How to assist small businesses hit by the pandemic with Game Theory

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My name is Thomas Daniels, attending Franklin Road Academy High School in Nashville, TN, and I work part-time as a barista in my town’s sole bubble tea restaurant. This place means a whole heck-of-a-lot to me, as it’s not only the first job I’ve ever had, but I enjoy working there immensely. My co-workers are playful, my boss is gregarious, and (most) of the customers are genteel and adore the restaurant as much as I do. However, being a small business, the pandemic hit Chill Spot economically in a really bad way. Our usual customers come less frequently, and new ones are incredibly rare, the imported goods (which is nearly all of them) that we are accustom to rose drastically in price, and we had to reduce our store’s hours to account for our employee’s schedules, among other reasons. With all these small changes that add up into a drastic change in how we do things and how secure the business is financial-wise, can the average small business stay afloat? That’s the question I asked myself, applied directly to Chill Spot, and I hope that, in using Game Theory, I can compare and contrast the benefits of different strategies and untimely find the best course of action Chill Spot can take to keep its profit as high as possible. 

— Intro and Defining Variables (with Calculations) —

To get started, we need to list out some facts and values surrounding Chill Spot so that we can implement them in a meaningful and theory-proving way. Furthermore, these numbers, although taken from statistics gathered by Square and UberEats, along with a few other online services, have to be met with a grain of salt. These do not account for orders paid for with cash, as well as large-ticket orders we serve at the desired location. To adjust, I have taken the mean number of the total customers who paid with cash over 6 different days (a full work week) and multiplied that value by the cost of the most commonly placed order, and then finally adding that to the total income earned by the restaurant. Here are the formulas I’m using to find the unknown data:

(Mean number of customers who paid in cash from a sample of 6 respective workdays)(The cost of the most common order recorded by Square) + (The mean of daily income since Feb 3rd, 2020 OR The mean of daily income since Feb 2nd, 2019 to Feb 2nd, 2020) = (Estimated total income per day since the pandemic began)

First, let’s calculate the mean of daily income since Feb 3rd, 2020, to symbolize the 

(6.5)($16.75) + (200$) = $300.00

Now, the mean of daily income from Feb 2nd, 2019 to Feb 2nd, 2020, symbolizes the income before the pandemic. Although I don’t have the exact mean number of customers who paid in cash from a sample of 6 respective workdays from a year ago, I multiplied the value by 136.7%, because 36.7% is the percent decrease in average customers we had from the period of Feb 2nd, 2019-Feb 2nd, 2020 compared to Feb 3rd, 2020 to now. 

(6.5)(1.367)($16.75) + (475$) = $623.83

For some context, I used Feb 3rd because it was the date the US released a state of emergency due to the pandemic. Furthermore, Square is a service that logs statistics based on those who pay electronically, through debit, credit, gift card, or one of our 5 delivery services. And, if you were just curious, the most common order is one bubble tea and one Persian Wrap ($5.25+$11.5=$16.75). As a student taking AP Statistics, I realize this number, statistically speaking, can be far from the true mean of customers who pay in cash, and can mess with my equations down the line, but I merely need a number to compare to my other values. As thus, the importance of accuracy in this particular value is much less so in solving with game theory compared to solving with statistics or business economics. 

Now, let’s define some other variables. These are much easier, as they are recurring and, in their respective timeframes, don’t change drastically. Here I’ll be listing the major expenses. 

Below are the expenses before Feb 2nd, 2020:

  • Water and Electric Bill – 148$ per work-day 
  • Boba Direct Supplies (tea flavors, cups, straws, etc.) – $19.71 per day
    • (Cost of one order)/(Mean days in a month) with an average of one order per month.
    • (600)/(30.44)
  • Food Stock/Cleaning Supplies/Disposables/Etc. – $11.42 per day
    • This number was difficult to calculate, but what I did was take the total recorded expenses that fit this category in the last month and divide by 30.44. This number should be under the typical expenses, as some were more than likely missed. 
  • Employees (can vary, but typically as follows below) – $328.5
    • One Cashier/Barista, One Kitchen, One Bounce Between (manager)
    • 10$ per hour, 12.5$ per hour, 14$ per hour
    • Open from 11 am to 8 pm (9h), Monday through Sunday

And below are the expenses after Feb 2nd, 2020:

  • Water and Electric Bill – 148$ per work-day 
    • No change
  • Boba Direct Supplies (tea flavors, cups, straws, etc.) – $31.61 per day
    • Note the cost increased by over 150%; this is due to most of these same products being imported directly from China to Chicago, then to our restaurant.
  • Food Stock/Cleaning Supplies/Disposables/Etc. – $11.42 per day
    • I did not have access to a month’s typical cost in this category for any month before Feb 2nd, 2020, so I will knowingly leave this the same.
  • Employees – $328.5 
    • Other than paycheck raises, of which I ignored, no change 
    • HOWEVER, note we changed the days we are open to no longer include Sunday due to the pandemic. 

With this information, we are going to add them up to then use them to subtract from our calculated total income to find the profit. 

Before: $623.83 – ((148)+(19.71)+(11.42)+(328.5)) = 116.2

After: $400.88 – ((148)+(31.61)+(11.42)+(328.5)) = -118.65

Note, these values are not important, and DEFINITELY not correct… but that’s completely fine! For the game theory, we are using to solve for plausible courses of action, all we need are rough numbers to give simpler values, so we can then use them in games to simulate scenarios and predict plausible solutions! 

Furthermore, note that before the pandemic, the estimated revenue was positive, while afterward, it became negative with a difference of nearly -200. Our goal is to theoretically make that difference as close to 0 as possible, and, if possible, greater than 0. 

First, let’s start with backwards induction, where we have two players and a tree diagram. The first player will be Chill Spot, the restaurant, and the second player will be The Customers. Both players will be making decisions that are in their own best interest, may it be financial gain, or gaining loyalty from the other, or you name it. We’ll have multiple paths, assigning point values for each player’s possible decisions as the game goes down the tree. Then, we’ll have a visual representation and be able to judge what decisions should and, more importantly, would be made!   

— Backwards Induction / Outdoor-Only Services? —

At the top of the tree, we have Chill Spot making a decision. First, let’s propose the most popular idea: Closing indoor seating. This would make work a bit safer in not dealing with as many possible covid transmissions, as well as give the employees more time to prepare orders and communicate with customers virtually as well as outside the restaurant. However, I would imagine customers prefer to have the option of indoor seating, compared to none. 

To start, we give each “solution” an imaginary value, representational of their real-world consequences. Then can represent cost, reward, popularity, infamy, etc., or any combination! 


( X , Y )

X – points added/subtracted to the row

Y – points added/subtracted to the column 

(In all of these games, the players (row and column) want the highest positive values and the smallest negative values) 

Using these values with the chart, we notice that if indoor seating were closed, the Chill Spot Online ordering service would win out, which stands to reason, as this is exactly what a lot of small businesses are doing. 

In this scenario, we can see Chill Spot, playing last, choosing to with ONLY our online service, rather than suffer from a percentage of every meal’s cost ordered from UberEats, DoorDash, Postmates, etc. going to their respective ordering service, rather than into the business. Knowing that decision, the customers would choose to use said online order(ing) service(s) since we can deliver to customers rather than forcing them to come into the store or wait outside. Knowing the customer’s decision, they’ll opt for the outdoor service to make more of a profit than allowing unsafe, time-consuming indoor dining.

— Nash Equilibrium / Should We Advertise? —

Now, let’s do a similar test to see if (an) advertisement would be wise. On one hand, yes, advertisement is amazing for drawing in customers and is rather independent of the open/closed state of our dining room. Yet, on another hand, it’s expensive, and even more so to keep up the advertisement’s frequency. We’ll see similar cost/benefit situations follow, but we’re already starting in the red, so even though the reward one option be incredibly desirable, the cost may not be very plausible 

The rows represent the cost to the business, while the columns represent the potential reward, as in popularity and recognition. It makes no sense for the column values, representing the second value in the pair, to be negative, as no active advertisement would drive away customers. Furthermore, the values in the rows, rather, the first values in the pair, are negative or the value zero, as the business paying for advertisement wouldn’t receive any monetary value. The values below are set accordingly. 

When we play the game and have both players choose what strategy is most optimal for themselves in each category combination, they would choose to advertise once or three times using social media, arguably more time consuming, or choosing to use radio to advertise multiple times, as the radio station earns more profit from more purchases of advertisement. What’s interesting is that our manager already has several social media accounts showcasing the restaurant and, of course, we wouldn’t be able to afford advertisement on the television, so the radio station seems to be the best possible unused outcome to our business!   

— Pareto Outcomes / Should We Change Our Supplier? —

In one final investigative test, I wanted to see the implication of switching products from our supplier in Chicago, BobaDirect, to local, similarly small-business, suppliers! This was suggested by my co-worker, whom I interviewed for opinions on setting values for the tests above, as she’s an avid bubble tea enthusiast, as well as a frequent Etsy shopper. I’ve done research on two nearby small business suppliers, along with Etsy, to determine the values below! 

My co-worker similarly suggested two types of small businesses we could buy from; Small Business 1 having cheap products that aren’t very good, and Small Business 2 having really popular, good products, but as such extremely expensive. BobaDirect being the company we currently use while Etsy is the online shopping app that showcases small business owners to shop from, as well as prices that have barely changed

As we can see above, the current strategy is to choose a solution that has any value on the line between (0,-2) to (-1,2) and (-1,2) to (-3,3). Rather, opting for no change (-3,3), Etsy (-1,2) or Small Business 1 (0,-2) are all plausible options, as they’re the highest and right-most options for after the pandemic strategies. That being said, Etsy wins out with the Pareto Outcome theorem.

Also, note how the figure representing before the pandemic is farther to the right and a touch farther up than the figure representing after the pandemic. This was to be expected, as safety protocols have made tasks consume more time and, furthermore, money. On top of that, the strategy changes from before the pandemic compared to after, leaving the “after-the-pandemic” solution to be way more uncertain and open-ended, as opposed to the surefire strategy that was highlighted in the before-the-pandemic figure. 

Having shown my employer my work, she’s noticed the plausibility of opportunity! Although we will not be going through with closing the indoor dining, since she believes the pandemic has been going for so long now, but she *has* made a deal with a local radio station to advertise our store in exchange for some food trades! Furthermore, we’re supporting other local businesses in Nashville and on Etsy to receive cheaper, yet high-quality products rather than our costly and infrequent regular bubble tea suppliers.

The overall lesson I wanted to teach was that game theory is surprisingly open-ended in its results, as they can be modified endlessly and interpreted in multiple plausible fashions. Situational strategy can be implemented in a number of creative and surprising ways, and letting logic surprise your expectations is always fun! But anyway, how awesome to see the real-world implications of my game theory studies! I know I’m happy, and so are a couple of small businesses in Nashville! 


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