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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>From Egoism to Altruism</title>
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<h1>From Egoism to Altruism</h1>
<p class="authors">
<strong>Palok (Paul) Biswas</strong><br>
<strong>Xiaojie Niu</strong>
</p>
<p>We investigate the conditions under which a society initially dominated by <em>selfish (egoist)</em> individuals
can
evolve to adopt <em>altruistic</em> behaviour as the norm. Inspired by <em>positive</em> and <em>normative</em>
economics concepts, we create an artificial economy initially characterized by egoism and explore how it can
transition to one where altruism prevails. We examine factors such as the <em>initial proportion of altruistic
individuals</em>, <em>wealth distribution</em>, and <em>social network structures</em>. Two network types
are
used: <em>Barabasi-Albert</em>, which likely clusters of individuals, and Erdos-Renyi, which simulates
small-world
networks. Some modelled dynamics include <em>wealth growth,</em> <em>trade</em>, <em>social influence</em>,
<em>wealth redistribution by altruists</em>, and <em>employment changes</em>. When approximately 80% of the
population in a society adopts a new behavior, we consider that the society has effectively shifted to a new
norm.
</p>
<p>
The model was inspired by the Boltzmann Wealth Model and the SIR model. In SIR model, a healthy agent can get
infected from their neighbour. There are other dynamics such as recovery, susceptibility, etc.
</p>
<h2 id="insights-from-the-literature">Insights from the Literature</h2>
<h5 id="network-effects-and-social-influence">Network Effects and Social Influence</h5>
<p>Liu et al. (2015) demonstrated the direct social influence of generosity and selfishness, finding that while
individuals reciprocate generosity, selfish behaviour tends to have a more substantial impact by shaping
expectations about future interactions. Fowler and Christakis (2010) found that cooperative behaviour can
cascade
through social networks, influencing subsequent acts of cooperation up to three degrees of separation.
Additionally,
Rand et al. (2011) highlighted that dynamic social networks, where individuals frequently update their social
connections, sustain high levels of cooperation by enabling cooperators to connect and disconnect from
defectors.
These findings suggest that network structure and social influence play crucial roles in propagating altruistic
behaviours. </p>
<h5 id="agents-reciprocate-if-benefited-by-altruism">Agents Reciprocate if Benefited by Altruism</h5>
<p>Trivers (1971) offered a model of reciprocal altruism, showing how psychological traits like trust, sympathy, and
guilt regulate altruistic behaviour and deter cheating. In a neurobiological context, Rilling et al. (2002)
showed
that cooperation activates brain regions associated with rewards, reinforcing reciprocal altruism. Axelrod and
Hamilton (1981) demonstrated through game theory and evolutionary models that reciprocity-based cooperation can
persist as an evolutionarily stable strategy even in asocial environments. These insights emphasize that
individuals
are likely to continue altruistic behaviour if they perceive reciprocal benefits, highlighting the importance of
psychological and neurobiological factors in facilitating the spread of altruism.</p>
<h5 id="egoism-and-altruism-may-originate-from-a-common-motivational-source">Egoism and Altruism May Originate from
a
Common Motivational Source</h5>
<p>Kago and Venkataraman (2023) discussed the blurred lines between altruism and egoism, suggesting that these
behaviours may originate from a common motivational source but manifest differently based on context. These
findings
collectively inform our investigation into the transition from egoism to altruism, emphasizing the roles of
social
influence, network dynamics, psychological factors, and the potential for cascading behaviours and evolving
stable
strategies in fostering altruistic norms.</p>
<h2 id="key-modelling-assumptions">Key Modelling Assumptions</h2>
<ol>
<li>
<p><strong><strong>Wealth Generation</strong></strong>: Wealth grows at a fixed rate, emulating returns on
investment. Salary is proportional to the initial wealth, and expenditure varies between a minimum and
maximum expenditure per timestep.</p>
</li>
<li>
<p><strong><strong>Trade</strong></strong>: A fixed network structure is used throughout the simulation run.
Two
network structures are considered: Barabasi-Albert and Erdos-Renyi networks. Agents randomly select a
neighbour for trade interactions, reflecting the stochastic nature of market interactions or social
exchanges. Trading only occurs when the agent has a positive wealth. During the trade, agents transfer a
predefined proportion of their wealth to the selected neighbour, simulating market transactions or
resource
sharing.</p>
</li>
<li>
<p><strong><strong>Sufficiency Threshold</strong></strong>: Agents are considered to have sufficient wealth
if
their wealth is above a certain threshold. Agents below this Threshold will receive donations from
altruistic agents.</p>
</li>
<li>
<p><strong><strong>Societal Influence</strong></strong>: Agents are influenced by the majority behaviour of
their neighbours. An agent adopts the majority norm with a certain probability.</p>
</li>
<li>
<p><strong><strong>Altruistic Wealth Redistribution</strong></strong>: There is a donation pool where
<strong><strong>altruistic</strong></strong> agents can donate a fixed proportion of their wealth. This
donation pool is distributed equally among all agents whose wealth falls below a sufficiency threshold.
This
redistribution mechanism simulates social welfare programs.
</p>
</li>
<li>
<p><strong><strong>Employment Dynamics</strong></strong>: Agents have an 80% chance of being employed
initially.
Unemployed agents have a probability of finding a job, while employed agents have a probability of being
laid off.</p>
</li>
<li>
<p><strong><strong>Norm Change Probability</strong></strong>: Agents have a probability of changing their
norm
to the majority norm of their neighbours. Agents also have a probability of changing their norms when
they
receive donations from altruistic agents.</p>
</li>
</ol>
<h2 id="experimental-setup">Experimental Setup</h2>
<ol>
<li>
<p><strong><strong>Initial Wealth</strong></strong>: Each agent is initialized with a predefined amount of
wealth. The distribution of this initial wealth can be:</p>
<ul>
<li>
<p>Equal</p>
</li>
<li>
<p>Unequal (exponential distribution)</p>
</li>
<li>
<p>Very Unequal (Pareto distribution)</p>
</li>
</ul>
</li>
<li>
<p><strong><strong>Initial Proportion of Altruistic Agents</strong></strong>: A small percentage of agents
are
altruistic (minority) at the start of the model run.</p>
</li>
<li>
<p><strong><strong>Network Structure</strong></strong>: Two network structures are considered:</p>
<ul>
<li>
<p>Barabasi-Albert</p>
</li>
<li>
<p>Erdos-Renyi</p>
</li>
</ul>
</li>
</ol>
<h2 id="results--discussion">Results & Discussion</h2>
<p>The key idea of this experiment was to see whether a small percentage of altruistic agents can influence others
to
become altruistic and shift the norm of the society. We have run the model with different initial wealth
distributions and network structures. Interestingly, a minority group of altruistic agents can influence the
majority to become altruistic when the wealth distribution is unequal. It doesn't work when wealth is
equally
distributed at the start or if the wealth is highly unequally distributed (pareto distribution). The network
structure also plays a crucial role in the spread of altruism. The Barabasi-Albert network is more effective in
spreading altruism compared to the Erdos-Renyi network. This is expected since Erdos-Renyi networks are
clustered together which prevents the spread of norms through social influence. The main results are displayed
below and the results for
all
other experiments can be found in the appendix.</p>
<p>Some interesting things we noticed:</p>
<ul>
<li>Selfish/Egoist norm is more persistent than Altruistic behaviour - as mentioned in Liu et al. (2015)</li>
<li>Network structure matters a lot for norm transition in a society</li>
<li>A altruistic society doesn't imply there will be less inequality in the society</li>
<li>Implementation of a redistribution policy has an impact on the inequality of the system. In the Boltzmann
model, we see that the system always ends in high inequality. Hence, policy interventions are necessary to
curb that behaviour</li>
<li>Transition is difficult in extreme states: perfectly equal distribution and highly unequal distribution.
This is especially true for altruistic behaviour to spread</li>
</ul>
<h3 id="unequal-distribution">Unequal Distribution</h3>
<h4 id="erdos-renyi-network">Erdos renyi network</h4>
<p>Unequal wealth distribution in erdos renyi network with the proportion of altruistic agents is 0.43
<!-- <img src="./plots/unequal_erdos_renyi_0.43.gif" alt="Image" style="max-width: 100%; height: auto;"> -->
<div style="display: flex; justify-content: center; align-items: center; margin: 30px 0;">
<img src="./plots/unequal_erdos_renyi_0.43.gif" alt="Equal wealth distribution in Erdos-Renyi network" style="max-width: 140%; height: auto;"></div>
</p>
<h4 id="barabasi-albert-network">Barabasi Albert Network</h4>
<p>Unequal wealth distribution in barabasi albert network with the proportion of altruistic agents is 0.39
<!-- <img src="./plots/unequal_barabasi_albert_0.39.gif" alt="Image" style="max-width: 100%; height: auto;"> -->
<div style="display: flex; justify-content: center; align-items: center; margin: 30px 0;">
<img src="./plots/unequal_barabasi_albert_0.39.gif" alt="Equal wealth distribution in Erdos-Renyi network" style="max-width: 140%; height: auto;"></div>
</p>
<h2 id="future-directions">Future Directions</h2>
<p>Future research could explore a continuum of selfish and altruistic behaviour instead of treating them as
discrete
entities, offering a more nuanced understanding of the motivational drivers behind these behaviours. This
approach
would allow for investigating how varying degrees of altruism and egoism coexist and influence societal
dynamics.
Additionally, incorporating dynamic networks where agents form connections based on trust and can differentiate
between defectors and cooperators would provide a richer simulation environment. Agents could have memories of
past
interactions, influencing their future decisions and fostering trust-based relationships. Further, implementing
a
utility function where agents derive utility from altruistic acts—where this utility exceeds the sum of their
wealth—would add a layer of complexity by integrating psychological satisfaction and social rewards into the
decision-making process.
Also, looking at the absolute wealth levels at the end of the simulation could provide insights into the
economic impact of
altruism and egoism.
</p>
<h2 id="code-availability">Code Availability</h2>
<p>Code for the model is open-source and can be found <a
href="https://github.com/pollockDeVis/sfi_hw_normal_change">here</a></p>
<h2 id="references">References</h2>
<ul>
<li>
<p>Axelrod, R., & Hamilton, W. D. (1981). The evolution of cooperation. Science, 211(4489), 1390-1396.
</p>
</li>
<li>
<p>Fowler, J. H., & Christakis, N. A. (2010). Cooperative behavior cascades in human social networks.
Proceedings of the National Academy of Sciences, 107(12), 5334-5338.</p>
</li>
<li>
<p>Kago, K., & Venkataraman, P. (2023). Possibility of conjunction between altruism and egoism.
Humanities
and Social Sciences Communications, 10(1), 1-5.</p>
</li>
<li>
<p>Liu, P. P., Safin, V., Yang, B., & Luhmann, C. C. (2015). Direct and indirect influence of altruistic
behavior in a social network. PloS one, 10(10), e0140357.</p>
</li>
<li>
<p>Rand, D. G., Arbesman, S., & Christakis, N. A. (2011). Dynamic social networks promote cooperation in
experiments with humans. Proceedings of the National Academy of Sciences, 108(48), 19193-19198.</p>
</li>
<li>
<p>Rilling, J. K., Gutman, D. A., Zeh, T. R., Pagnoni, G., Berns, G. S., & Kilts, C. D. (2002). A neural
basis for social cooperation. Neuron, 35(2), 395-405.</p>
</li>
<li>
<p>Sun, Z., Ye, C., He, Z., & Yu, W. (2020). Behavioral intention promotes generalized reciprocity:
Evidence
from the dictator game. Frontiers in Psychology, 11, 772.</p>
</li>
<li>
<p>Trivers, R. L. (1971). The evolution of reciprocal altruism. The Quarterly review of biology, 46(1),
35-57.
</p>
</li>
</ul>
<h2 id="appendix">Appendix</h2>
<h3 id="equal-distribution">Equal Distribution</h3>
<h4 id="erdos-renyi-network-1">Erdos renyi network</h4>
<p>Equal wealth distribution in erdos renyi network with the proportion of altruistic agents is 0.47
<!-- <img src="./plots/equal_erdos_renyi_0.47.gif" alt="Image" style="max-width: 150%; height: 200%;"> -->
<div style="display: flex; justify-content: center; align-items: center; margin: 30px 0;">
<img src="./plots/equal_erdos_renyi_0.47.gif" alt="Equal wealth distribution in Erdos-Renyi network" style="max-width: 140%; height: auto;">
</div>
</p>
<p>Equal wealth distribution in erdos renyi network with the proportion of altruistic agents is 0.3
<!-- <img src="./plots/equal_erdos_renyi_0.3.gif" alt="Image" style="max-width: 100%; height: auto;"> -->
<div style="display: flex; justify-content: center; align-items: center; margin: 30px 0;">
<img src="./plots/equal_erdos_renyi_0.3.gif" alt="Equal wealth distribution in Erdos-Renyi network" style="max-width: 140%; height: auto;">
</div>
</p>
<h4 id="barabasi-albert-network-1">Barabasi Albert Network</h4>
<p>Equal wealth distribution in barabasi albert network with the proportion of altruistic agents is 0.58
<!-- <img src="./plots/equal_barabasi_albert_0.58.gif" alt="Image" style="max-width: 100%; height: auto;"> -->
<div style="display: flex; justify-content: center; align-items: center; margin: 30px 0;">
<img src="./plots/equal_barabasi_albert_0.58.gif" alt="Equal wealth distribution in Erdos-Renyi network" style="max-width: 140%; height: auto;">
</div>
</p>
<p>Equal wealth distribution in barabasi albert network with the proportion of altruistic agents is 0.2
<!-- <img src="./plots/equal_barabasi_albert_0.2.gif" alt="Image" style="max-width: 100%; height: auto;"> -->
<div style="display: flex; justify-content: center; align-items: center; margin: 30px 0;">
<img src="./plots/equal_barabasi_albert_0.2.gif" alt="Equal wealth distribution in Erdos-Renyi network" style="max-width: 140%; height: auto;">
</div>
</p>
<h3 id="unequal-distribution-1">Unequal Distribution</h3>
<h4 id="erdos-renyi-network-2">Erdos renyi network</h4>
<p>Unequal wealth distribution in erdos renyi network with the proportion of altruistic agents is 0.43
<!-- <img src="./plots/unequal_erdos_renyi_0.43.gif" alt="Image" style="max-width: 100%; height: auto;"> -->
<div style="display: flex; justify-content: center; align-items: center; margin: 30px 0;">
<img src="./plots/unequal_erdos_renyi_0.43.gif" alt="Equal wealth distribution in Erdos-Renyi network" style="max-width: 140%; height: auto;">
</div>
</p>
<p>Unequal wealth distribution in erdos renyi network with the proportion of altruistic agents is 0.13
<!-- <img src="./plots/unequal_erdos_renyi_0.13.gif" alt="Image" style="max-width: 100%; height: auto;"> -->
<div style="display: flex; justify-content: center; align-items: center; margin: 30px 0;">
<img src="./plots/unequal_erdos_renyi_0.13.gif" alt="Equal wealth distribution in Erdos-Renyi network" style="max-width: 140%; height: auto;"></div>
</p>
<h4 id="barabasi-albert-network-2">Barabasi Albert Network</h4>
<p>Unequal wealth distribution in barabasi albert network with the proportion of altruistic agents is 0.39
<!-- <img src="./plots/unequal_barabasi_albert_0.39.gif" alt="Image" style="max-width: 100%; height: auto;"> -->
<div style="display: flex; justify-content: center; align-items: center; margin: 30px 0;">
<img src="./plots/unequal_barabasi_albert_0.39.gif" alt="Equal wealth distribution in Erdos-Renyi network" style="max-width: 140%; height: auto;"></div>
</p>
<p>Unequal wealth distribution in barabasialbert network with the proportion of altruistic agents is 0.35
<!-- <img src="./plots/unequal_barabasi_albert_0.35.gif" alt="Image" style="max-width: 100%; height: auto;"> -->
<div style="display: flex; justify-content: center; align-items: center; margin: 30px 0;">
<img src="./plots/unequal_barabasi_albert_0.35.gif" alt="Equal wealth distribution in Erdos-Renyi network" style="max-width: 140%; height: auto;"></div>
</p>
<h3 id="very-unequal-distribution">Very Unequal Distribution</h3>
<h4 id="erdos-renyi-network-3">Erdos renyi network</h4>
<p>Very unequal wealth distribution in erdos renyi network with the proportion of altruistic agents is 0.5
<!-- <img src="./plots/very_unequal_erdos_renyi_0.5.gif" alt="Image" style="max-width: 100%; height: auto;"> -->
<div style="display: flex; justify-content: center; align-items: center; margin: 30px 0;">
<img src="./plots/very_unequal_erdos_renyi_0.5.gif" alt="Equal wealth distribution in Erdos-Renyi network" style="max-width: 140%; height: auto;"></div>
</p>
<p>Very unequal wealth distribution in erdos renyi network with the proportion of altruistic agents is 0.3
<!-- <img src="./plots/very_unequal_erdos_renyi_0.3.gif" alt="Image" style="max-width: 100%; height: auto;"> -->
<div style="display: flex; justify-content: center; align-items: center; margin: 30px 0;">
<img src="./plots/very_unequal_erdos_renyi_0.3.gif" alt="Equal wealth distribution in Erdos-Renyi network" style="max-width: 140%; height: auto;"></div>
</p>
<h4 id="barabasi-albert-network-3">Barabasi Albert Network</h4>
<p>Very unequal wealth distribution in barabasi albert network with the proportion of altruistic agents is 0.55
<!-- <img src="./plots/very_unequal_barabasi_albert_0.55.gif" alt="Image" style="max-width: 100%; height: auto;"> -->
<div style="display: flex; justify-content: center; align-items: center; margin: 30px 0;">
<img src="./plots/very_unequal_barabasi_albert_0.55.gif" alt="Equal wealth distribution in Erdos-Renyi network" style="max-width: 140%; height: auto;"></div>
</p>
<p>Very unequal wealth distribution in barabasi albert network with the proportion of altruistic agents is 0.38
<!-- <img src="./plots/very_unequal_barabasi_albert_0.38.gif" alt="Image" style="max-width: 100%; height: auto;"> -->
<div style="display: flex; justify-content: center; align-items: center; margin: 30px 0;">
<img src="./plots/very_unequal_barabasi_albert_0.38.gif" alt="Equal wealth distribution in Erdos-Renyi network" style="max-width: 140%; height: auto;"></div>
</p>
</body>
</html>