn to solve this problem by tying models more closely to real systems.)
This model could be thought of as approximately representing people who buy and operate local businesses: it assumes investors are familiar with investment opportunities within a limited range of their own experience, and that there is no cost of entering or switching investments (e.g., as if capital to buy a business is borrowed and the repayment is included in the annual profit calculation).
## Entities, state variables and scales
The entities in this model are investor agents (turtles) and business alternatives (patches) that vary in profit and risk. The investors have state variables for their location in the space and for their current wealth (*W*, in money units).
The landscape is a grid of business patches, which each have two static variables: the annual net profit the business there provides (*P*, in money units such as dollars per year), and the annual risk of the business there failing and its investor losing all its wealth (*F*, as probability per year). This landscape is *19 × 19* patches in size with no wrapping at its edges.
The model time step is one year, and simulations run for 25 years.
## Process overview and scheduling
The model includes the following actions that are executed in this order each time step.
* *Investor repositioning.* The investors decide whether any similar business (adjacent patch) offers a better trade-off of profit and risk; if so, they "reposition" and transfer their investment to that patch, by moving there. Only one investor can occupy a patch at a time. The agents execute this repositioning action in randomized order.
* *Accounting.* The investors update their wealth state variable. *W* is set equal to the previous wealth plus the profit of the agent's current patch. However, unexpected failure of the business is also included in the accounting action. This event is a stochastic function of F at the investor's patch. If a uniform random number between zero and one is less than *F*, then the business fails: the investor's *W* is set to zero, but the investor stays in the model and nothing else about it changes.
* *Output.* The World display, plots, and an output file are updated.
## Design concepts
### Basic principles
The basic topic of this model is how agents make decisions involving trade-offs between several objectives—here, increasing profit and decreasing risk.
### Emergence
The model's primary output is mean investor wealth, over time. Important secondary outputs are the mean profit and risk chosen by investors over time, and the number of investors who have suffered a failure. These outputs emerge from how individual investors make their trade-offs between profit and risk, but also from the "business climate": the ranges of *P* and *F* values among patches and the number of investors competing for locations on the landscape.
### Adaptation
The adaptive behavior of investor agents is their decision of which neighboring business to move to (or whether to stay put), considering the profit and risk of these alternatives. Each time step, investors can reposition to any unoccupied one of their adjacent patches, or retain their current position. In this version of the model, investors use a simplified microeconomic analysis to make their decision, moving to the patch providing highest value of an objective function.
### Objectives
In economics, the term "utility" is used for the objective that agents seek. Investors rate business alternatives by a utility measure that represents their expected future wealth at the end of a time horizon (*T*, a number of future years; we use 5). This expected future wealth is a function of their current wealth and the profit and failure risk offered by the patch:
U = (W + T P) (1 - F)T
where *U* is expected utility for the patch, *W* is the investor's current wealth, and *P* and *F* are defined above. The term *(W + T P)* estimates investor wealth at the end of the time horizon if no failures occur. The term *(1 - F)T* is the probability of not having a failure over the time horizon; it reduces utility more as failure risk increases. (Economists might expect to use a utility measure such as present value that includes a discount rate to reduce the value of future profit. We ignore discounting to keep this model simple.)
### Learning
There is no learning.
### Prediction
The utility measure estimates utility over a time horizon by using the explicit prediction that *P* and *F* will remain constant over the time horizon. This assumption is accurate here because the patches’ *P* and *F* values are static.
### Sensing
The investor agents are assumed to know the profit and risk at their own patch and the adjacent neighbor patches, without error.
### Interaction
The investors interact with each other only indirectly via competition for patches; an investor cannot take over a business (move into a patch) that is already occupied by another investor. Investors execute their repositioning action in randomized order, so there is no hierarchy in this competition: investors with higher wealth have no advantage over others in competing for locations.
### Stochasticity
The initial state of the model is stochastic: the values of *P* and *F* of each patch, and initial investor locations, are set randomly. Stochasticity is thus used to simulate an investment environment where alternatives are highly variable and risk is not correlated with profit. Whether each investor fails each year is also stochastic, a simple way to represent risk. The investor reposition action uses stochasticity only in the very unlikely event that more than one potential destination patch offers the same highest utility; when there is such a tie the agent randomly chooses one of the tied patches to move to.
### Collectives
There are no collectives.
### Observation
The World display shows the location of each agent on the investment landscape. Graphs show the mean profit and risk experienced by investors, and mean investor wealth over time. An output file reports the state of each investor at each time step.
## Initialization
Four model parameters are used to initialize the investment landscape. These define the minimum and maximum values of *P* (1000 and 10,000) and *F* (0.01 and 0.1). The values of *P* and *F* for each patch are drawn randomly from uniform real number distributions with these minimum and maximum values.
One hundred investor agents are initialized and put in random patches, but investors cannot be placed in a patch already occupied by another investor. Their wealth state variable *W* is initialized to zero.
## Input data
No time-series inputs are used.
## Submodels
* *Investor repositioning.* An agent identifies all the businesses that it could invest in; the neighboring (eight, or fewer if on the edge of the space) patches that are unoccupied, plus its current patch. The agent then determines which of these alternatives provides the highest value of the utility function, and moves (or stays) there.
* *Accounting.* This action is fully described above ("Process overview and scheduling").
@#$#@#$#@
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