Phone Adoption in a Complex Multi-layered Network
When one of my Korean friends told me that Samsung phones were much more popular than iPhones in South Korea, I almost didn’t believe him. It seemed to me like most of my friends from South Korea on campus had iPhones, so how could it be possible that Samsung was more popular? Sure enough, I looked online and found that Samsung phones represented more than 69% of the South Korean mobile phone market, as opposed to the United States’ 24%[1, 2].
Although I was dumbfounded by this statistic, the phenomenon reminded me of my global ignorance and the homophilous nature of the network representing my social life. It also makes me think about the idea of behavioral adoption in a complex network. In class, we discussed the adoption of behavior through an adoption threshold and the inability of behavior to diffuse into dense clusters. Many of the examples we reviewed were binary, either the behavior is adopted, or it isn’t. However, the phone market is more complicated than simply adopting cell phones or not. I like to think of it as an infinite amount of options that is part of the set
S ={ No adoption, Adopt iPhone, Adopt Samsung, … , Adopt some other Phone X}
When introducing a seemingly infinite amount of adoptions, the network becomes more complicated than initially expected. To familiarize this amount of adoptions with the concepts we have discussed in class, we will say that any person will adopt a new phone type if a fraction q of their friends also use the phone. This could mean that one phone could “overwrite” another in the network.
The idea that one phone can “overwrite” another in the network is important to show exactly why timing and location in the network mean everything. In the case of the United States, Apple is a California-based company, and the iPhone was released in the United States in June 2007[3]. By the time the first Samsung Galaxy was available globally in June 2009[4], networks were already well on their way to adopting the iPhone. In the case of South Korea, the iPhone remained unreleased until November 2009, which although only a couple of months after the Galaxy’s release, this time coupled with the fact that Samsung had their employees utilize the Galaxy for personal use was enough of a push to have the Samsung Galaxy completely take over South Korea before Apple even had a chance.
Recently in Korea, news outlets have reported that young members of the population prefer iPhones to Samsung, a survey finding that the iPhone market share for younger generations (18-29) in the cellphone market (18-29) has risen to 65%[5]. Why is it the case that there are different findings between age groups and countries in the global network? Multi-layer networks are important.
Multi-layer networks are the idea that people exist in multiple different layers of networks at once that are not necessarily connected. Think about one layer being the friends on a social media network, whereas another layer could include the people you interact with at your job. The main idea to grasp from our understanding of multi-layer networks is that it is the same individuals show drastically different behavior on different network layers, meaning that it is difficult for behavior to transfer through layers[6]. This is important to the idea of iPhone vs. Samsung because of the perplexities existing in the network of South Koreans. We see that there is a layer of a young generation that is adopting new behavior (the adoption of the iPhone instead of Samsung), and the popularity is spreading through this layer. However, it is very difficult for this to spread to the older generation because their layer can be seen as one dense cluster. As this younger generation gets older, I am curious to see if the iPhone continues to grow in popularity due to diffusion of adopted behavior, or if there is something about age that causes individuals in South Korea to prefer Samsung (I’d like to think it’s the former).
Sources:
- United States Mobile Vendor Market Share: https://gs.statcounter.com/vendor-market-share/mobile/united-states
- South Korea Mobile Vendor Market Share: https://gs.statcounter.com/vendor-market-share/mobile/south-korea
- History of the iPhone: https://en.wikipedia.org/wiki/History_of_the_iPhone
- Samsung Galaxy (original): https://en.wikipedia.org/wiki/Samsung_Galaxy_(original)
- Young Koreans favor iPhones over Samsung Galaxy: survey: https://www.koreaherald.com/view.php?ud=20230720000592
- Analysis of Influence of Behavioral Adoption Threshold Diversity on Multi-Layer Network: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10047583/
The Power of Social Networks in College Settings: Unlocking Opportunities and Fostering Community
The college experience is often defined not just by academic pursuit but also by the intricate web of social networks that students navigate. These networks, formed through friendships, clubs, classes, and online platforms, play a crucial role in shaping one’s college journey. This concepts of social networks and understanding and leveraging them can unlock opportunities and foster a sense of community for students.
Many concepts in Networks apply to this college setting, including:
Graph Theory: Applying graph theory to college social networks allows us to visualize and analyze the complex relationships between students, faculty, and organizations. These networks can be mapped out as nodes (individuals or groups) connected by edges (relationships or interactions), revealing patterns and hubs of activity within the campus community. These mappings not only reveals the underlying patterns and central hubs within the campus community but also serves as a crucial tool for universities. This information can help universities enhance their operations, foster better community engagement, and make more informed, data-backed decisions that reflect the needs and dynamics of their campus population.
The Impact of Weak Ties: Interestingly, casual acquaintances or connections in a college setting can be surprisingly influential, perhaps even more so than one’s strong ties. Weak ties such as classmates in different majors, members of various clubs, or even guest speakers at events, can act as bridges to different social circles or opportunities, offering access to diverse ideas, internships, projects, and more. These weak ties can be a source of support, information, and opportunties, guiding students through academic choices and career paths. They create a network that is rich in diversity and potential, where students can explore and develop various facets of their interests and skills.
Strong Triadic Closure: The principle of Strong Triadic Closure states that if person A has strong ties to persons A and B, then the B-C edge (relationships) is likely to form. This concept is highly observable in college networks where social circles often overlap. For instance, if two students have strong ties to a common friend, such as a roommate or classmate, they are likely to interact and potentially form their own connection. In fact, I’ve personally observed this phenomenon in action: I tend to be at least acquainted with my close friends’ close friends, and they often know mine as well.
Social networks in college settings are dynamic systems that significantly impact a student’s experience. By understanding and harnessing the theory and concepts behind these networks, students and universities can unlock a wealth of opportunities, access diverse perspectives, and build a supportive community.
Bayes’ Rule in the World of Healthcare
As the landscape of healthcare continues to evolve, clinicians find themselves grappling with an ever-expanding pool of patient data, diagnostic tools, and treatment options. Navigating the complexities of health insurance as a recent college graduate, you enroll in your company’s plan only to face a surprising $300 monthly premium. The puzzle deepens when you discover that health insurers, like their counterparts in auto insurance, employ Bayesian reasoning to assess risk and set premiums.
Your age and overall health suggest a lower initial probability of significant medical expenses. However, factors such as sedentary lifestyles among young professionals are considered, triggering Bayes’ Rule. This calculates the probability of incurring medical expenses, factoring in your status as a young adult with a sedentary lifestyle, contributing to the elevated premium.
Understanding this, you proactively adopt healthier habits, incorporating exercise and balanced nutrition to lower your risk profile potentially. Simultaneously, you recognize health insurance as a vital safety net, aligning with Bayes’ Rule principles in accurately estimating risk.
In the realm of clinicians facing an expanding pool of patient data, Bayes’ Rule emerges as a pivotal tool. This probabilistic framework guides the updating of beliefs based on new evidence. It aids clinicians in navigating diagnostic uncertainties and treatment efficacy assessments, enhancing diagnostic accuracy and contributing to evidence-based decision-making.
This exploration into Bayesian reasoning highlights the synergy between probability theory and medical practice. Real-world examples showcase how Bayes’ Rule shapes clinical intuition, guiding rational medical choices for better patient outcomes. We’re watching as technology advances through ways like incorporating Bayes’ Rule, where probability theory becomes a powerful ally in optimizing healthcare decisions.
Bayes’ Rule for Clinicians:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3153801/
https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1008&context=joap
Disease Modeling, R Naught, Fallacies
We’re taught that r naught, the value indicating spread potential of a disease. The two variables representing population size and transmissibility, make a general model for spread potential. However, disease modeling is much more complex than this in the real world, and this calculation isn’t complex or robust enough to capture the full picture of a disease. It assumes that the population is equally susceptible, that there is no variability in infectiousness, ignores contextual factors, not account for immunity, and oversimplifies disease dynamics. Moreover, it is a static measurement and does not change in response to the evolving dynamics of an outbreak, such as changes in population behavior, public health interventions, or seasonal effects.
I think it’s a good general introduction to disease modeling, but isn’t robust enough to capture all disease out there and all populations out there. It’s important to keep this into account when using this formula.
The failure of r naught: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3157160/
The Importance of Weak Tie Relationships in Maintaining a Healthy Lifestyle
Imagine the number of people you might interact with on a normal day. This includes more than just the friends in your social circle, your boss at work, and the people you live with. Think about the number of brief interactions you might have with other passing people, like the server at Chipotle, passing coworkers, a seat buddy in a large lecture hall, etc. These represent weak ties in your life, whereas the friends in your social circle, your boss at work, and the people you live with are the strong tie relationships in your life—amongst others, of course. Just as discussed in class, these ties are the types of edges that connect the nodes—you and the people you interact with—and form a network. Strong ties represent closer, tighter relationships, while weak ties represent loose, casual relationships. This BBC article stresses the importance of these seemingly insignificant weak tie relationships just mentioned.
You must have noticed the effect of the absence of weak tie relationships during the COVID-19 pandemic, though you might not have recognized it this way. Lockdown limited the number of interactions we had every day to just being with strong tie relationships—family, close friends over Zoom, Facetime, video games. There were no more run-ins with your old lab partner while walking to class or break room gossip sessions with your coworkers. The monotony of this strong-tie-relationship-only lifestyle became limiting to not only variety in social interactions, but also for creativity and even mental health.
According to a study referenced in this BBC article, those with “larger networks of weak ties tended to be happier overall,” and on days with more weak tie interactions, participants “experienced more happiness and a greater sense of belonging.” These casual conversations and moments with weak tie relationships are often more light-hearted and easy-going, allowing for less stress and burden than the more heavy and serious interactions with a strong tie relationship.
The diversity inherent in weak tie relationships introduces variety into our social landscape. These connections expose us to different perspectives, ideas, and experiences not prevalent within our immediate social circles. Weak ties become a source of creativity, offering inspiration beyond the confines of strong tie relationships. So make sure to maintain those weak tie relationships and interactions, as they are more important than you might think.
ESS in academic literature: terminological nuances
The article “The semantics of stability: evolutionarily stable strategy in biology and economics literature” discusses the concept of ESS in both biology and economics literature, tracing its origins to Maynard Smith and Price and its subsequent adoption across various scientific disciplines.
A refinement of ESS by Taylor in 1989 introduced m-stability and δ-stability conditions, further enhancing its mathematical rigor. However, the text highlights a terminological issue as it represents the original authors of ESS, Smith and Price. The “evolutionarily stable strategy” is often falsely expressed as “evolutionary stable strategy,” leading to potential confusion. This misnomer is comparable to a similar issue in economics with the term “socially responsible investing.” Analyzing historical data from 1973 to 2022, the study identifies a growing trend in the incorrect usage of ESS terminology, with a significantly higher rate in economics literature compared to biology. Statistical analyses, including the Mann-Kendall test, reveal these trends over time and differences between biological and economic literature.
In the context of discussing”evolutionarily” and “evolutionary,” their primary concern is not the conceptual distinction, but rather the impact on database searches. The juxtaposition of “evolutionary” and “stable” in an incorrect form might lead other readers like myself to falsely envision the evolutionary stability of a typical game. According to the article, misconception is clarified by acknowledging that expected payoffs in games can change with new information, challenging the notion of a constant equilibrium.
Although evolutionary equilibria may be m-stable but not actually δ-stable, fostering polymorphism and variation, these are often overlooked in simplified models. Recognizing the tendency for models to simplify, it is emphasized that these realistic intricacies, though essential, may distract general audiences and learners from grasping the underlying mathematical principles.
Reflection:
This article helped me understand the nuances in ESS beyond what we discussed in class on a semantic level, and its potential mis expressions as “evolutionary stable strategy”. Conceptually, they differ, and while it matters more in the context of writing a research paper, or in a networks class where we give deeper into game theory and strategies, I definitely will take into account this subtle distinction as I continue to learn about networks.
Sources!!!
https://www.frontiersin.org/articles/10.3389/fevo.2023.1229093/full
https://www.nature.com/articles/246015a0
https://link.springer.com/book/10.1007/978-981-19-4979-1
Proof of Work: The Better Cryptocurrency Model
The two key mechanisms for updating and maintaining the blockchain are Proof of Work( POW) and Proof of Stake (POS). Ethereum the second biggest cryptocurrency by market capitalization has recently switched from POW to POS, with its developer touting its efficiency and sustainability.
Proof of Work: Bitcoin Model
Bitcoin operates on a POW system, a decentralized trustless network that relies on miners and nodes in the network with dedicated hardware and software. The first miner solves the problem and receives a block reward in newly issued bitcoins and transaction fees. This incentivizes miners to validate transactions and secure the blockchain. This effort creates a natural barrier to entry and prevents a single entity from easily taking control of the blockchain.
Proof of Stake: Ethereum Model
In POS, validators, rather than miners are responsible for constructing the next block. Owners of the cryptocurrency can stake their tokens and become eligible validators. The security of the chain depends on the proportion of honest validators in the committee. Rational validators must weight the cost of validating block legitimacy against potential rewards and penalties.
Nash Equilibrium in Blockchain Mechanisms
Both POW and POS mechanisms involve decision-making based off of the Nash Equilibrium. POW has a zero-profit equilibrium, where miners enter and existed the game based on expected profits. While POS, validators decide whether to validate a block by maximizing payoffs.
Why is POW better than POS?
POW is inherently resistant to a Sybil attack while this is not the case for POS. A sybil attack happens in digital networks where a single entity controls mutiple nodes to comprise the networks. This can happen in Ethereum due the possibility that a single wealthy entity has alot of ethereum as a result can create alot of validators.
Energy Concerns and the Path to Sustainability
One of the most cited criticisms of POW is its energy consumption. While its true the Bitcoin mining consumes a significant amount of energy, this ignores the current efforts towards sustainability. Many mining operations are increasingly powered by renewable energy sources. Furthermore, Bitcoin mining has accelerated renewable technology as there is need for cheaper energy. Moreover, the energy used in POW can be seen as the cost of maintaining a secure, decentralized and trustless financial system.
Future of POW
While alternative methods like POS are gaining popularity, POW remains the primary player. Its proven track record makes it the number one choice when security and trust are priority. The ongoing innovations in renewable energy and mining technologies enhance the sustainability and efficiency of POW systems.
Nuances of The Evolutionarily Stable Strategy in Vampire Bats
Pretend for a second that you are a vampire (bat) that needs to drink (usually, animal blood) every two nights to survive. Each night, only ⅔ of the population successfully feeds and ⅓ go hungry. After returning to your roost, you have the option to either share what you foraged with others or to withhold.
The following table displays a payoff matrix for the scenario. If both bats withhold, there is a neutral effect. If they both share, both are slightly negatively impacted. If one bat shares and the other bat withholds, the bat that shares is harmed while the bat that withholds benefits.
| BAT B | |||
| SHARE | WITHHOLD | ||
| BAT A | SHARE | -2, -2 | -5, 5 |
| WITHHOLD | 5, -5 | 0, 0 | |
First, I used the strategies discussed in class to find if there are any pure Nash equilibrium or dominant strategies. If A shares, B would withhold. If A withholds, B would withhold. If B shares, A would withhold. If B withholds, A would withhold. It’s evident that withholding is the dominant strategy for both Bat A and Bat B, and none would want to deviate from the strategy. Furthermore, the Nash equilibrium would be for Bat A and Bat B to withhold, for a payoff of 0 for each.
Now, determine whether the pure strategy Nash equilibrium is an Evolutionarily Stable Strategy. An ESS is defined as a strategy that cannot be invaded by another strategy if a small fraction x decides to deviate from the popular strategy. Suppose we are in a population that mainly withholds. That is, x represents the small fraction that would deviate to share and 1-x represents the rest of the population that withholds.
In a population that mainly withholds
If Bat A withholds,
(1-x)(5)+(x)(0)=5-5x
If Bat A shares,
(1-x)(-2)+(x)(-5)=-2+2x-5x=-2-3x
Since 5-5x>-2-3x for a small X, withholding is shown to theoretically be an evolutionarily stable strategy.
However, interestingly enough, in a 1984 study by G.S. Wilkinson, most vampire bats choose to share in an act of altruism. I would like to explore why they contradict the conclusion of the evolutionary stable strategy as well as the shortcomings of game theory when applied to real-life scenarios.
The vampire bat situation is unique due to repeat encounters, since bats tend to roost together for years. As a result, these bats that they would share/withhold with are not complete strangers. There is a high chance of them meeting again and then perhaps needing blood from them in the future to survive– so they are more inclined to be altruistic in hopes of reciprocation. Furthermore, there is a high risk of dying or harming the population by not sharing, thus, the stakes are a lot higher. It’s also been observed that hungry vampire bats are more likely to receive aid. The fact that not all vampire bats are able to feed each night raises the question whether game theory can even be applied to this situation, since it’s so complicated.
To experiment, I will set a different scenario with higher consequences for withholding that more accurately account for realistic long-term effects. That is, change the payoff for both withholding from 0 to -5 and adjust the others slightly as well.
| BAT B | |||
| SHARE | WITHHOLD | ||
| BAT A | SHARE | -2, -2 | -4, 6 |
| WITHHOLD | 6, -4 | -5, -5 | |
The pure strategy Nash equilibriums are (SHARE, WITHHOLD) and (WITHHOLD, SHARE). There is no dominant strategy for either player. There also exists a Nash equilibrium with mixed strategies, since the players would randomize between (6, -4) and (-4, 6), and neither can increase its expected payoff by playing an alternate strategy. The following is the computation of the payoff for a mixed strategy Nash equilibrium.
Payoff for Bat A
−2(q) − 4(1 − q) = 6q − 5(1 − q)
-2q-4+4q=6q-5+5q
2q-4=11q-5
1=9q
q=1/9
Payoff for Bat B
−2(p) − 6(1 − p) = −4p − 5(1 − p)
p=1/9
These are symmetrical since the table proposed is symmetrical, and demonstrates that both bats would cooperate with the other 1/9 of the time but choose to betray 8/9 of the time to have the highest possible personal payoff.
Despite the modification, it still appears that according to pure game theory statistics, these bats will choose to withhold the majority of the time. Perhaps there are more complicated approaches and methods beyond what was discussed in class, but this displays one of the many limitations of utilizing such a model to apply to real life situations.
Sources:
Wilkinson, Gerald S. “Reciprocal Food Sharing in the vampire bat.” Nature, vol. 308, no. 5955, 1984, pp. 181–184, https://doi.org/10.1038/308181a0.
Metzler, Dirk. Evolutionary Ecology – LMU, evol.bio.lmu.de/_statgen/EvolEcol/ws1718/ess_handout.pdf.
Srivastava, Saniya, and Heidi Zhang. Modeling Altruism in Evolutionary Biology Using Game Theory, math.mit.edu/research/highschool/primes/circle/documents/2021/Srivastava_Zhang.pdf.
The Power of The Education Signal
In economics, the Signalling Theory was first discovered by Michael Spence. Spence experimented and found a positive correlation between an agent’s (educational) credentials and a principal’s belief/judgment towards the agent’s capabilities. In simple words, someone with an (objectively) good educational background is seen as more capable to other parties than someone without (objectively) good education.
This correlation stems from the principles of Markets with Asymmetric Information. Markets characterized by asymmetric information refer to an environment where not all sellers and buyers receive the same information. There will be a party that knows some information that the other party does not know. This information imbalance between sellers and buyers can cause challenges in reliability, effort, and stability.
When referring to education signalling, the sellers are the employees and the buyers are the employers. In the job market, the sellers have more information than the buyers. The sellers know the type of educational background they received and the skillset they hold. However, the buyers only know what is being told to them by the sellers. Therefore, the sellers have more accurate information. Therefore, sellers with objectively higher educational backgrounds can raise the “prices” or values of their credentials for their prospective buyers than sellers without this educational background.
Overall, Spence found that even if education did not actually contribute anything to an employee’s productivity, it could still have value to both parties. If the appropriate costs and values are established, the market for education and hiring will be influenced by this information asymmetry. For example, employees with purchase more “good” education to raise their value in the job market. Employers will be willing to pay more for “good” employees with higher-quality education.
As a college student, this is fascinating. I often hear the phrase “you’re from Cornell, you don’t have to worry about finding a very good job”. This stems from our society’s belief that all you need to secure a “good” job is an objectively good educational background. However, this is becoming less fitting as employers are becoming more focused on well-rounded and diverse individuals.
What is more powerful: more followers or following?
In chapter 12, “The goal is to understand power not just as a property of agents in economic settings, or in legal or political settings, but in social interaction more generally — in the roles people play in groups of friends, in communities, or in organizations. A particular focus is on the way in which power is manifested between pairs of people linked by edges in a larger social network.” When applying this to social media metrics, ones number of following determines the level of popularity and (arguably) influence/power they have within their community. If we look at social media, such as Instagram, as a network, the node refers to a profile page and the links refer to the group of followers (in-links) and following (out-links). Nodes or profile pages are able to communicate and interact with each other through links across networks. For example, my group of followers all have in-links towards my page, forming my own cluster. However, some of my followers follow other profile pages that I am not following, and therefore they have out-links to different clusters. Overall, social media is a conglomerate of clusters.
An overarching question is how power varies depending on the types of links within a node’s network. In the social media context, the amount of power I have to influence my cluster/community depends on the strength of my in/out links and the number of in/out links. In the social media context, a weak link refers to one where I follow them (or they follow me) because of a mutual and nothing else. I don’t truly know them and will most likely never actually form a meaningful relationship in real life with them. On the other hand, a strong link refers to someone I follow (or they follow me) because we have a real relationship in real life. However, when we return to the topic of power, the strength of links (weak or strong) does not really matter when it comes to spreading messages because social media is a platform that distributes information systematically: to your following network (and outside if your account is public). It barely factors in the strengths (at least not supported with the current technology). Therefore, the power of a node’s ability to spread information rests in the number of out vs in links present in ones network. More specifically, in-links are followers who will receive the information that is announced from the node. Therefore, having a higher number of in-links is fundamentally more powerful for a node within a social media network context.
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