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Electricity Systems

The field of Power Systems in Electrical Engineering covers a wide range of subfields, from generation to transmission networks, to distribution. There are many ways of analyzing a system, each serving a different aspect for control and monitoring. Typical problems in Power System Engineering involve testing the performance of a network, for example seeing the response electrically of what would happen is a branch was taken down or what happens to a node voltage-wise if we increase the Load. To consider the economic effects, a process called economic dispatch tries to figure out which generators are needed to supply a given demand. Economic Dispatch, as defined by FERC (the federal energy regulatory commission), is “the operation of generation facilities to produce energy at the lowest cost to reliably serve consumers, recognizing any operation limits of generation and transmission facilities”.

In economic dispatch, generators give both a cost function and a generation capacity. The demands, which now collectively refer to a group of consumers (an assumption made under wholesale trading), wants to find the lowest price to pay for their power needs. While this is typically a quadratic optimization problem, we can analyze it from the point of view of markets. If we associate a group of demands as agents and the generator’s power output as an object, this becomes an ideal allocation problem. As an aside, under normal circumstances the generators would have the economic authority here but because Power is a utility, there is heavy government oversight, by FERC, that ensures that the demands are not abused. Some factors that influence pricing is the positioning of these generators, the resource used the produce the power, the immediate necessity of the generator, the distance of a demand from a generator, and the priority with which a demand wants to ensure they always get power. These factors create different prices per generator that a demand wants to pay. Since each demand wants to pay the least amount of money, they would have a strict, but complete (since demands need power even if they must pay a lot for it) preference over which generators they want. Unlike the allocation problem described in class, demands rarely receive all the generation capacity of a single generator, and sometimes a group of demands can remove most of what a generator can supply, forcing a demand to use what capacity remains in a generator, along with whatever he needs more from his next available choice. To complicate matters, the generators have an incentive to supply the demands that pay them the most, which would be the demands who both have this generator high on their preference but would still pay more than other demands. This can get more complicated still, since some demands can be managed by entities who value other non-monetary incentives, such as wanting to use renewable energy-based generators, even though for them it would cost more than other generators. This forms a rather complex two-sided market, where both sides have a priority of who they want to sell to/buy from that need not be based purely on price, with multiple edges between nodes.

Power System Operations by Antonio Cornejo and Luis Baringo.

 ISBN 978-3-319-69406-1

NBA Trading

Most of the professional sports leagues in the U.S. allow trading among clubs, which can be viewed as a miniature economy, especially in NBA. For instance, players’ service under contract with NBA can be exchanged in the system. The maximum parties involved in one trade can be all the NBA teams, in theory. There are rules governing what can be traded, for example, multiple players in one team can be used to trade for one player in another team, as long as the salaries paid to those multiple players are similar to the salary paid to that one player. Every team has a salary cap, which is the total amount of money that one team can spend on paying salary to the players. In the 2017-2018 season, it’s set at 99 million. If we only focus on trading among the team, money may not be a currency at all, although money is involved in this system as the salary pays to the players. For instance, if player A’s salary is too far away from player B’s salary, the team which player A serves cannot just pay the player B’s team the difference and make the trade happens, technically. It’s a good choice because it will prevent the rich team to just buy out all the best players in the league. Clearly, the tradeoffs in switching to use money as part of trade will be the spike of imbalance between the teams.


Therefore, this market is very similar to a weakly preference with initial endowment matching. Each team will have a preference for who they want to get in exchange for their own “initial endowment(s)”(they could be multiple players’ service). However, the preference of each team is not known, publicly.



Some features of this market are the deadline for the exchange and non-centralized trading practice. For instance, in order for team A to trade with team B for certain player(s), team A must individually talk to team B about it, and team A is not even sure whether team B wants to trade those players in the first place. Therefore, a good alternative practice may be to set a date and ask each team to post who they want to use for exchanges. After that, ask them to submit a preference out of the available players that are posted. This will more likely to solve the information inefficiency in the marketplace.





Beach Rentals as a Market

The market I have chosen to describe here is the market of rental beach chairs and umbrellas on public beaches, particularly in Hilton Head Island, South Carolina, where I worked last summer. One set is defined as two chairs and an umbrella. I have attached pictures of Shore Beach Service’s sets below.

What is being exchanged or allocated here is beach chairs and umbrellas in exchange for money. The market may include just a few sets, or a large amount of sets (up to ~120) depending on the area of beach. Each set must be set up the same distance apart from each other, and must be in a straight line parallel with the shore line. Each set of chairs and umbrellas costs a certain amount of money, however, there is also an option to tip the beach patrol who is renting the chairs and umbrellas. In this case, the renter is not only purchasing a chair and an umbrella, but they may also be purchasing comfort, shade, cooler temperature and perhaps a decreased risk of passing out due to the heat. In addition, the option to tip means that the customer can also attempt to exchange additional money for increased customer service and even the chance at a temporary friendship with the beach patrol, who is more likely to check in on and chat with customers who tip.

The feature of this market design is that all customers have the opportunity to choose their favorite set of umbrellas and chairs, out of all the available sets in the row. For example, imagine there are 10 sets of two chairs and one umbrella. They are set up in a straight line along the beach. Customers who arrive first will get their top choice of set; perhaps the one of the sets on the end, as that is always popular. Customers who arrive later will get their first choice out of the remaining available sets. While renters could be “assigned” sets, this is not ideal, as they are less willing to be happy with the beach patrol and less willing to tip. There does exist a  priority order f over a where f(1) = a1 is the first agent to arrive, and f(10) = a10 is the last agent. This is essentially a matching market, however, the matching is not pareto-efficient and not a serial dictatorship because customers can have weak preferences. To illustrate, a1 arrives first and can choose whatever set out of the 10 that they wish, however, they may prefer both end sets equally, in which case they will  be assigned one of those two sets randomly. Then a2 arrives an hour later and settles for the other open set on the end of the line, even though a1’s set S1 is a2’s first choice. The problem here is that the weak preferences allow for random assignment that could create two different potential matchings M and M’, where M’(a2) > M(a2) and M’(1) is equally as happy as M’(1), meaning that the matching is not pareto-efficient.

The matchings are not always in the core, either. Some customers may arrive and realize that they want to be placed in a set (s2) next to their friends set (s1), but there is already a renter sitting in that set. The matching mechanism, i.e. the beach patron, cannot force renters out of their set in favor of another renter, but the two agents may talk to each other after being assigned sets and decide to swap their initial endowments (sets). The fact that these renters can form a coalition of agents and create a different matching M’ where M’(a) ≥ M(a) and M’(b) > M(b) shows that the matching of beach rentals is not in the core.

Daily Choices as a Market

Every person makes hundreds of choices each day. And I would contend that most of the choices made are incorrect. Whenever you aren’t being productive, you could be. And when you are being productive, there are steps that could have been taken to maximize that efficiency. Instead, as is evidenced by my writing of this post 90 minutes before the deadline, we make incorrect decisions: we procrastinate; we eat poorly; we inefficiently use our time.

I think that many incorrect decisions can be boiled down to a single concept. Despite knowing better, we greatly prefer choices that benefit us sooner at the cost of time and effort later. From a markets perspective, every task available at a given time provides to us a certain utility. For example, eating a cookie surely has a very high utility while you’re eating it, and a measurably negative utility for the rest of its stay in your body. In this way, we could theoretically map our lives as the cross product between points in time and the choices available at those points in time. To take this a step further, we could approach this set as a problem from which we are trying to derive the greatest utility. Therefore, every decision made is actually just an attempt to minimize the loss of utility caused by subpar decision-making at a certain point in time.

What results is, given values, a very basic problem in dynamic programming. What path of choices, each of which provide a utility over the span of a time, throughout my entire life would yield the greatest overall utility. In this game we have no enemy, no opponent; the only limiting factor is our primitive brain that is entirely incapable of making the right decision time after time. We can strive to minimize the loss of utility, but ultimately, I’m still going to eat a cookie every now and then, and I’m still going to submit my assignments an hour before the deadline.


Allocation of Young Talent Into The NBA

Once a year, in early June, sixty basketball players are drafted from colleges and universities around the country to join one of the thirty professional teams in the National Basketball Association (NBA). The following is a concise overview of how the National Basketball Association allocates young talent into their billion dollar industry. In essence, the National Basketball Association has some very good teams that win a lot, and some very bad teams that lose a lot. The NBA Draft is a way to keep the NBA very competitive for all teams.

There are thirty professional teams in the NBA. The best eight from each of the two conferences (a total of 16) qualify for the playoffs and have a chance to win the championship. The fourteen remaining teams that do not qualify for the playoffs are entered into a mechanism called the NBA Draft Lottery. There are 82 games in the NBA season, and the team with the most losses and the least wins has the highest chance of winning the Draft Lottery and getting the first pick in the NBA draft (i.e. the best player in college or around the world). The order of the first fourteen teams in the draft is determined this way, giving the very worst teams the highest chance of getting the first, second, or third picks in the draft. The commissioner literally draws out of a hat (that has predetermined odds and percentages based on the season results) to determine the order of the first fourteen teams. After the lottery, and the order of the first fourteen is already decided, the order for the sixteen other teams is set. The team with the best record of all 82 games gets the very last pick (the 30th pick) in the draft. The second-best team gets the 29th pick, and so on. There are a total of 2 rounds in the draft, allocating the best sixty collegiate players to professional teams. The order is the same for both rounds.

There actually is an abstract form of currency in this market. Very often teams will trade their current players, and/or their future draft pick position to move up or down in the NBA draft. If a professional team sees a college player that would fit the team’s needs very well, but the player is expected to go very early in the draft, this team can trade their current players and their draft position to move their position up in the draft.



(Note: The information in this post comes from my knowledge of the National Basketball Association.)

College Admissions as a Market

One real world situation which could be interpreted as a matching market is college admissions, specifically college admissions in the United States. In this well-known market, college students create an application to make themselves appear as a more attractive candidate to a college, and colleges accept what they believe are candidates that will want to attend their college and make their college appear more prestigious. Therefore, the exchange being allocated is acceptances on both parts, since there exists the decision to accept a student on the part of the college, and the decision to accept a college on the part of the student. Further, in this simplified version of this real life phenomena we can consider currencies in this market could be considered to be acceptance letters given to students by the colleges and acceptances given to the college by the students.

A feature of this market that could constitute a “design choice” of this market is the way that a college makes its decisions on which candidate to accept. For example, some colleges may decide that they value GPA more than extracurricular activities, whereas other colleges may decide that they value standardized test scores more than any other potential factor. Since in the real world prestigious colleges in the US tend to score the candidate “holistically,” or at least that is what they say, students as a result try to portray themselves in their application as this idyllic balanced candidate. It is not difficult to imagine what would happen if prestigious colleges used different design choices, as we can look at East Asia as an example. These colleges’ “design choices” solely care about a test score, and therefore students spend a lot of extra time in “cram schools” preparing for this potentially life-changing test. This change in the market’s “design choice” has implications for the mental health of society, as student suicides are higher in these countries as a result of the monumentous pressure resulting from these tests.

This market is not strategy proof. Students could effectively lie about their choices by applying to multiple schools early decision, effectively saying all of these schools are my top choice when in reality they are restricted to only accepting one school. This is something some students actually do, however is not supposed to be allowed. The colleges are then under the impression that this particular student holds the college in their number one slot in their ranked preferences, but this was not the case.

Nintendo’s Amiibo Market in US

As a major selling point for one of the largest video game companies, Nintendo, amiibo figures have been popular these years since they were launched by Nintendo due to the customizations they bring to various games. Simply by tapping the amiibo figures onto the game console (i.e. Nintendo Switch), players can unlock special contents which will appear in the games they are playing.

This essentially is a two-sided market where Nintendo/game developers who program the amiibo figures receive money and players receive the figures as well as extra digital elements in games. The currency is money, given by players, to Nintendo/game developers. In this situation players always have weak/strong rank-order preferences over amiibo figures while to reach the greatest number of paying players, the game developers tend to program for those amiibo figures of characters in popular games first. That’s probably the reason why the most popular amiibos feature the most various contents.

One market feature is the programmed mechanism between different digital contents and amiibo figures, which is specifically, the kinds of digital contents players can get after tapping their amiibo figures on game consoles. This market feature is worth exploring as different designs directly change the things being exchanged in the market.

In current design, digital elements appear randomly for each amiibo figure no matter what specific figures players are using, and figures of characters in those specific games can be used in some other games too. The latter design element benefits players as they are not restricted to use their figures in only one game, while an alternate design for the randomly appearing mechanism is to program those more special, rare digital contents which are hard to get without amiibo figures in games to those more expensive figures. By connecting the “internal” digital values with the external prices of amiibos, the new design may enhance strong preferences among players.






Political Votes as a Market

An example of a real-world situation that can broadly be viewed as a market is the market for “votes” in the House of Representatives. In this market, votes, from representatives, are being exchanged or allocated to bills. Representatives can decide how to allocate these votes based on their own political preferences or needs. Preferences may refer to something such as ideology while needs may refer to something such as ‘the need to pass their own bill’ so they may trade votes. If one were to argue for a currency in this economy, the best example of a currency would likely be ‘support on future bills’. If some representative gives his or her vote away to another representative, on a bill they really have no vested interest, they likely will seek support or some other political favor in the future. This ‘currency’ will not necessarily be traded because in some cases a politician might just vote in favor of a bill because it fits with their ideology rather than because they expect to get something out of it.

An example of a market design employed in this ‘market’ is the rule for how an agent will distribute his or her votes in a given congressional session.  For example, an agent (representative) will usually follow the following steps: 1) if they sponsored a bill, they will allocate their vote to this bill 2) if they did not sponsor this bill, then they look to see whether the bill aligns with their party agenda/their own ideology, if so they might allocate their vote to this bill 3) if they see room for personal gain, politically or personally, then they will vote in favor of the bill. This ruleset for how some representative votes is not necessarily substantive, as there is a comprehensive literature on voting behaviors amongst legislators which suggests factors such as religion and schooling background might also play a role in determining how a legislator will allocate their vote. The three listed rules are important, however, because if a representative were to randomly assign votes it would throw the market into disarray as there would be no clear indicator to outside parties (for example: constituents, lobbyists, and companies) which bills are going to pass and within the market representatives would have a hard time gathering support for their bills as there would be no clear indication who they should ask for support.



Applebee’s is a Market

In the 21st century, classic American eateries such as Applebee’s and Ihop are struggling heavy. Analysts blame the fact that these casual dining chains no longer get traffic from millennials and other young peoples. For this market I will use ‘Applebee’s’ to represent this whole group of struggling food giants. Recently, Applebee’s has had to close down hundreds of locations as it continues to shake its “dated” appearance while still appealing to its older clientele who still love Applebee’s. This is a fine example of a two side matching market with currency. On one side is your Applebee’s and the restaurants that are popular these days (i.e. McDonalds, Panera, Chipotle, other places that are appealing for young people). The other side of the market is a sample of the millennial generation and older people like baby boomers. We match each of these people to their favorite go-to restaurants for a casual dinner. The ‘currency’ is not money in this scenario, although each customer still pays for their food, but increased reputation and power of Applebee’s if they are able to garner support from more millennials. Money is not the currency because while they eventually do need a higher steady revenue, right now they must take a hit and change their demographics. In exchange, millennials want a pleasant dining experience where they can get trendy foods, served quickly, at a price that they like. Old people want a warm, familiar establishment and do not care as much about price. The reputation ‘currency’ that Applebee’s receives from a match with millennials is far more valuable than that of a match with an old person.

The ‘market’ itself can be defined for a time interval (such as a financial year) in which millennials go out to eat. A feature of the market is that preferences update dynamically as we see trends occur. Customers have a binary preference list of restaurants they habitually eat at. Preferences are determined at the start of the quarter by preference of food, brand recognition, and their habits of where they had eaten in previous markets. However, if one restaurant becomes more popular with young people, a millennial’s preference may change during the year if he is swayed by new culture and he could be rematched. Old people provide a negative ‘currency’ when they match with Applebee’s as it effects the preference list of millennials and other young people. It becomes less of a vibrant atmosphere and is less cool because eating in a place with many old people is sometimes weird. Young people may choose to not preference Applebee’s and go match with Panera or Chipotle or McDonalds if too many of these matches occur. Furthermore individual Applebee’s franchises might be less concerned about attracting youth if they are still making immediate money with old people even though they will struggle in the future. As Applebee’s reputation changes, they hope that more millennials will preference it and they can prosper. An interesting dilemma is how to change their culture so that it could appeal to both older generations AND millennials in the future such that all reputation or ‘currency’ received is positive in the market. We will wait and see as they continue to change their menu.


Modeling the entry level tech labor market

Tech positions have ballooned over the past decade, and applicants and employers alike have increasingly dedicated more resources to finding the perfect match(es). We can view such a labor market as a two sided market, or a bipartite graph between applicants and employers, with the employers each offering an entry level new grad software engineer position or equivalent. Construct edges from applicants a to employer e if a fulfills e’s requirements and applies to the position offered by e. We define a transaction in this market as an applicant a accepting an offer by employer e; we can view this as an exchange of applicant a’s labor and time for employer e’s salary and benefits. Modeling this market is of particular interest due to its continuous growth in participants, the implications of, and the fact that its a market that I myself have already participated in a flavor of (internships) and will likely enter in the immediate future.

Labor or job markets in general has a currency – real money. As previously stated we can view transactions as applicants selling their labor and time in change for a salary, usually offered in the form of a contract, containing salary, RSUs, perhaps options, and other benefits. This currency is only available from employers and not other agents (applicants). Thus, we view this as a two sided market. Over the course of the hiring season, usually late summer to the end of the fall semester, employers offer positions, send out rejections, while applicants may withdraw from interviews, accept, or decline offers. As a two sided market, both the agents (the applicants) and the employers have preferences. These may not necessarily be strict and are not complete in the context of the whole job market, but may be complete in the context of the subset of the agents who applied to x position or the subset of the employers of whom applicant a applied to. Considering this, it’s interesting to consider the notion of strategyproofness Considering that employers spend consider resources and time to do the interview process with an applicant, which often involves a final half day on site interview, employers often screen for interest and the likelihood of the applicant accepting the offer. With that in mind, its easy to see that when companies are guaging interest through resumes, cover letters, HR screens, or even seemingly harmless fun questions on the application (i.e. “what’s your favorite superhero”) or just outright “why do you want to work for us,” it is beneficial for the applicant to embellish and conceal the employers true position in their preference ordering. So, this market is not strategyproof.

One interesting feature of this market is negotiation and the fact that the currency offered by employers in the form of salary and benefits is flexible and thus preference orderings of both applicants and employers is subject to change, both throughout the interview process and negotiation. Through the interview process, as employers obtain more signals about the applicant, their preference ordering may change and the applicant may or may not move on. During negotiation, the applicant may leverage employer offers against each other. If the market were to outlaw negotiations and the currency that an employer offers is set in stone – this would likely result in a matching market which heavily favors employers as applicants would not have the leverage to increase their payout, net gain for employers.

Furthermore, with online platforms such as linkedin, github careers, dice, and other technology job platforms, there is the trend of increased search by applicants. Due to this, its not uncommon to see employers offering offers to applicants who have already matched with a more preferred employer and thus do not renegade. As a result, employers must screen from an increasingly large pool, spending much more resources, a self-feeding loop. All this results in seemingly negative gain in time and resources on both the part of the agents and employers. Lets investigate an alternative where we avoid this seemingly negative net gain on both parties. If employers introduce longer applications with more required fields, they narrow the field while also screening for high interest. However, they might lose out of highly qualified candidates. Likely this will result in a net negative gain as most reputable tech companies (competitors) have short 1 click applications, and candidates will choose to simply skip. What about simply optional fields? In fact, this already exists in the form of questions like “why us”, “what’s your favorite superhero.” This approach seems amenable from the employers perspective, as doesn’t scare away qualified applicants, but also gauges interest and helps the screening process. In short, any friction we introduce is subject to the trade-off between a smaller candidate pool and thus less resources in screening and a larger pool with more highly qualified candidates.

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