Stacks of Cash: A Game Theory Application of What To Do When A Credit Card Reader Breaks

Everyone always tells you to carry cash. My dad has drilled that into me and my brother since we were young, and it’s proven correct more times than once. However, I still never carry cash. The cost of going to the ATM, getting cash out, and then actually carrying a wallet is simply too high for me.

I have too much trust in society. I figured that since we are such a technologically-driven world that every establishment has a Square App, Shopify, or PayAnywhere or any one of the dozens of credit card readers that are on the market now. I am also big believe in NFC, which doesn’t even require a card – just a smartphone.

So picture this – I am finishing my Saturday night grocery shipping at Aldi’s (best time to go, no one is ever there) and get in line. I do this EVERY week. The family in front of me pays with cash (this is important), and then it is my turn. I was already a little stressed because I couldn’t get all my stuff on the moving belt quickly enough, and I felt like the cashier was judging me. Nothing unusual, yet.

So he rings everything up, tells me my total, and I get out my credit card. I insert it into the chip reader, and it is declined. I was horrified. I noticed the card had a bit of dirt on it from my run earlier, so I wiped it off and tried again.

Declined.

I tried my debit card (which I know has money on it). Declined. Declined. Declined. A line is starting to form. I am sweating. Everyone is looking at me with pity in their eyes and I don’t know what to do.

I hear the decline sound again, but from a different register. Sweet relief. It wasn’t just me! Apparently, all of Aldi’s card readers went out.

The Aldi’s crew called their Help Desk, and no one answered. So people started to get nervous. The registers could only accept cash or check. Cash-only customers were sent to the front of the line to check out, and leave.

A trend emerged. The”prepared ones” stepped forward, cash ready, and paid, and left. Us card holders were left behind, holding our useless pieces of plastic and wishing that we had thought to bring a checkbook.

After another 20 mins, another trend emerged. 

People were thinking about leaving their carts behind to go get money. Or they were thinking about leaving in general, abandoning their carts completely.

One woman went and got her checkbook. Another drove off to an ATM. I called my friend for cash (big shout-out to Bonny, saved me there). Others waited it out, hoping that the registers would get fixed, and making the implicit assumption that the registers would get fixed in less time than it would take them to go and get cash.

Others just left their carts entirely, like the girl behind me. She had two items, and we lamented over our ill-timing (remember, the card reader went out on me). Once the Aldi’s crew said there was no ETA on the wait time, she dropped all her stuff and walked out of the store.

I waited until my friend brought me cash, about 42 minutes after the reader went out.

The Payoffs: Do I Stay or Do I Go?

I made a payoff tree of what I think everyone was thinking. 

Interpret these numbers as (x, y) where x is the payoff to the cash holder and y is the payoff to the card holder, out of ten. So a (2, 5) would be a 2 payoff to the cash holder and a 5 payoff to the card holder.

Source: Author

(Card – Go Get Money – Registers Closed) (4, 7 ) Starting from the card holder line on the right, as a card holder, it is of a higher utility to me to go and get cash, and return, and have the registers still be closed. I get a payoff of seven here.

(Card – Go Get Money – Registers Open) (4, -4) If I return with my cash, and the registers are re-opened, not only did I waste time in line, but I also wasted time to go get money, when I could have just sat in line, so I get a payoff of -4.

(Card – Wait – >20min) (4, -2) & (Card – Wait – <20min) (4, 0) If my wait time was more than 20 minutes, I am irritated and angry, and I just want to leave. If the card readers start working again, I think about how I just could have left and could have come back tomorrow. What a waste of time! I get a payoff of -2 because I am pissed off. If my wait is less than 20 minutes, I am fine. Not doing too bad, not doing too great. I get a payoff of 0.

(Card – Leave) (4, 1) If I leave the store entirely, I get a payoff of 1. I know I don’t have to wait in line, but I do worry that the registers opened as soon as I left – but that’s a sunk cost, so I don’t truly consider it. I am just happy to be out of line, but not super happy because I didn’t get my groceries.

(Cash- Pay & Leave) (2, 5) Moving to the the cash holders, they get a payoff of 4 in all of the previous no matter what the card holders do. They are sitting pretty, and they know they get to speed through the lines. But what if they decide to pay for someone else? (This happened once). They get a high social utility, but they are out of some money, which is never a good thing. They get a payoff of 2 here, because they know they get to speed through the line, and that they helped someone, but now that someone owes them money.

(Cash- Pay For Others) (7, 0) If the cash holders pay and leave, they get a payoff of seven. They smirk at the silly card holders, or zoom by without making eye contact. Card holders are low-key salty, but they can’t control the situation, so they get a payoff of zero.

The highest payoff for the card holder here is to go get money and return to still-broken registers. But how do we know that the registers will still be broken when we come back? We don’t, as we have imperfect information. The following payoff tree takes that into account.

The Advent of Imperfect Information

Source: Author

But remember, if the card holder leaves, they have no way of knowing if the register will be fixed when they return. That’s a risk of time value. Let’s assume this matrix is after 30 minutes of waiting have passed, so the payoffs are different from the previous tree. Here, we are going to evaluate the payoffs of the manager too, so the payoff reads as (card holder, manager).

(Card – Leave the Store) (3, -2) Starting from the left, if the card holder just chooses to leave the store entirely, they get a payoff of 3. The manager knows they just lost a customer (and probably lost them for a few weeks due to the negative experience), so they get a payoff of -2.

Moving to the right side, let’s say the managers have the chance to fix the register, or to not fix it. The card holder has already left the store, so they don’t know if the register is fixed or not, represented by the circle at their decision node.

(Card- Go Get Money – Fix – Return) (-4, 3 ) If the registers are fixed and the customer returns with cash, they are infuriated. They wasted time, gas, and money, only to have the register fixed when they return – they could have just waited it out and used their card. They get a payoff of -4. The manager is happy that they are back and with money (but not so happy that the customer is angry) so they get a payoff of 3.

(Card- Go Get Money – Fix – Leave) (1, -2) If the customer goes to get cash and doesn’t return to the store at all, they get a payoff of 1. No more waiting in line! However, still no groceries. The manager is sad that they lost a paying customer, so they get a negative payoff of -2.

(Card- Go Get Money – Do Not Fix – Return) (4, 1) If the customer returns with cash and the registers still aren’t fixed, they are ecstatic! They made the right decision to go get some cash, and now they can get their groceries too. They get a payoff of 4, still a little miffed about driving away, returning, and the cost of waiting. The manager is bummed that the registers aren’t fixed, meaning that they still have a bunch of angry customers to deal with, but they are happy that this customer returned, and that they made a sale. They get a payoff of 1.

(Card- Go Get Money – Do Not Fix – Leave) (1, -4) If the registers do not get fixed and the customer drives off without returning, they get the same payoff of 1 that they got from leaving when the registers were fixed. The customer has no idea if the registers were ever fixed, so their payoff is the same in either scenario. The manager is freaking out at this point – the registers are broken, customers are leaving and not returning, and they are losing sales. They get a payoff of -4.

Here the Subgame Perfect Nash Equilibrium is for the Manager to not fix the register, and for the customer to return. That provides the maximum payoff for each decision node. So note that: tell the Manager to not fix your card reader, go get your cash, and come back. That’s the highest relative payoff for the both of you.

Customer vs. Customer: Wait and See

Source: Author

What’s the probability that one customer will wait given that the previous customer waits? Is there a herd mentality that follows something like this, like how everyone follows that one person who crosses the street illegally? Or is this more of a separate decision-making process?

(Wait, Wait) (8, 2) Let’s say we have two customers, cleverly named Customer 1 and Customer 2, and their payoffs are represented as (Customer 1, Customer 2). Customer 1 was in line first, so they get a payoff of 8 from waiting, because they know that they will be served first. Customer 2 knows that they have to wait in addition to how long that they have already been waiting, so they only get a payoff of 2 when Customer 1 decides to wait too.

(Leave, Wait) (9, 1) When Customer 1 decides to leave, Customer 2 is now first in line and gets a payoff of 9! No more waiting around! Customer 1 is bummed that they didn’t get their groceries, but glad they don’t have to wait anymore, so they get a payoff of 1.

(Wait, Leave) (0, 1) If Customer 2 decides to leave, Customer 1 gets pretty nervous. What if everyone starts to leave, and the register never gets fixed? Also, it’s lonely now. No one to talk to. And they were already first, so it’s not like they get to move to the front. They get a payoff of 0. Customer 2 is happy to leave, but once again bummed with the whole no groceries deal. They get a payoff of 1.

(Leave, Leave) (6, 4) If both customers decide to leave, Customer 1 gets a payoff of 6 because they led the pack, but are still pretty bummed that they didn’t get their groceries. Customer 2 is bummed about the groceries, and they feel like a follower, so they get a payoff of 4.

Calculating the Mixed-Strategy Nash Equilibrium leaves us with a 4/5 probability that Customer 1 will wait and a 1/5 probability to leave. There is a 6/13 probability that Customer 2 will wait, and a 7/13 probability that they will leave. Customer 2 is about as likely as to wait as to leave, but Customer 1 is more likely to simply wait it out.

The probability that both wait? Simply multiply the probabilities that Customer 1 waits times the probability that Customer 2 waits to get 36.9%. So if you’re first in line, you’re much more likely to wait, and you get a higher payoff from doing so. If you’re second in line, the chances that you wait are pretty low – so you might as well just go ahead and leave.

Conclusion

So basically, if you don’t have cash at the grocery and the chip readers run out, make it into a game theory blog. It passes time faster 🙂

Overall, if you can convince the manager to not fix the register as you go get and cash, you will be better off. Also, try to be first in line with the card reader breaks. Most importantly, carry cash or a checkbook so you don’t have to deal with this in the first place!

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