Networks

Video Game Lootcrate Keys: Part 2 – Power Law

 

 

 

This is a follow-up post to Bingsong Li’s post about the Applecraft economy.

Part 2: Power Law Phenomena and Inequality in Applecraft

Greetings, fellow Adventurers of Applecraft!

Today, let’s embark on an exploration into the heart of our economy and uncover the reasons why selling keys instead of opening them leads to a power law distribution in the game among the fraction of players possessing rare items.

Power Law Distribution:

The decision to sell keys instead of opening them for poor players ensures a safer, albeit less potentially rewarding, path. This risk-averse strategy results in a power law distribution among players based on the number of rare items they possess. The power law equation for the fraction of people having k very rare items is often expressed as:

where:

• P(k) is the fraction of players who own k very rare items.
• α is the exponent determining the shape of the power law distribution. This depends on how often players sell their keys to wealthier players as well as the probability of winning a good item.

Understanding the Impact:

Using the above observation about the power law in our community let us observe how this phenomena further affects our experience of the game!

• Inequality among Players: This strategy perpetuates inequality among players. Those who sell their keys avoid the risk of losing value but miss out on the opportunity to obtain rare items. Consequently, a small fraction of the player base accumulates a disproportionate number of rare items due to their willingness to take risks, spend more, and exploit the variability inherent in opening crates.
• Concentration of Wealth: As a consequence, a select few become significantly wealthier in the game compared to the majority. They hold a higher number of rare items, often the most valuable, increasing their in-game wealth and status. This concentration of rare items among a small fraction of players mirrors real-world wealth concentration dynamics.
• Reinforcement of Inequality: The cycle perpetuates as the rich get richer. With more resources (in-game currency or wealth), players can afford to take risks repeatedly, increasing their chances of acquiring rare items. This ongoing cycle of risk and reward contributes to a widening gap between the rich and poor within the game.

These are some of the reasons that lead games to become obsolete. The richer players get reacher and the new players joining the game are incentivized when seeing the immense discrepancy between these top players and themselves.

• Improving the game system: With all that said, a way of improving the crate system and mitigating the power law the game makers could make a system where a user with less in-game wealth is more likely to win a good item than a person with more in-game wealth as well as decrease the probability of winning a rare item when paying real money to buy keys. This would however disincentivse people from spending money on the game, which could again be undesirable.

Conclusion:

The power law phenomena resulting from the optimal strategy of selling keys for poor players and the subsequent concentration of rare items exacerbate inequality among players. This trend, while reflective of individual player strategies, underscores the broader impact on the game’s economy and the disparities among its participants.

As a final thought, I believe that to counter the effect of power law and the subsequent inequality of wealth in the games you, the adventurer, should ultimately prioritize your enjoyment and satisfaction within the game. Some players find pleasure in the thrill of opening crates, while others prefer the stability of selling keys.

With all this said, farewell adventurer!

Videogame Lootcrate Keys – Buy or Sell?

Rules and Assumptions of the Game

This post will be talking about the crate system in Applecraft – an online Minecraft server using the concept of risk in betting in Chapter 22.

1. At the start of the month, every player gets a certain number of keys
2. Every key represents an opportunity to take part in a lucky draw, where they can win an item worth a certain number of diamond blocks (DBs, the game’s currency).
3. Every player has their own individual wealth and can either use the key or buy/sell the key with other players. In this month, if the player uses their key:
   1. The jackpot is worth 8 * 64 DBs and everything else is worth on average 16 DBs.
   2. There is a 2/67 chance the player gets the jackpot (worth 8 * 64 DBs)
   3. There is a 65/67 chance the player gets something else (worth 16DBs)
4. If the player sells their key: they’re guaranteed to get the expected value of ~32DBs

For a more detailed explanation, please see https://wiki.applecraft.org/wiki/crates-and-rares

Key Claim: When faced with the option of whether to use their key, a poorer player’s dominant strategy is to sell their key rather than use it, even if the expected payoffs are equal (between buying versus using)

Modeling Risk

Looking at these numbers, the price of 32DBs per key seems fair and there’s no difference between whether the player sells or opens their key. However, the key is that poorer players are more risk averse than rich players, and so follow a more logarithmic utility of wealth.

Logarithmic Utility of Wealth – Textbook Page 697

If a poor player opens all 31 of their keys this month, there is a 60.9% chance of them winning the jackpot (P(X>=1) in a Binomial distribution where n = 31, p=2/67). That means there’s a 39.1% chance they’ll not win a jackpot.

If you’re an ordinary player and end up with no Jackpots after 31 keys, their payoff per key is -16DBs. However, if they’re rich, they have the option of buying another 31 keys. Perhaps this time, they’ll get lucky and get 3 Jackpots. You’ve now turned a profit (made more money than had you sold all your keys). If you’re still unlucky, you can buy more keys (so on and so forth) until you get lucky. How probability works is that the average value you get per key will get closer and closer to 32DBs the more keys you buy (aka Central Limit Theorem). This is why rich players can afford to take risks.

The basic idea is that to a poor player, you’ll either get very lucky or (most likely) lose a bit of value on your key. If you’re rich, getting unlucky a few times is ok, and you can keep buying keys until you get ~32DBs on average of value out of each key from winning jackpots. Therefore, if you’re a poor player, you should take the less risky option and sell your keys.

When Should Poor Players Open Their Key

1. Other players are offering to pay much less than what the key is worth. This is unlikely because the market for keys is usually the largest (high supply high demand), so the prices are close to their true value.
2. The crate is *not too risky* – e.g. if the price for a key is 64DBs and most items in the crate are worth ~64 DBs

Illustrating “following the crowd” at Cornell

Whether we realize it or not, the behavior of others greatly influences the decisions we make in our daily lives. Being a part of a social group stems from human nature: people want to “follow the crowd” because it can be informational, like a long line in a restaurant hinting at how good the food is, they can receive some sort of direct benefit, or they believe it is the social norm. In the context of our networks course, we discussed how certain behaviors spread within a social group as well as the likelihood that those behaviors would spread to others. 

To demonstrate this concept in a more applicable way to the Cornell student population, let’s say that a group of 8 friends at Cornell tend to go to the library to study only on the weekends. Let’s call this behavior of going to the library on the weekend behavior A. After this behavior has been around for a while, one of the friends in the group, let’s call them Sarah, decides that she want to study every day after dinner instead. Let’s call this new behavior of studying after dinner behavior B. Determining which friends in the group will or will not convert to Sarah’s new behavior depends on the threshold value q. The threshold value basically says that any person will switch to the new behavior if a certain percentage of the person’s neighbors have adopted the new behavior. For example, if the threshold value = 0.4, then that means that a person that has the old behavior will adopt the new behavior if at least 40% of their neighbors adopted the new behavior, with the number of neighbors dictated by connections to the person. Simply put, if Sarah has a connection with another friend Billy, that only has one other connection, then 50% of Billy’s connections will have the behavior, so he will adopt behavior B as well. If each person in the group is only connected to one other person in the group, then the behavior will spread to the rest of the group members. However, in a more likely scenario, friends within a group will all be connected to each other by multiple edges, meaning that if more people already practice behavior A, then it will be harder to adopt behavior B since A is more popular. For example, if another member of the group, let’s call them Harry, has connections with 3 other people (including Sarah), then only 33% of his neighbors have behavior, so it won’t spread to him. This example I have provided demonstrates how a behavior can either be adopted or not within a friend group, giving an idea for how it happens in daily life. 

This course has revealed to me how interconnected we are as a society and how quickly information, behaviors, and ideas can spread. I never really thought about it as in depth as this course has taught me, but I can now identify it in my own personal life as well as educate others about it.

Bitcoin’s Rabbit Hole of Proof-of-Work

Bitcoin, the enigmatic digital currency that ignited the cryptocurrency revolution, operates on a unique mechanism called Proof-of-Work (PoW). This system, while innovative, has sparked heated debates about its energy consumption, environmental impact, and long-term viability. Let’s delve into the labyrinthine world of Bitcoin mining and explore its intricate workings while considering what we have learned about cryptocurrency.

Imagine a vast digital puzzle, one so complex that only the most powerful computers can solve it. In the realm of Bitcoin, miners compete to solve these cryptographic challenges, using specialized hardware to perform complex calculations. The first miner to crack the code earns the right to add a new block to the Bitcoin blockchain, a public ledger that records all transactions. As a reward, they receive newly minted Bitcoin and transaction fees, a concept we’ve explored as a course.

Solving PoW puzzles requires immense computational power, which translates to significant energy consumption. Bitcoin mining operations often rely on fossil fuel-powered electricity grids, raising concerns about their environmental footprint. Estimates suggest that Bitcoin’s annual energy consumption exceeds that of entire countries like Argentina and Sweden, and so as the Bitcoin network grows it will surely require even more computing power and energy. This raises concerns about the long-term sustainability of the system, and if the concentration of mining power in the hands of a few large mining pools could centralize control and compromise the network’s security.

The PoW debate has fueled the quest for alternative mining mechanisms that are more energy-efficient and secure. Promising contenders include:

• Proof-of-Stake (PoS): This system replaces energy-intensive calculations with staking, where miners lock their Bitcoin holdings as collateral to validate transactions. PoS significantly reduces energy consumption and promotes broader participation in the network.
• Hybrid models: Some proposals combine PoW and PoS elements, aiming to leverage the strengths of both mechanisms while mitigating their drawbacks, such as the Proof of Activity (PoA) concept.

Bitcoin’s future hinges on finding a balance between security, sustainability, and decentralization. While PoW has played a pivotal role in Bitcoin’s success, its energy footprint and scalability limitations necessitate the exploration of alternative approaches. The quest for a more sustainable and equitable Bitcoin mining landscape is ongoing, and its outcome will shape the future of this revolutionary digital currency.

Remember, the future of Bitcoin and, by extension, cryptocurrency is not predetermined. By engaging in critical dialogue and exploring innovative solutions such as PoA, we can help pave the way for a more sustainable and equitable digital future using what we’ve learned from ECON2040.

Navigating the Digital Polis: The Politics of Web Information and Online Communities

Introduction

The digital age has converted how we access statistics and interact with each other, bringing to the forefront the complicated politics of web statistics and online groups. This weblog publish explores the multifaceted dynamics of those digital spaces, inspecting how they shape public discourse, affect social norms, and present both demanding situations and possibilities in our increasingly linked global.

 

The Democratization of Information

The net has democratized records, breaking down traditional limitations to know-how and permitting on the spot get admission to to a widespread array of facts and perspectives. This accessibility empowers people, allowing them to stay informed, train themselves, and participate in international conversations.

However, the sheer quantity of statistics to be had online may be overwhelming, leading to difficulties in discerning credible resources from misinformation. The proliferation of fake information, biased reporting, and agenda-pushed content has end up a sizable situation, impacting public opinion or even swaying elections.

 

The Power Dynamics in Online Communities

Online communities, from social media systems to boards and virtual gatherings, have turn out to be critical areas for verbal exchange and connection. These groups frequently foster a sense of belonging and offer structures for shared hobbies, activism, and guide.

Yet, these spaces aren’t without their electricity dynamics. Issues including censorship, moderation policies, and the affect of algorithms in shaping what customers see and engage with are principal to the politics of on line groups. These factors can create echo chambers, increase sure voices over others, and have an effect on the general tone and direction of discussions.

 

The Role of Big Tech

Tech giants play a pivotal role in governing the virtual panorama. Their selections on facts privacy, content material moderation, and set of rules layout have far-reaching implications. These groups wield considerable strength, no longer just in controlling the flow of information, but additionally in shaping cultural and political narratives.

The debate over the obligations of those tech groups is ongoing. Questions round regulating speech, defensive consumer privacy, and making sure truthful and obvious practices are at the leading edge of discussions approximately the destiny of the internet.

 

Challenges of Governance and Regulation

Governing the virtual space poses specific challenges. Balancing the need for open, loose communique with the necessity to curb dangerous content and incorrect information is a delicate task. Different countries have approached this with various stages of law, reflecting broader political and cultural contexts.

The worldwide nature of the web further complicates law, as content material often crosses borders and falls underneath multiple jurisdictions. This worldwide size requires cooperation and speak between international locations and stakeholders to develop powerful and equitable governance strategies.

 

Conclusion

The politics of net information and on-line communities are crucial to information our modern-day digital society. These platforms now not handiest reflect but also shape social, cultural, and political realities. As we navigate this evolving landscape, it’s far vital to foster vital questioning, suggest for ethical practices in tech governance, and sell a wholesome, inclusive digital discourse. In doing so, we are able to harness the capability of the internet to enrich our lives and give a boost to our worldwide community.

 

Balancing Acts: Understanding the Robustness and Fragility of Food Webs and Financial Markets

Introduction

In the problematic tapestry of our world,  apparently disparate systems – food webs and financial markets – exhibit fascinating parallels of their robustness and fragility. This blog put up targets to discover those complicated networks, dropping light on their resilience, vulnerabilities, and the intricate balance that governs their stability.

 

The Dynamics of Food Webs

Food webs, the networks of who eats whom in the herbal global, are incredible examples of ecological complexity and stability. They display robustness through their potential to face up to and adapt to changes, together with the lack of particular species or environmental shifts. This resilience is regularly attributed to biodiversity, in which a wealthy form of species guarantees purposeful redundancy – if one species is misplaced, every other can satisfy its ecological role.

However, meals webs also showcase fragility, specifically in the face of speedy, big-scale adjustments. The extinction of keystone species, the ones that have a disproportionately massive impact on their environment relative to their abundance, can result in cascading results all through the net. Climate change, habitat destruction, and pollutants further exacerbate these vulnerabilities, threatening the delicate equilibrium of those systems.

 

The Complex World of Financial Markets

Financial markets, similar to ecological systems, show a mix of robustness and fragility. Their robustness is obvious of their ability to take in shocks and recover from monetary downturns. Diversification techniques, in which investments are spread throughout various assets, assist in mitigating dangers and making sure the resilience of portfolios.

Yet, financial markets also are inherently fragile. They are liable to systemic risks, in which the failure of one thing, like a major bank or economic organization, can trigger a considerable crisis. Market self assurance performs a vital function in this fragility – panic promoting, hypothesis, and herd conduct can fast destabilize markets, leading to crashes and economic recessions.

 

Interconnectedness and Its Implications

Both food webs and economic markets are defined through their interconnectedness. In meals webs, the interdependence amongst species approach that changes in a single a part of the device may have unexpected effects in another. Similarly, in financial markets, globalization and the interconnected nature of economies suggest that crises can swiftly propagate across the globe.

 

Adapting to Change and Uncertainty

The challenge in handling both food webs and monetary markets lies in expertise and adapting to their complicated, dynamic nature. In ecological structures, this involves conservation efforts, protective keystone species, and mitigating human-precipitated environmental changes. In financial markets, it calls for strong regulatory frameworks, danger management techniques, and a cautious approach to innovation and financial engineering.

 

Conclusion

The study of food webs and financial markets affords valuable insights into the character of complex systems. Both showcase a sensitive stability between robustness and fragility, encouraged through their interconnected and dynamic systems. Recognizing these parallels lets in us to higher admire the subtleties of those systems and the crucial significance of retaining their balance in the face of trade and uncertainty.

The Ripple Effect: How Opinions, Fads, and Political Movements Spread Through Society

The Spread of Opinions
Opinions in society regularly propagate via a complex community of influencers and social connections. Key figures inclusive of celebrities, politicians, or social media influencers wield full-size strength in shaping public opinion. Their endorsements or criticisms will have a profound effect, frequently placing off a sequence response across their community of fans.
Social media systems, particularly, play a pivotal role in opinion formation. These virtual spaces can emerge as echo chambers, reinforcing existing ideals and accelerating the unfold of opinions that align with the bulk inside these circles. This phenomenon is further compounded via affirmation bias, wherein individuals favor records that corroborates their pre-current views.
Moreover, traditional and virtual media stores drastically impact public opinion. The framing of news tales, the choice of narratives, and the emphasis on particular issues can subtly guide public notion and discourse, shaping the collective opinion on a big range of subjects.

The Rise and Fall of Fads
Fads constitute a captivating component of societal conduct, frequently pushed by using a collective quest for novelty and a feel of belonging. These trends, ranging from style picks to viral social media demanding situations, emerge from the human preference to be a part of a group and live modern-day with the present day tendencies.
The explosive growth of social media has been a catalyst for the rapid unfold of fads. These systems allow traits to quickly advantage traction, achieving a worldwide target audience in a remarkably brief time. The virality of social media content material guarantees that a fad can emerge as an overnight sensation.
However, the character of fads is inherently transient. They regularly revel in a meteoric upward thrust in reputation, handiest to fade away as fast as they regarded. This fleeting recognition is attributed to the saturation and overexposure of the fashion, coupled with the relentless pursuit of the next new and interesting component.

The Dynamics of Political Movements
Political moves constitute a extra based and sustained form of collective conduct, frequently rising from grassroots activism and shared ideologies. These actions are driven through a not unusual goal or cause, rallying people round social, economic, or political troubles.
The growth of political actions is extensively prompted by means of the capability to mobilize supporters and correctly communicate their message. The advent of digital structures has revolutionized this procedure, permitting actions to attain a much broader audience and have interaction with supporters greater at once and personally.
Additionally, the success of political movements regularly hinges on their capacity to resonate with the public’s sentiments and address prevailing troubles. Movements that efficaciously faucet into the collective focus can benefit giant momentum, influencing public policy and societal norms.
In conclusion, the unfold of opinions, fads, and political actions is a multifaceted system stimulated with the aid of social dynamics, media, and technological improvements. Understanding these patterns is essential for comprehending our society’s evolving panorama and the forces that form our collective conduct.

 

Can Checking Blocks Be a Nash Equilibrium in Ethereum’s Proof-of-Stake?

Ethereum’s transition to Proof-of-Stake (PoS) introduced a novel security mechanism where validators stake their own Ether (ETH) to validate transactions and secure the network. However, a crucial question arises: is it rational for validators to diligently verify block validity before voting, or can they “free ride” on others’ efforts and still earn rewards?

Let’s analyze this through the lens of Nash equilibrium, a concept from game theory where all players in a system choose their best strategy given the strategies of others. In the context of Ethereum, validators are the players, and their strategies involve either checking block validity before voting (costly but potentially ensures network security) or simply voting without checking (less costly but risks approving invalid blocks).

If all rational validators check block validity and vote yes only for valid blocks, then the probability of an invalid block slipping through is extremely low. This benefits everyone, including the validators themselves, as it protects the network and maintains the value of their staked ETH.

However, individual validators face a temptation to “free ride” on the efforts of others. Checking validity incurs a cost (C) while voting without checking is cheaper. If enough other validators are checking, a single validator might reason that their own check won’t significantly improve security, and they can save the cost. This behavior, if widespread, can lead to a scenario where no one checks validity, compromising the network’s security.

The crux of the issue lies in the pivotal validator: the one whose vote determines the block’s acceptance or rejection. In a large validator pool, the probability of a single validator being pivotal is small. This means that even if they check a block and find it invalid, their vote might not be enough to sway the outcome. Therefore, the potential gain from checking (preventing an invalid block) might not outweigh the cost for a pivotal validator.

For non-pivotal validators, the incentive to check is even weaker. Their vote is unlikely decisive, and the cost of checking outweighs any potential gain. This creates a free-riding trap: rational validators, seeing that others are not checking, choose not to check themselves, further weakening the network’s security.

A large-scale free-riding equilibrium, where validators do not check validity, would significantly compromise Ethereum’s security. Malicious actors could potentially forge invalid blocks and gain an advantage over honest validators. This could erode trust in the network, leading to decreased value and adoption.

To avoid the free-riding trap, several solutions are available:

• Punishing free-riders: Implement slashing penalties for validators who vote for invalid blocks without checking. This incentivizes validators to be more diligent.
• Rewarding checkers: Offer bonus rewards for validators who actively check block validity. This directly incentivizes the behavior that benefits the network.
• Encouraging collective responsibility: Implement mechanisms that promote collaboration and information sharing among validators, fostering a culture of shared responsibility for network security.

In conclusion, while checking block validity appears beneficial for the overall network health, it might not be a Nash equilibrium for individual validators in a large PoS system like Ethereum. This raises crucial questions about long-term network security and the potential for free-riding behavior. Exploring solutions that incentivize checking and discourage free-riding is critical for ensuring the robustness and sustainability of Ethereum’s PoS system.

Network Effects and Information Cascades in Fake News

Misinformation, or fake news, spreads at shockingly high rates on social media. One example that the article “Fale News Spreads Fast, But Don’t Blame the Bots” mentions surrounds the submersible that lost contact in an attempt to view the Titanic this summer. On TikTok, there was a video that reached nearly 5 million views supposedly showcasing the screams of the passengers shortly before their death. However, this video was a clear example of fake news in that the audio was actually from the popular video game series, Five Nights at Freddy’s, rather than the passengers. Fake news like this often circulates the internet, spreading up to 10 times faster than accurate news, according to a 2018 MIT study. This can be driven by many factors, like that the vast majority of Americans receive their news from apps like Twitter, FaceBook, and TikTok where any user of these apps can evolve into a news source for its wide potential audience. A second factor is that many users’ goal is to receive as many clicks and engagement as possible on their posts, so spreading lies is a common strategy to accomplish this.

Another reason, which strongly relates to the contents of this course, is people’s friends engaging in or spreading fake news. An information cascade happens when someone within a social network observes the decisions of people surrounding them and then makes the same choice or adopts the same behavior without verifying the information themselves. In the case of fake news, if one person’s friends repost something containing misinformation on social media, it could trigger a cascade of other people doing the same. People in networks also often have thresholds for adopting the aforementioned choice or behavior, and, for fake news, if a person sees multiple of their friends reposting or engaging with a fake news post, their threshold for sharing or engaging with the same post may be lowered. This experience may also be heightened due to the social validation that many users on social media may seek out. When they notice many of their friends engaging with or supporting the post, and if it is shared with them, they may feel pulled to do the same. Furthermore, the structure of a social network may play a role in these processes as well. If a person who is highly influential or popular within a network shares, engages with or supports a post containing misinformation, this could impact the spread of it within the rest of the network. Information cascades, network effects, and other social mechanisms play a large role in the spread of online misinformation.

Article: https://pirg.org/edfund/articles/misinformation-on-social-media/

Walt Disney Word’s Disney Genie+: The Payoff Matrix and Perfect Matching

Walt Disney Word’s Disney Genie+: The Payoff Matrix and Perfect Matching

After having worked at Walt Disney World this past summer, I really grew to appreciate the intricate process and immense detail that goes into each attraction and experience. Additionally, after having taken Networks, I noticed some similarities between the concepts learned in class and how Disney implements techniques in their parks. With hundreds of thousands of guests visiting the park each day, techniques such as perfect matching and the payoff matrix can be applied to create the most positive experience for the guests visiting the parks. 

Recently, Walt Disney World Resort has implemented a new feature within their mobile app, the Disney Genie+. This is a feature that guests can purchase which has multiple aspects to help improve their experience and plan their day. 

One feature of the Disney Genie+ is the “My Disney Genie Day” feature. Especially in parks like the Magic Kingdom, there is so much to do that it may be difficult for each guest to realistically get to each of their favorite attractions and eat at their preferred restaurants. This “My Disney Genie Day” allows the guests to be able to select certain attractions they would like to ride, shows they would like to watch, and characters that they would like to meet, as well as the times that they would like to do them. This feature can be beneficial, as it uses other user’s input in order to decide when the wait times will be highest and lowest at certain times of the day. 

This concept, how the app can choose between the attractions, can be closely related to the payoff matrix. For each attraction in the park that the guest prefers, we can imagine there being a certain algorithm of the App, which knows each user’s input. We can think about the varying user input via a payoff matrix. In the payoff matrix below, there are two guests that the app is comparing, David and Yian, who have certain preferences of what they would like to do at 4 p.m. This matrix can represent the payoffs that are best maximized when they choose certain attractions (which are in the place of “strategies” in this example). With example numbers below, there is a Nash Equilibrium suggested of David riding “Jungle Cruise”, and Yian riding “Space Mountain”, which are both the best responses to the other guests in the park, to maximize their payoffs (minimize their wait times so they can best allocate their time throughout the day). 

In addition to the “My Disney Genie Day”, one of the most crucial features, and one that provides a significant portion of revenue within the parks, is the Disney Genie+’s Lightning Lane. This feature costs the guests around $20 a day, varying with peak crowds during the holiday seasons and by park demand. This feature allows the guest to join a separate line that supposedly reduces their wait time. In order to keep people buying this experience, it is crucial that each ride is loaded efficiently and with maximum capacity. 

For example, working in Attractions, Disney tries to maintain a guest flow with a certain number of guests riding each hour. This helps to keep wait times down as much as possible amidst the high crowds. In thinking about how to load these ride vehicles most efficiently, it may help to think about the scenario with regard to perfect matching, especially when there are certain height limits and preferences for each guest. For example, on Disney’s “Slinky Dog Dash”, the loading of the vehicles depends on a few factors. This can be demonstrated via the perfect matching diagram below:

In this scenario of loading the vehicle, perfect matching does not exist. When deciding who to place in the vehicle, there are certain ratios that must be used in order to make the Genie+ Lightning lane proportionately faster than the Standby. Additionally, each vehicle has a special seat, known as the TAV, which is wheelchair accessible. Only those with wheelchair access can sit in the TAV, and no other seat has wheelchair access. Therefore, in this scenario, it would make sense to fill the TAV, even if they are on standby. However, with this amount of people let through the waiting queue, there is 1 remaining seat, but 2 adults still waiting. Filling this last seat for perfect matching would depend on whether or not the party would like to separate. 

Filling the ride vehicle is an almost perfect example of perfect matching. Each node (guest) would like preferences for specific slots (N(S) = Seats). Constricted sets may include certain parties that have particular preferences in which they don’t want to separate, or have children under 6 years old (who cannot ride alone). Therefore, to maximize effectiveness, it is important to fill the queue preceding this stage of the ride according to the various demographics of the guests in line. Being able to have a full vehicle for each round of loading demonstrates the importance of perfect matching knowledge within the context of Walt Disney World’s theme parks. The same concept can be applied to Disney’s other attractions, shows, restaurants, and hotels. 

Overall, this blog post illustrates the real-world application of concepts from Networks, such as perfect-matching and the payoff matrix. Increased experience with these concepts can be beneficial to large hospitality and entertainment companies such as the Walt Disney World parks, which aims to both maximize efficiency and guest experience each day, on each attraction, and with each experience. 

Additional Information Used:

https://www.travelweekly.com/Travel-News/Hotel-News/Disney-earnings-fiscal-Q1-2022

 

 

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