Bargaining is the process of two (or more) parties attempting to agree on the price for a transaction. Game theoretic approaches attempt to find two strategies from which neither party is motivated to deviate. These strategies are said to be in equilibrium with one another. The equilibriums available in bargaining depend on the the transaction mechanism and the information of the parties. Discounting (how long parties are willing to wait) has a significant effect in this process. This episode discusses some of the choices Kyle and Linh Da made in deciding what offer to make on a house.
Data Skeptic
[MINI] Bargaining
[music] Data skeptic mini-episodes provide high-level descriptions of key concepts related to data science and skepticism. Our topic for today is bargaining. [music] So Linda, we've got some news, huh? We have some news that is about to drop. We made an offer on a house. We did more than that. We made three offers on three houses. No, two offers on two houses. You don't even know how many offers we made. Wow. Two offers on two houses and one of them. One of them got back to us. Yeah. So we are in first place for this house. It seems like it's basically a done deal. So I want everyone to know the Data Skeptic Home Sales Project will live on, regardless of us completing this transaction. There's a lot more work to be done, so if there's any volunteers come join our Slack channel. I've got some big announcements coming about that down the road. We're actually going to do some episodes featuring the whole process of constructing a data product, I think. I wanted to ask you an important question about the house. Are you happy? I don't know. We're about to spend a lot of money in the house and you don't know if you're happy or not. We'll find out once we move in. Once I start commuting to work, it's far from work. Yeah. It's not on the West Side at all. It's not even West Side adjacent. So how come we decided to make an offer? Why didn't we wait for a different house? We just thought it was good enough. Good enough. What could we have done if we didn't want to try and close this house? Not made an offer. And what would we have done then instead? Look for another house. Yeah. And maybe made an offer there. Now these people, they made a counter offer that was slightly different, right? But we could have been like unacceptable. We counter your counter, right? We could have gone back and forth. Or the first property we did. We offered an amount, they asked for a different amount. But you've said to me a couple of times that there is a value to being done with this process, right? How much time do you invest in a weekly basis looking at properties? Oh, it depends. Going to open houses. So I've been using Redfin and they send me automated emails. They're pretty good about that. Yeah, that one's okay. Then I also search on my own and then I start making a list about where the houses are. Then I start working with people to schedule an in-person. A lot of time. And then anyone that I'm interested in, Redfin emails me when they have a pending sale. So I take them off my list. So there's a cost to all that, right? There's our time. And then when we go to put in an offer, so we want to minimize the price and they want to maximize the price. Sure, sure. And why don't we just pay their maximum price and be done with it? Well, I think on this occasion, we thought that they would accept if we offered a little bit more. Yeah, we were strategic. But at a previous house, we offered less than the asking price, right? Yeah. Why didn't we just offer 50,000 more than the asking price? We don't have that money. Well, I mean, there's another property in which we could have done that, right? Or we could have offered 10,000 more. We don't have that. Oh, 10,000 more? Yeah. Well, it's more a question whether we think it's worth it. There's a couple of points here. The first point I want to make is about discounting that a dollar today is better than a dollar tomorrow. That you giving, that me receiving a dollar? Yeah. Today's, yeah. I mean, actually, it's kind of irrelevant because between now and tomorrow, you're not going to run it and put it in a savings account or anything. But maybe another way to put this is if I offered you $100 tomorrow for something, or I said you can get $200 three days later, that's a way better deal, right? You'll wait the three days. I will. Yeah. In your head, you have something that's called discounting. What if I offered you $100 tomorrow or $1,000 in 20 years? 20 years. Yeah. Oh, I would definitely take tomorrow because 20 years, I don't know where I'm going to be. Did we offer the maximum we could have offered? No. We offered what we thought was right, correct? Yes. Actually, we offered a little lower. Yeah, I mean, I think we thought our maximum was higher. But we were like, man, let's just put on our first offer and see. Why do we do that? Why didn't we just go to the max? Well, because we had a feeling that someone was going to counter, then we're going to have to raise it. So we just put in some buffer. Yep. I'm going to talk about the Rubenstein bargaining model, which is this, it comes from this aerial Rubenstein guy. He wrote these classic papers and I think the 80s that I read a long time ago that are really good. So first of all, the buyers, we have our valuation, right? We decided what we thought the house was worth. That's called our private valuation because we didn't tell the seller, right? Yeah. And then presumably it was worth less, well, actually, in this case, maybe not. But if we think it's worth less than what the seller thinks, then there's no point in talking to him. If we think it's worth $1 and he's like, I would never sell this for less than $2, then there's no point in even having a conversation. But if the seller will let go of it for a price below what we would pay for it, then there's an opportunity for a transaction. Okay. So what if there's a big difference? What if we say, oh, this house is worth $2 and the seller says, I actually privately think the house is only worth $1. Well, great. We're both going to come out of this happy, right? He's going to get at least his value and we're going to get at least our value. But how do we decide how to split the difference? I don't know. Just split down the middle. Well, that's when people start saying something that is different than what they actually value. Yeah, and talk is cheap and talk doesn't matter and all these things. So we make a series of offers back and forth and that's what this Rubenstein bargaining model is all about. There are a couple of cases. There's complete information games where we know the seller's value and the seller knows our value and it's known common knowledge that we both know these things. I know that you know it and you know that I know that they know it and that sort of thing. In the case of common knowledge, there's one obvious solution. There's what's called an equilibria strategy that's based on each of our discounts. So whoever is willing to wait the longest for their money, they actually have a little bit of an advantage and more or less you give more of that pie to the person who will wait the longest. You made a pie recently, right? Last weekend you want to talk about it? Oh, that was a carrot cake. Yeah. I also made pumpkin zucchini bread. Oh, so I guess pie didn't describe either of those things. But the cake was around, right? Yes. So imagine that you have the most basic way. You're like the round one. I had just planned out my head. I didn't use the wrong word. It was called a carrot cake. Yes, you had a carrot cake. Now the carrot cake, let's think of that as the difference. You have a cake and you want to share it and everyone wants to eat it. There's definitely cake here that is like, you know, there's room for a transaction to happen. The question is how do we divide up that pie, that cake, evenly between us? And in the case of common knowledge where each of us knows how much the other likes the cake, there's a pretty obvious solution. When it becomes interesting is when there's an incomplete information game. That means that one of the parties doesn't know the value of the other party. So maybe the seller knows what it's worth because he had it appraised. But he doesn't know our valuation. So he has to have a belief about it, like maybe he believes it's small or large. But there's a probability distribution that can describe his belief. A probability distribution. Yep. That's someone made. Like, do you think there's any possibility that the seller believed we thought the house was worth double what we offered for it? No. Yeah, obviously not. What about half? Half the price of what it's currently listed. Yeah. No. Well, I think I may be phrasing it. We put the offer in. Yeah. We put it in way above half because that would be an insulting offer. So somewhere between half and double is our valuation. And the seller doesn't know where exactly. But he can have a belief about it. The back and forth steps of negotiation come down in the Rubenstein model to trying to ascertain the private information of the other person through a series of offers that ultimately come down to this discounting. How long either person can wait? Wait for what? Wait for a close of this transaction. Wait to come to agreement. Because we could sell the property. Yeah. We could always quit early and be like, all right, fine. We just agree to whatever price you say. But we might hold out for a better price. Okay. So we saw the house on Saturday via private appointment and decided we were going to put an offer in probably that day or the next day. Yep. Then I went online and I saw there was an open house scheduled the following day. So we saw the house on Saturday. The open house is scheduled on Sunday from 1 p.m. to 4 p.m. And then we decided, well, we don't want to put an offer so that the entire open house, they will say and brag, like, we have an offer and it's above asking price. Because then that wouldn't mean that they will definitely submit. Anyone who wants an offer or wants to buy the house will submit it above asking price. That's fast, right? And they may even bump it up like way more than what we haven't valued at. So we were like, no, they should go into open house without any offers. Right. So that we can get it for the lowest price possible. So we waited, we signed the contract. And then we sent the offer 30 minutes after the open house closed. And then we also put a time box and said they have to reply within 24 hours. Yeah. So that any offers that come in would have had to come in between now and 24 hours. And we'll have to see what they would probably receive. Like, is it ad? Is it above? And at that case, would they just, if it was at or around the same value, like within $1,000 of hours, would you just go to the first person? I don't know, maybe. Yeah, we don't know exactly what they would do there. But I'm glad you described it exactly like that. Because I think our strategy was pretty good. We had this action. I'm going to analyze it for you the way a game theorist might hear. We had this action of placing an offer and engaging in negotiation. And had we done that sooner, we would have given some power to the seller. Because the seller, like you said, could have told everybody at the open house. Like, oh, we already have an offer. This is basically wrapped up. If you want it, you got to come in strong. But we robbed them of that opportunity by holding back our offer and then making it with this short window. So the discount was very high. They have to respond quickly. And if any other offers come in, they might come in slow. And those people would have to come around with their offer very quickly because we gave only a day. So we gave a somewhat high offer. Right. We went into a little over asking not much, though, as a way of signaling. That's a part that's called signaling. You're saying, hey, we're trying to shut down your process. Because we would have given you what you ask. We're going to give you more than that. But you have to say yes, almost immediately. So we blocked other sellers. That was kind of like an attack. That's our strategy. And it seems like it worked. Or was it luck? Well, that's a good question too. So in a sequential repeated game like this, we'll have to see after we buy several more houses and take a measurement. But yeah, what if we had offered just one dollar less or something? I don't know. I wanted to cover just this Rubenstein model. I know we didn't get deeply into the equilibrium of that game. But I think the important part to learn is that bargaining is a sequential game. When there's incomplete information, we have to represent that as a probability distribution we have over the beliefs of the other. And the Rubenstein model has been solved for complete information games and one sided incomplete information games. That's where one seller knows has common knowledge of each values, but the other side does not. The case where the actual like real world case, where we don't know the seller's true valuation and the seller does know our true valuation, that would be called two sided incomplete information games. And I don't think there are any equilibrium solutions for that. So there isn't necessarily one known perfect way of engaging in these types of bittings. So it would be wrong of me to claim we had the best strategy, because we can't know for sure. But we did get the house, so that's pretty cool. Well, we haven't signed anything yet. So my question is, do data scientists use this? Oh, great question. So I just did, right? Did you do anything with it? I did a lot of strategizing. Remember, I was talking to the lady and I figured out that thing about the open house. So you're doing like game theory? Yeah. So this is game theory. That's right. Whatever you hear me talk about equilibria, that's game theory. And in your fair, game theory doesn't necessarily overlap that much with data science, but it can. And it doesn't some cases. So the most common way is in auctions. Not just like eBay, but actually the most interesting auction, the one I worked on for a number of years, indirectly I worked on it, is the ad auction networks. So there's two basic kinds. I worked on search engine marketing, SEM, but there's also real time bidding auctions. And they have all these different interesting mechanisms, like first order and second order auctions that have different equilibria solutions. So like in the online space, it uses this thing called the victory auction, where you pay the second price, which is actually a good mini episode for another day. To answer your question, do data scientists use this? They do definitely an ad tech. So people working on placing ads and bidding on ads, auction stuff is huge there, and it uses the bargaining model. But I think there's also probably some other areas I'm not thinking of. And it's worth a good data scientist looking at bargaining, because I think there's a lot of interesting overlaps here between how machine learning models use decision boundaries, and how they use these piecewise linear convex solutions in a lot of these problems. So I think data scientists could also learn a lot. They might bring home to other applications from looking at some game theory stuff once in a while. Well, as always, Lindy, thanks for joining me. Thanks for joining me. Can you imagine very soon they'll be recorded from the new data skeptics studio? Well, I think you'll have to renovate that studio. Yeah, we're going to have a nice studio. That's pretty cool. And last bird noise is probably for those who complain about the bird noises on some episodes. What do you mean Yoshi will still be here? Yoshi's going to get her own podcast soon. No. Yeah, I think that would be awesome. She doesn't have much to say. She says I love you. She shakes like that. Anyway, until next time, I just want to remind everyone to keep thinking skeptically of and with data. More on this episode visit data skeptic.com. If you enjoyed the show, please give us a review on iTunes or Stitcher. (beeping)