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Decentralized Organizations as
Multi-Agent Systems:
A Complex Systems Perspective
Shruti Appiah
University of Waterloo
I take no action yet people transform themselves,
I favor quiescence and the people right themselves,
I take no action and the people enrich themselves,
I am without desires and the people are themselves pristine.
- Lao Tzu, 500 BC [1]
1
Table of Contents
1. Introduction………………….………………….………………….…………………….………..3
2. A case for decentralized and distributed systems………………………………….………..5
3. Methods………………….………………….………………….………………….………………..8
3.1 Agent based models
3.1.1 Organizational incentivization mechanisms…………….………………….8
3.1.2 Agent based models for social conformity………………………………….11
3.2 Graph theoretical models
3.2.1 Analyzing organizations as a social graph………………………………....13
4. Conclusion………………….………………….……………….………………….……………….18
5. Limitations and recommendations………………….………….……………………………..19
6. References………………….………………….………………….…………………………..……20
7. Appendix………………….………………….…………………………………………..…………21
2
1. Introduction
Traditional hierarchical organizations have long been studied, and lay the foundation in
many organizational management courses. The advent of a new type of economy - the
peer-to-peer economy - calls for a shift in organizational culture to reflect that of a
complex distributed system. The primary philosophy behind such systems is to tap into
the potential of emergence - “the whole is greater than the sum of its parts” - of
self-organized autonomous complex systems.
In the absence of hierarchy in organizations, the social system constituting the members
of the organization functions as a complex adaptive system, similar to what is observed
on large-scale computer networks such as the internet, or distributed systems like the
blockchain. This project frequently compares a decentralized organization to the the
blockchain because of its truly distributed nature. On the contrary, the internet does
posses same some degree of centralization in the form of centralized clouds,
geographically localized service providers, siloed end-user application data, and
exclusivity in access to academic work. It appears to be more decentralized than
distributed, with a growing trend towards greater centralization with players like Google
and Facebook.
Coordination in such organizations may prove challenging since human agents do not
behave as simply and rationally as would ants, bees, birds, or servers on the internet.
Humans establish social norms in the form of memes, have the tendency to fall prey to
cognitive bias, are capable of spreading rumors intentionally or not, and being affected
by external political, economic, and environmental factors. These complications give
raise to a myriad of faults and nuances which are challenging to account for in a rigid,
crisp-logic computer program.One would have to be an expert in psychology, sociology,
and behavioral economics in order to accurately codify all human tendencies and build a
realistic computer simulation.
3
One way to tackle this problem would be to narrow down the scope of the study
sufficiently enough that only a small subset of psychosocial phenomena are exhibited.
Researchers have developed some popular social models this way, one of them being the
Schelling model of racial segregation.
In this project, an agent-based mathematical model (ABM) to simulate the dynamics of
an intra-organizational incentive structure has been developed. Although the model
does demonstrate some outcomes of implementing an organizational incentivization
mechanism, it does make an assumption that its human agents behave rationally.
For this reason, this report also delves into modelling an organization as a social graph.
The reader may borrow some of the presented ideas as a starting point to build their
own models, should they wish to study organizational behavior.
4
2. A case for decentralized and distributed systems
In an organizational context, decentralization could mean anything - from having only
team-level management to complete distribution of authority with individual
self-managing members. This project examines the latter type of organizational
structure. Being inspired by distributed systems like the blockchain, these organizations
should similarly offer benefits like intra-organizational transparency and accountability.
For an organizational incentivization mechanism, these properties can be achieved by
simply implementing the process on the blockchain. This would involve creating a ‘coin’
and codifying all the rules of the system as smart-contracts on the blockchain. Members
of the organization can opt in or out of this system depending on how much they favor
the rules of the system. In the future, another process could be deployed to decide the
rules in a democratic manner. Currently, there are some blockchain-based systems that
offer this functionality. One of them is BoardRoom, which aims to bring the power of
governance to everyone. The benefits of distributed system for an organizational
incentivization mechanism are discussed below.
Transparency
All the actions and exchanges happening within the system manifest themselves as
cryptocurrency transactions on the blockchain. i.e. every action results in a trade of
coins between two members. The transactions pass only if they comply with all the rules
specified in the system’s smart contracts. These can be viewed by any other member on
the system free of cost. If implemented in a company-wide private blockchain instance,
it would look similar to the transaction history list offered by public services like
EtherScan [2], except that this information would only be visible to the members of the
organization.
Openness
5
All the rules of the system are coded in smart contracts and can be stored in a online
code repository, thus making it viewable by all members of the organization. It is to be
noted that not all members may necessarily be able to interpret the code. This problem
can be solved by leaving several human language comments in the code or having a
separate constitution that accurately reflects the laws outlined in the smart contract. [3]
Accountability
One of the biggest reasons why scaling organizations turn away from decentralized flat
structures is due to the difficulties associated with holding members accountable for
their responsibilities. In this system, transaction histories would be stored on the
blockchain database forever. This database - being distributed - is viewable by all
members of the organization. This extensive timestamped record of everyone’s actions
can be used as a source of ‘truth’ to help with conflict resolution.
Fairness is another benefit that implementing this on a codified system brings. Since all
members play on an equal ground, members on the system cannot illegitimately favor
one member over another. If a bad actor performs any backhanded transactions to
another member, they will be caught immediately. Since all the coins are stored on the
system, nothing can be hidden from other members. Thus, there is inbuilt fairness and
fair competition despite the presence of the inevitable wealth inequality caused by the
80/20 rule and power laws.
Scalability
As opposed to traditional centralized organizations, decentralized systems are not faced
with limitation problems that occur with scarce resources, services, and funds. For
instance, consider that the company appointed a ‘fund allocation manager’ to regularly
distribute the incentives to members. As the organization scales in size, this person
could be limited in terms of their efficiency, the amount of liquid funds available to
them, and how quickly they can transmit funds to a member located thousands of
6
kilometers away from them. The fund allocation manager could act as a bottleneck to
smooth wealth flows. These problems are avoided in a distributed system because funds
are exchanged between individual members (peer-to-peer) and not centrally stored or
routed. Since the system is geographically distributed, transactions can happen much
more quickly. Transaction speed is often touted to be the biggest value that distributed
peer-to-peer economies bring to the table.
Increased reliability
Centralized systems are also more prone to failure due to having a single point of attack.
If an attacker targets just the central node or source of control, the resulting failure can
trickle down and eventually render the entire system useless. Such centralization
failures are akin to the 2008 stock market crash and the October 2016 Distributed
Denial of Service (DDoS) attack that brought down Twitter, Github, and several other
internet services. [4] Failures such as cascading failures are still possible in a
decentralized system since it is a highly interconnected complex network.
Decentralized systems also allow for fault tolerance, especially near self-organized
criticality. Due to its inspiration from a blockchain-like decentralized network, the
system is subject to failures related to consensus, such as Byzantine faults. Byzantine
faults happen when some nodes in the network are traitorous and appear to be in
different states (say on/down) to different nodes. This incoherency in information
available to different sets of nodes delays the system’s arrival at consensus, or can cause
dangerous pseudo-consensus, where the nodes in the system appear to be at consensus
even when they are not supposed to be i.e, they appear to be at consensus just because
some nodes are at a favorable state by satisfying conditions using false information
provided by the traitor nodes. [5] In a social context, this would be analogous to people
exhibiting hypocritical behavior, i.e saying one thing and doing another. A member may
be able to participate and claim incentives for a project, yet not have actually
contributed to it.
7
In addition to the above value-adds, distribution of authority is also a strategically
advantageous move. In organizations with several layers of management, employees
have a tendency to feel apathetic due to feeling like they are being constantly looked
over. For centuries since the Industrial Era, economic philosophers have tried to solve
the problem of highly specialized jobs causing a feeling of a lack of purpose and yet
companies still deploy extensive top-down management structures. Studies have shown
that high performers prefer to work in highly autonomous environments. Power
decentralization improves employee attitudes, increases autonomy, raises the average
individual responsibility and initiative. [6] It is to be noted that flat organizations do not
offer any ready benefits past a certain scale (5000 members). Therefore, although the
the system itself can be scaled beyond that limit, some key changes need to occur in the
structure of the organization which would call for a shift in the topology of the system
from a completely flat organization to one with some level of hierarchy.
8
3. Methods
3.1. Agent based models
3.1.1 Organizational incentivization mechanisms
Consider an organization with several independent projects, each consisting of a team of
self-organizing members. Being humans, the members of such an organization act out of
self-interest most of the time, and thus devote all their attention to developing their own
projects. However, such an organization, like any other, does have organization-wide
operational needs such as coming up with a mission statement, organizing
company-wide trips and events, creating an intranet, and so on. Certainly, members
have a greater interest in working on their own project than to contribute the central
projects because there is no incentive for them to do so. How would such an
organization garner its members’ attention towards these fundamental needs?
In a flat organization without lines of command, it does not make sense to order
members to participate in organization-wide projects. Typically, the organization would
rely on volunteerism to get such work done. However, traditional volunteerism may be
an unreliable means to seek consistent labour, as there would be no accountability, roles
and responsibilities would be ambiguous, and the system could be riddled with
uncertainties.
Mechanism Design
Mechanism design, or reverse game theory, is used to find the most optimal solution for
designing incentives for a group of agents acting simultaneously. [7]
Objective
The objective of this project is to study if and how an organizational incentivization
scheme will increase member participation in central organization-wide projects.
9
Players
Members of the organization.
The game
Members of the organization transact, donate, and accept coins while occasionally post
or participate in organization-wide projects.
Initial Conditions
Members start with unequal distribution of coins.
Rules
The rules of this game are outlined in the code WealthModel.py
, shown in the Appendix
(See page 21).
Outcomes
The outcomes of this game are members of the organization participating in projects
and being rewarded for completing them.
Model characteristics
Stochastic
In order to reflect the stochasticity of the real world, the model contains several
instances where randomness is introduced. Stochasticity is introduced through random
selection of agents for receiving donations, random participation in projects, and so on.
Probabilistic
Although this property is similar to stochasticity, it is explicitly stated to illustrate that
there are ways in which the probability of outcomes can be pre-specified. This model
can accommodate situations where outcomes can be moderately predetermined. For
example, if it has been previously determined through data analysis that the
organization being examined is highly altruistic, the probability that the altruism switch
is ON can be increased from the default probability of 0.5.
10
Default setting with P(agents exercise altruism) = 0.5
altruism = random.randint(0,1)
if altruism > 0:
# perform donations
Setting for a highly altruistic society with P(agents exercise altruism) = 0.75
altruism = random.randint(0,3)
if altruism > 0:
# perform donations
Probabilities can also be considered in the graph-based study when the relationship
between two nodes is ambiguous (See Page 16 of this report). Besides this, the overall
transitivity index of the system is also represents a probability, i.e the probability that
two nodes in the system are connected.
Markov
The system is modelled as a Markov random field (as in an Ising model of
ferromagnetism). Future events only depend on the present state, and not on the chain
of preceding past states. Given that the model is stochastic and is run through
incremental time steps, the process can be described as being a discrete time Markov
chain.
11
Results
Figure 1: Agent-based model simulating the wealth distribution in an organization with a project
incentive mechanism over time. This is a scenario without any taxation schemes. Starting with
timestep = 1 with an unequal distribution of wealth, the wealthy agents have the tendency to
remain wealthy through time.
Measuring success
Success is measured by comparing the total number of participants, on average, that
have contributed to projects. A member can be counted more than once if they have
participated more than once. As the taxes imposed on the wealthy and the
rewards/incentives for project participation increase, more members contribute to
projects overall.
12
Iteration of running the agent-based model
Total participants at 60 timesteps
Iteration 1
10
Iteration 2
26
Iteration 3
19
Iteration 4
31
Iteration 5
8
Iteration 6
20
Iteration 7
18
Iteration 8
17
Iteration 9
18
Iteration 10
35
Average number of participants at 60 timesteps
20
Table 1: Calculating the average net number of participants after a given timestamp
With a tax of 30% of total wealth imposed on any member possessing more than 7 coins,
and the reward per project participant being 2 coins, the average number of participants
after 60 timesteps is observed to be 20. This is a more desirable result compared to the
scenario in which there is no incentive mechanism, hence no taxes and no participation
rewards.
3.1.2. Agent based models for social conformity
Humans have the tendency to conform to social norms and accept ideas they hear
repeatedly. Certainly, each person’s idea acceptance threshold is different and some may
be impressionable while others skeptical. Memetics involves the study of propagation of
ideas from one human to another in a society in order to form social norms, and
eventually, a culture. The word ‘meme’ is inspired from the word ‘gene’ which is used to
transmit genetic information. [8]
13
An organization is also constituent of humans who spread and adopt ideas. The
agent-based model shown in Figure 2 depicts the idea states of an organization over
time. [9] Different colors represent different ideas. The system starts with ample
diversity of opinion. With every time step, the agents choose to adopt the majority
opinion of their neighbours.
Figure 2 : Agent-based model demonstrating the spread of memes over a population over time.
(a) Timestep = 0 (b) Timestep = 3 (c ) Timestep = 35 (d) Timestep = 137. Opinion consensus is
achieved over a relatively short timespan.
This meme spreading model is inspired from the Schelling model of racial segregation.
It appears to be sensitive to initial conditions. In some cases, like Figure 3, the
simulation keeps running for several time steps without reaching opinion consensus.
This could arise due to there being two or more equally sized majority opinions. When
there is such a tie, a person’s opinion in the next state is determined by a randomizer
that chooses between the two competing opinions of the cell’s neighbours. In other
conditions, consensus is reached relatively quickly (see Figure 2). However, in all cases,
diversity of opinion is lost over time.
14
Figure 3: Agent-based model showing spread of memes where opinion consensus is not reached
even after 1180 timesteps (bottom right state).
Although it may seem indirect, there is a correlation between widespread opinion and
the price of a stock or a cryptocurrency. In March 2017, a cryptocurrency called
Ethereum hit its all time high of $53 after a 350% increase since late February. [10] This
is partly due to its increased press attention over this time span. Since the value of the
organizational incentive coin is also determined by the market - i.e, the members of the
organization - it is important to take into account the sociocultural aspect of reputation
into the model.
Once truthful information transfer is incorporated into the system, it is time to consider
corrupt information transfer - such as rumors - as well. Gossip protocols can be studied
to formulate the underlying mechanics of rumor spreading. [11] These network
protocols have been inspired by the form of communication that happens in closed
social systems, i.e. those with a fixed number of members and a boundary, and can be
used to reverse engineer complex social interactions by comparing them to simple
server-to-server communications.
15
3.2 Graph theoretical models
3.2.1 Analyzing organizations as a social graph
Figure 4: Mesh network topology consisting of several interconnected circles and clusters of
sub-circles (Note: number of circle-to-circle connections are arbitrary)
The social networks constituting an organization contain many hubs of highly connected
nodes, which may be clustered into groups of highly connected clusters. There is scale
free formation of hubs in the network, i.e they can be as big as imaginable, and the
network possess behaviour that is independent of scale. These networks also follow
power laws and have a non-Gaussian probability distribution of events because
conventionally “unlikely” or catastrophic events are more likely than what a
linearly-thinking human would expect. Scenarios such as a person holding a
disproportionately high amount of wealth, or a node being disproportionately highly
connected compared to its peers are not to be seen as anomalies.
16
Consider a graph with vertices (or nodes) V and edges (or connections) E.
In an organizational model, the vertices are analogous to members of the organizational
network, and the edges are analogous to relationships between the members.
If two members are not directly connected through a single edge, their relationship can
be defined by the geodesic distance D between them.
such that the sum of edge weights over all possible number of vertices n is minimized.
If the graph is unweighted, i.e. all edge weights are equal to 1, then
such that the number of edges between Mi and Mj is minimized.
Assumptions and simplifications
The following general assumptions about the network have been made:
1. The graph is undirected. This assumption has been made for simplicity and
because it more closely reflects the nature of the ideal flat organizational model
with no unidirectional lines of command or authority. [12]
2. The edges do not have weights. All relationships are considered to be standard
and equal in strength.
Social interactions
Social interactions can be studied by analyzing the flow of information between three
nodes or persons in a network. Groups of three nodes are referred to as triads
. They are
the smallest social structures which can represent the nature of the entire organization.
[13] It is worthwhile to study these structures while analysing organizational graphs
because they provide insight into the behavior and complications that arise upon the
17
addition of an extra node to a dyad. These include the group interaction dynamics,
cluster formation, and network faults, all of which can be used to determine the
network's global behavior.
Figure 5: Types of triads. (a) Isolation, nodes don’t interact. (b) Couple, two nodes interact and
the other is left in isolation. (c ) Structured hole, two nodes interact with the same node but not
with one another. (d) Cluster, all nodes interact.
Transitivity
Transitivity describes the extent to which the nodes in network tend to form clusters.
The organization is assumed to have a transitivity index of 1, and thus is modelled as a
complete mesh network. This means “a friend of a friend is my friend”, but “a friend of a
friend of a friend is not necessarily my friend”. Information can transmit from one node
to the nodes that are its direct, 1st connections, and also to their connections, i.e its 2nd
connections. This forms a 3-edged triad of nodes.
The rationale for this assumption is that the transitivity indices of social networks are
distinctively higher than those in a network with connections assigned stochastically.
[14]
18
Figure 6: Transition from a coupled interaction to a cluster. (a) Couple (b) Structured hole (c)
Partially transitive (d) Cluster
Figure 6 demonstrates information flow as connections between nodes. Starting from
the left, M2 transmits information to M1 and M1 shares this information with M3. The
graph in (c ) demonstrates the situation in which there is some uncertainty in whether
the information received by M3 from M1 is the same as the information transmitted
from M2 to M1. Assuming that M1 is a good player who does not corrupt the
information, the three nodes M1, M2, and M3 all have the same information, thus
making it a closed
triad.
Had the assumption about the transitivity being 1 not been made, the triad is considered
to be partially transitive, as shown in (c). There may or may not be a connection between
M3 and M2, and the probability of this connection is associated with the transitivity
index of the system. If the transitivity index of the system is less than 1, the probability
of a triadic closure shown in (d) would be less than 1 as well.
The degree of transitivity of a social network indicates how tightly knit it is. The
interconnections between different nodes could be used as a starting point to study the
interactions within a system. Based on the frequency and strength of interactions,
insights about the relationships that exist within an organization can be derived. This
metric is especially useful while devising simulations for the spread of ideas, like the
agent-based model described in Page 11-12. The obtained values can be used to
19
determine the probabilities that a person’s opinion would change, since a person is more
likely to be influenced by the opinions or ideas of someone that is close to them.
Power dynamics
The organizational model must account for implicit hierarchy by describing roles and
minor ego-networks. Ego networks describe the direct connections of a single person or
node - called the ‘ego’ - in a network. They consist of the set of directly connected nodes,
and the associated edges that connect them to the primary ‘ego’. Even though there are
no formally-assigned power holders, informal power structures emerge.
Over time, without deliberate power distribution, these ego networks become stronger
and more unbalanced, thus moving the entire organization towards centralization.
Power dynamics in a social network can be studied by utilizing directed graphs,
particularly by analyzing the types and the frequency of certain types of directed triads.
20
4. Conclusion
Decentralized organizations with distributed authority offer plenty of benefits and can
bring about cohesion through emergence. However, when faced with the challenge of
getting members to contribute to certain projects without the use of order or command,
the organizational designer is left perplexed. One would have to devise mechanisms to
garner the members’ attention towards these central projects. This project explored one
such mechanism - an incentive scheme. The results of the agent-based simulation
showed that the project participation did indeed increase with an increase in the
incentives.
In addition to agent-based models, this project also offers a starting point to studying
organizational social systems as a social graphs. Triads, which form the atomic units
that can describe the behaviour of the entire organization can offer a good starting point
to go about designing an organizational model. The census of different types of triads
each with a different transitivity occurring in a population can give insight into the
frequency and types of interactions in the system.
Before simulating any organizational social system, the researcher has to make a clear
distinction between the importance of its central components - the individual persons
versus the relationships that exist between people. For a given problem, if studying the
individual entities brings more insight, they would pick an agent-based or cellular
automaton model. Likewise, if relationships characterize the societal dynamics better,
they would choose a graph theory based approach.
21
5. Limitations and recommendations
Quality of work cannot be measured using the current organizational incentives
agent-based model. An empirical study can be performed to compare the quality of
completed projects when there are no incentives to the quality of completed projects
when there is an incentive scheme. It is expected that the quality declines with an
incentive scheme because participants would be motivated by extrinsic motivators, i.e
coins, instead of intrinsic, i.e interest and personal satisfaction. However, this
hypothesis can only be confirmed through empirical research.
The meme spreading agent-based model makes the assumption that all agents are
equally likely to be influenced by the majority opinion. This may not be the case in real
life. Several factors determine the probability in which a member would change their
opinion, such as their degree of impressionability, the relationship they have with the
people holding the majority opinion, and the frequency at which they are exposed to the
majority opinion. The latter two factors can be accounted for by using the metrics
obtained from the triadic approach.
One of the primary simplifications made in the social graph models is the use of
undirected triads. Using directed graphs will provide more insight into the interactions
and ego networks occurring in the system. Members can be clustered based on their
conditional triad census, which is the number of a certain type of directed triad. Most of
the groundwork in social informatics is based on directed triads and the ego networks
that are formed as a result.
22
6. References
[1] "History of Chinese Political Thought, Volume 1", Google
Books
, 2017. [Online]. Available:
https://books.google.ca/books/about/History_of_Chinese_Political_Thought_Vol.html?id=Bn
19BgAAQBAJ&printsec=frontcover&source=kp_read_button&redir_esc=y#v=onepage&q&f=fa
lse. [Accessed: 01- Apr- 2017].
[2] "Ethereum Blockchain Explorer", Etherscan.io
. [Online]. Available: https://etherscan.io/.
[3] A. Tanenbaum and M. Steen, Distributed
Systems,
Principles
and
Paradigms
, 1st ed. 2017.
[4] N. Woolf, "DDoS attack that disrupted internet was largest of its kind in history, experts
say", the
Guardian
, 2017. [Online]. Available:
https://www.theguardian.com/technology/2016/oct/26/ddos-attack-dyn-mirai-botnet.
[5] H. Hsieh and M. Chiang, "Improvement of the Byzantine Agreement Problem under Mobile
P2P Network", IERI
Procedia
, vol. 10, pp. 45-50, 2014.
[6] L. Porter and E. Lawler, 111, University
of
California,
Berkeley
"The effects of "tall" versus
"flat" organization structures on managerial job satisfaction".
[7] T. Börgers, An
introduction
to
the
theory
of
mechanism
design
, 1st ed. Available:
http://www.econ.yale.edu/~dirkb/teach/521b-08-09/reading/2008-mechanismdesign.pdf
[8] A. Asunción, Memetics: An Evolutionary Theory of Cultural Transmission. Available:
http://www.sorites.org/Issue_15/alvarez.htm
[9] D. Masad, Github repository: Project-Mesa, color_patches. Available:
https://github.com/projectmesa/mesa/tree/master/examples/color_patches
[10] "Ethereum (ETH) price, market caps etc. | CryptoCurrency Market Capitalizations",
Coinmarketcap.com
[Online]. Available: https://coinmarketcap.com/currencies/ethereum/.
[11] D. Shah, Gossip Algorithms. Available: http://web.mit.edu/devavrat/www/GossipBook.pdf
[12] R.J. Stoll, D. Subramanian, Hubs, Authorities, and Networks: Predicting Conflict Using
Events Data. Available: https://www.cs.rice.edu/~devika/conflict/papers/stollsubramanian.pdf
[13] "Introduction to Social Network Methods: Chapter 8: More Properties of Networks and
Actors", Faculty.ucr.edu
, 2017. [Online]. Available:
http://faculty.ucr.edu/~hanneman/nettext/C8_Embedding.html.
[14] D. J. Watts and Steven Strogatz (June 1998). "Collective dynamics of 'small-world'
networks". Available:
http://www.nature.com/nature/journal/v393/n6684/full/393440a0.html
23
7. Appendix
import random
import math
import mesa
from mesa import Agent, Model
from mesa.time import RandomActivation
from mesa.space import MultiGrid
from mesa.datacollection import DataCollector
#Global variables
treasury = 0
economy_scale = 15
project_participation = 0
def compute_gini(model):
agent_wealths = [agent.wealth for agent in model.schedule.agents]
x = sorted(agent_wealths)
N = model.num_agents
B = sum(xi * (N - i) for i, xi in enumerate(x)) / (N * sum(x))
return (1 + (1 / N) - 2 * B)
class WealthModel(Model):
"""A model with some number of agents."""
global treasury
def __init__(self, N, width, height):
self.num_agents = N
self.running = True
self.grid = MultiGrid(height, width, True)
self.schedule = RandomActivation(self)
self.datacollector = DataCollector(
model_reporters={"Gini": compute_gini},
agent_reporters={"Wealth": lambda a: a.wealth}
)
# Create agents
for i in range(self.num_agents):
a = WealthAgent(i, self)
self.schedule.add(a)
# Add the agent to a random grid cell
x = random.randrange(self.grid.width)
y = random.randrange(self.grid.height)
24
self.grid.place_agent(a, (x, y))
def step(self):
self.datacollector.collect(self)
self.schedule.step()
def run_model(self, n):
for i in range(n):
self.step()
print("step = ", step())
"""tax_period = step()%10
if tax_period == 0
return_tax(self, treasury)"""
class WealthAgent(Agent):
""" An agent with fixed initial wealth."""
def __init__(self, unique_id, model):
super().__init__(unique_id, model)
self.wealth = 1
x = random.randint(0, self.model.grid.width-1)
y = random.randint(0, self.model.grid.height-1)
print("X Y", x, "and", y)
if self.model.grid.is_cell_empty([x,y]) == False:
rich_pos = (x,y)
rich_receivers = self.model.grid.get_cell_list_contents(rich_pos)
rich = random.choice(rich_receivers)
inequality_c =4
rich.wealth += inequality_c
def move(self):
possible_steps = self.model.grid.get_neighborhood(
self.pos, moore=True, include_center=False
)
new_position = random.choice(possible_steps)
self.model.grid.move_agent(self, new_position)
## Daily expenses
# At every step, the agent makes a transaction with one of their
neighbors
def daily_transactions(self, coins):
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cellmates = self.model.grid.get_cell_list_contents([self.pos])
if len(cellmates) > 1:
other = random.choice(cellmates)
other.wealth += coins
self.wealth -= coins
## Altruism
# At every step, the agent makes a 50/50 choice of whether to donate
money or not
# If the agent chooses to donate, they donate
def donate_money(self):
neighbours = self.model.grid.get_neighborhood(self.pos, moore=True,
include_center=False
if len(neighbours) > 1:
altruism_c = 3
if self.wealth > altruism_c:
altruism = random.randint(0,1)
if altruism != 0:
for i in neighbours:
poor_cell_choice = random.choice(neighbours)
poor_cell_contents =
self.model.grid.get_cell_list_contents([poor_cell_choice])
if len(poor_cell_contents) != 0:
poor =
random.choice(poor_cell_contents)
# If my neighbour's wealth is less than 20% of my wealth,
# I will donate to them an arbitrary sum of money less than 30% of
my wealth
if poor.wealth < 0.2*self.wealth:
print("Oh no, my neighbour is poor!", poor)
max_donation = int(round(0.3*self.wealth))
donation = random.randint(0, max_donation)
poor.wealth += donation
self.wealth -= donation
break
else:
pass
## Taxes
# At every step, the agent's wealth is checked.
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# If their wealth exceeds a certain amount, they are taxed 30% of their
wealth.
# Upon paying tax, the agent is admitted to the Committee and can post a
public project
def collect_tax(self):
global treasury
tax_c = 7
if self.wealth > tax_c:
tax = math.floor(0.3*self.wealth)
treasury += tax
self.wealth -= tax
print("TREASURY NOW =", treasury)
## Reward agents
# Agents who have participated in projects are rewarded with a bounty for
completing the project
# Bounty coins are taken from the Treasury
def project_reward(self, width, height):
global treasury
global project_participation
treasury_c = 6
if treasury > treasury_c:
self.grid = MultiGrid(height, width, True)
x = random.randint(0, self.grid.width-1)
y = random.randint(0, self.grid.height-1)
if self.model.grid.is_cell_empty([x,y]) == False:
position = (x,y)
potential_receivers =
self.model.grid.get_cell_list_contents(position)
receiver = random.choice(potential_receivers)
reward_c = 2
receiver.wealth += reward_c
treasury -= reward_c
project_participation += 1
print("TOTAL PARTICIPANTS = ", project_participation)
def step(self):
#self.move()
if self.wealth > 0:
expenditure_c = 1
self.daily_transactions(expenditure_c)
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self.donate_money()
self.collect_tax()
self.project_reward(economy_scale,economy_scale)
All source code and running instructions can be found at
https://github.com/ShrutiAppiah/Simulating-an-Economy-ABM
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