To recap the series so far, part 1 talked about economics (comparative advantage), algorithms (pursuing vs. choosing) and marketing (personalizing your message and standing out from the crowd). The second part applied simple algebra to “hack” OkCupid’s match percentage. Is there any quantitative theory that I haven’t yet mangled in the pursuit of dating advice?
Part 3 – Don’t hate the game
“Love is a game that two can play and both win by losing their heart.” – Eva Gabor
Game theory is a laughable attempt to simplify complex and uncertain human interactions to simple models in which rational actors choose from a limited set of strategies in pursuit of simple, well known payouts. The sparse triumphs of game theory have come from informing straightforward problems like nuclear disarmament and counter-terrorism. Only a maniac could think to apply game theory to the infinitely more complex problem of texting after a date.
We’ll use the simplest matrix form notation of game theory. Our games will have two players: Alice and Bob. This is by mathy convention and because threesomes are hard, not because I have anything against gay orgies. Alice and Bob have a lot of possible actions they can take at any stage of a relationship, those fall into two broad classes: actions that are beneficial to the other person (messaging, setting up a date, commitment, being a loving partner for decades) and actions that don’t and are primarily selfish. Let’s broadly call these Woo and Neglect. The actions Alice and Bob take result in outcomes for both of them, anything from the small joy of a “you’re cute” text to the heartbreaking pain of a “ur Kut” text. The outcomes are not necessarily selfish: happiness for your beloved is included. Of course, we’ll reduce all that complexity to simple numbers – each player is trying to get the best outcome, in our game – the highest number.
Let’s start with a simple game to become familiar with the notation: wooing gives 3 points to the other player. For example, wooing is simply liking the other person:
| Liking Game | Bob woos | Bob neglects |
| Alice woos | Alice gets 3 , Bob gets 3 | A: 0 , B: 3 |
| Alice neglects | A: 3 , B: 0 | A: 0 , B: 0 |
In this game, neither player has a strong incentive to do anything: wooing is costless but it doesn’t help you personally. Alice and Bob both like to be liked, but can’t do much about it.
Let’s add a wrinkle: wooing gives 3 points to the other but costs 1 point to yourself. For example, wooing is telling the other person that you like them and asking them on a date. The costs are things like losing the option to ask out someone else and the effort of planning the date.
| Dater’s Dilemma | Bob woos | Bob neglects |
| Alice woos | 2 , 2 | -1 , 3 |
| Alice neglects | 3 , -1 | 0, 0 |
We’ve ended up in a tricky situation: every player prefers to neglect regardless of the other’s choice. Whether Alice woos or neglects, Bob will always get more by neglecting. Both players prefer mutual wooing, but will end up in the bottom right mutual neglect square! This thorny predicament is the classic Prisoner’s Dilemma, in which both players’ self-interest prevents their cooperation. The prisoner’s dilemma has been extensively researched for six decades usually with the goal of finding a solution that makes both players cooperate (woo) for mutual benefit. These solutions fall into three broad classes:
- Utilizing super-rational timeless decision theory. This requires either being a super-intelligent reasoner with access to the other player’s decision-making source code, or reading a 120-page PDF which seems a lot harder.
- Enforcing a cooperation contract. If the Alice and Bob can remove each other’s “neglect” option, they end up in woo/woo for lack of alternative. Common ways to try and achieve this are entering into holy matrimony or, for those that are really serious, changing your status on Facebook. This is slightly less arduous than reading a long PDF, but may still not work for everybody.
- Playing the “game” several times and rewarding the other player’s “woos” by using a tit-for-tat strategy.
The simplest example of tit-for-tat is a promise to keep wooing as long as the other person does. Instead of analyzing a series of games we can fold that incentive into the outcomes of a single game. If mutual-wooing is rewarded, it gives an extra 3 points to yourself because you’ll partner will woo in the next round. Let’s see how the game looks like with 3 points for each player added to the woo/woo square:
| Stag Hunt | Bob woos | Bob neglects |
| Alice woos | 5 , 5 | -1 , 3 |
| Alice neglects | 3 , -1 | 0, 0 |
This game is called the Stag Hunt (the name comes from a scenario in which two hunters must cooperate to hunt a stag, not from a scenario where the hunters meet for a stag party). The new scenario changed an adversarial game into a game of cooperation: each player does best by matching what the other player does. If Alice woos, Bob gets an extra 2 points (5 instead of 3) from reciprocating the woo. If Alice neglects, Bob gains an extra 1 point by neglecting as well.
Finally, our model is telling us some interesting things. The first thing to note is that the stag hunt has a chance to end up in woo/woo only if both players get more from their wooing being reciprocated than from neglecting. For example, maybe Bob doesn’t like Alice that much, her reciprocated affection is only worth 1 points to him instead of 3.
| One-Sided Stag | Bob woos | Bob neglects |
| Alice woos | 5 , 3 | -1 , 3 |
| Alice neglects | 3 , -1 | 0, 0 |
Even though Alice still wants mutual wooing, Bob can always do at least as well for himself by neglecting. As soon as he neglects, it makes sense for Alice to do the same and the pair will end up in the bottom right neglect/neglect square. No matter how strong Alice’s feelings are, it takes two to tango. The same will happen if the rewards for neglecting are high, for example, if Alice has many suitors and wants to keep her dating options open.
Let’s go back to the original Stag Hunt. Alice tries to match Bob’s move, but what if she doesn’t know which move he’s making? Imagine the scenario: last night was Alice and Bob’s first date, pleasant but not breathtaking. Did Bob like her too? What if he did but he has other dates set up? Will he text her to ask her out again? What if someone told him that real men wait 3 days to text back? What if it was 7 days?
To account for uncertainty, Alice can look at the game probabilistically. If Alice thinks that there’s a probability P that Bob will woo her, her expected outcomes for each action are as follows:
Outcome for wooing = P x 5 + (1-P) x (-1) = 6P – 1
Outcome for neglecting = P x 3 + (1-P) x 0 = 3P
Alice will prefer wooing if 6P-1 > 3P, or in other words if P > 1/3.
This doesn’t sound so bad: as long as Bob thinks there’s a 1 in 3 chance that Alice is waiting for him and Alice thinks there’s a 1 in 3 chance he’ll eventually ask her out both players will end up in the best situation. The problem is that the threshold probability for a happily-ever-after is sensitive to even small changes in the payouts (ignore for the moment that the payouts are made up anyway).
Let’s say that Alice and Bob both read this excellent guide that makes it extremely easy for them to set up another date with a good looking stranger. Let’s assume that this gives them an extra 1 point for neglecting, since neglecting means going back to the endless well of OKCupid for a new match.
| Stag Hunt in the age of OkCupid | Bob woos (probability P) | Bob neglects (probability 1-P) |
| Alice woos | 5 , 5 | -1 , 4 |
| Alice neglects | 4 , -1 | 1 , 1 |
Alice’s outcome for wooing is still 6P-1, but now her outcome for neglecting is 3P+1. To justify wooing, she needs 3P > 2, or P > 2/3 – a much higher bar! That’s the lament in the age of OkCupid: the easier it is to get a first date, the harder it is to get to a fifth.
Personal note: a lot of people confuse this lesson with a different one, namely that the easier it is to find casual sex, the harder it is to find a lasting relationship because guys will not commit to a woman when they can sleep around for free. This strikes me as utterly false, I have never lost respect or affection for anyone because they had sex with me. Quite the opposite! The familiar trope of dating being a contest of wills in which the man wants sex and the woman wants a ring turns romance back into a prisoner’s dilemma, and prisoner’s dilemmas rarely result in lasting happiness. In online dating it may be hard to tell apart the guys that are looking for long-term relationships (high P) from those that don’t (low P), but I don’t think the guys themselves shift their preferences in response to the “market” that much.
What can Bob and Alice do to end up in the top left corner? One solution is to increase the reward for wooing, if Alice got 20 points from Bob’s affection, she would wait for his text even if she thinks it’s not likely to arrive. Whenever there’s a good game theory equilibrium to be had you know that the European pied flycatcher will take advantage of it: a sexy flycatcher male will mate with several females in different nests, the less attractive male will attract a single female by giving her his undivided attention.
Increasing your attractiveness is hard, not everyone has smooth back feathers, a skill in nest construction and a pitch-perfect mating song. There’s an easier way to win at coordination games: pre-commitment. In most cases in life you want to keep your options open, but in coordination games (and even some adversarial games) the best move is to get rid of uncertainty by getting rid of some of your options.
When I started dating in NYC I heard every possible advice regarding the post-first date text from “If you don’t text in 30 minutes to check that she made it home OK she’ll know you don’t give a shit about her” to “Anything less than a week makes you seem desperate”. The problem is, there’s no right answer that works for everyone. Some women will give up if I don’t text the same day and find someone else, and some will see it as breaking a norm if I do. Here’s what I ended up saying at the end of every first date:
I had a great time tonight, I’m going to text you tomorrow at 8 pm and if you’re into me we can set something up for next week.
Here’s the game theory translation:
I commit myself to playing “woo” for a day, so if you want to coordinate you can play “woo” without being afraid of uncertainty. Since you know exactly when to expect my text, if I don’t hear back from you tomorrow I’ll see that as a clear signal that you’re playing “neglect” and accordingly will switch to “neglect” from that point on.
Both of us have a day to decide if we like each other, but I have eliminated any chance of our relationship failing because of unpredictability and bad coordination. It felt a little awkward the first time I did it, but the real awkwardness is stressing for days over what should be simple and fun – telling someone you like them. Ladies, there’s nothing at all about this strategy that wouldn’t work equally well for you.
This week a girl who saw my profile on OkCupid read this blog, so we had no choice but to have lunch to discuss romantic game theory for three hours. She said that she always texts within 24 hours if she doesn’t hear from the guy first. If the guy doesn’t like her, she just saved herself time. If the guy was just shy, she helped him out. And if the guy doesn’t like girls texting him first, he’s not the man for her anyway.
There’s a general theme that cooperating with a partner is much easier than overpowering an opponent. In the end, everyone in your dating pool has the same goals, every interaction from message to marriage should be seen as an opportunity to coordinate. Yet, a lot of the dating advice you read treats it as antagonistic competition, advising you to look for an edge and keep your cards close to your chest. Next week I’ll explore a different foundation to build romance on: total honesty, total openness, total vulnerability. And BDSM.
PUTANUMONIT 
Some time ago you mentioned that the one who asks the best partner out, then the second best, etc. will end up with the best possible outcome, whereas the one who waits for other people to ask gets the worst. How is this proved?
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LMGTFY: See page 11 here (theorem 1.2.2 and 1.2.3).
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This was very interesting if a bit abstracted.
So say you message a bunch of people, you get three messages back. You schedule three dates, and they end up going well enough that all three of them would like a second date with you. What do you do then?
Or suppose you take the strategy of just dating people one at a time. When do you stop and decide to commit to one person?
I guess more generally I’m asking – how does pre-commitment solve the problem of buyer’s remorse? (which is the pitfall of many internet relationships due to the wide selection – not that I have numbers)
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To your second question: Under some circumstances, you can reject the first n/2.718… people and take the first person who’s better than all of the rejected ones. Or the last, if you’re unfortunate. Picks the best person 1/2.718… of the time.
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I’m glad you asked!
One date is probably not enough information, so you should see the ones you like a couple more times. And then… you do a decision matrix to figure out which one you’ll have the best relationship with. Yes, it sounds like the dumbest idea ever, which is why it’s going to be the last post in the dating series :)
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I may be going into more detail on some subjects touched upon in this essay then you went into. I may be reiterating the same thing in different ways. It may contradict some of what you said. I don’t know these things. I’m not trying to correct you or speak for you. I am exploring these issues more and in a way that makes sense to me. I am posting because others may find my diversion valuable. The purpose of this paragraph is to clearly state my purpose here and my thoughts on how this essay relates to yours.
You touch on a point in this article that I find intriguing. If coordination is better than competition then why is there so much advice dealing with dating as a competition? I might take issue with the claim to frequency: we might read different parts of the internet or I may be misunderstanding you when you say “a lot” but I have encountered more dating advice that basically comes down to “communicate more and better” while often giving strategies for doing so than I encounter advice along the lines of “how to trick members of your preferred gender into doing things they are loath to do.” I will not deny that there is “a lot” of the latter advice but there is also “a lot” of the former. I also won’t deny that there are sub-cultures in which the latter is more often repeated. However, without doing a survey (and thus with no reliability), I think the former is more common than the later.
A root question I have is “is there anyone for which it is advantageous to adopt a competitive strategy to dating as opposed to a cooperative one?” There answer I come up with is: at most for a quite small number of people.
You bring up and dismiss a framework for dating: that all men want nothing but sex and all women want nothing but marriage. If this were an accurate description of our species then a competitive dating strategy may seem like it is more advantageous. After all a man interacting with a woman would want to get as much sex and as little marriage out of the interaction as possible while a woman interacting with a man would do the opposite. Since their interests don’t align a strategy that maximizes one’s own goals at the expense of the other would be the best strategy.
Even in this situation, a cooperative strategy tends to give better results than a competitive strategy. If the man and women would openly and honestly talk about their desires and goals for the relationship and engage in a mutually respectful negotiation about how much sex and marriage to have then they are following a cooperative strategy and will come to an equilibrium. If the man and women rather try and gain as much of their preferred activity and as little of the other as possible without their partners assent or even knowledge then they are following a competence strategy and will come to an equilibrium.
The cooperative strategy favors the better negotiator while the completive strategy favors the better scoundrel. Over large numbers of couples, the expected value of where on the spectrum of sex and marriage the equilibrium would be reached of trying one strategy or the other would likely be quite close to one another. The competitive strategy also in general requires greater effort and resources while the results achieved by negotiation tend to have benefits that results achieved through duplicity lack more so than the opposite. This means that only if one is significantly better at being a scoundrel then being a negotiator, would the completive strategy be advantageous.
Even in this abstracted and incorrect universe that is designed specifically to assist the cause of using a competitive dating strategy, most people would be better off using a cooperative strategy then a competitive strategy.
A more accurate but still completely wrong universe would be one in which each member of our species either (in sexual/romantic interactions) only cares about maximizing sex or maximizing marriage. This means that in any given population a percentage of both the male population and the female population would care only about maximizing sex and a percentage would only care about maximizing marriage. The important thing is that it is unlikely that in a given population these percentages would be the same even if these percentages would be the same for an arbitrarily large population.
If one is dealing with a like minded individual, it seems that cooperation would be strictly preferable over competition as both partners want the same thing (a lot of sex or a lot of marriage depending). This means that a portion of the population (the closer the percentage difference in this dichotomy between the sexes is, the larger the portion of the population would be able to do this) would be able to pair off with like minded people. There would still be a portion that, in order to get either sex or marriage, has to deal with their preference opposites. The presence of queers doesn’t change the analysis in any substantial way (sexuality queers can just pair off with like minded members of their own gender which makes the problem worse for heterosexuals and genderqueers complicate the analysis but these changes don’t effect the underlying dynamics as they relate to the original question).
In this more accurate but still unrealistic universe, the number of people who would find competition over cooperation to work better would be smaller but non-zero.
In reality, however, the purposes people have for dating don’t fall into these two categories. There are people who favor sex and find marriage distasteful and people who favor marriage and find sex distasteful for sure but there are also people who want a lot of both and people who want a little bit of both. There are all sorts of other combinations and even reasons for dating that have nothing to do with sex or marriage.
This divides people into more categories meaning people would need to mix between categories more but it also brings the categories closer together. Somebody who wants both sex and marriage is in a different category from somebody who wants marriage and doesn’t care about sex which is in a different category then someone who wants marriage and wants to avoid sex. While the person in the first and last categories have discongruent interests they both have congruent interests with the person in the middle category. The closer the categories are, the more likely it is to find someone in some category of congruent interests.
In short, the closer the categories are to each other, the better one has to be at being a scoundrel as opposed to a negotiator for a completive strategy to be advantageous. In small populations, when everyone else interested in pairing off has, there may be situations where the only options for someone wanting to have sexual/romantic interactions is to deal with someone from a distant category but this phenomenon lessens then disappears as populations get larger.
In short, there should be, at most and only in isolated populations, very few people for which a confrontational strategy for dating would be advantageous compared with a cooperative strategy. Why then, is there so much advice on how to win the competition of dating?
In answering this question I am going to take diversion to a completely different topic: breasts. For most of human history all over the world, either the size and shape of breasts had no bearing on a woman’s attractiveness or large breasts were scene as being anything from awkward and comical to ugly and repulsive and in no way viewed as sexually attractive. It is only in the 20th century that cultures developed in which large breasts became sexually desirable and an attractive feature. Prior to this, if breasts impacted beauty judgments at all, it was pertness, firmness, and shapeliness that mattered and large breasts were viewed as being detrimental to all three in general.
Despite this fact I have read and heard explanations for why men are physiologically wired to desire large breasts and I have consumed fiction set in other times and cultures in which large breasts were considered sexy. What is, in any historical sense, a particularity to a specific number of cultures and times, is being treated as universal.
The reason for this is simple: people want to think they’re normal. If I like large breasts then it must be a normal thing to like and this is better if it’s for some innate biological reason rather than because of a peculiarity of a culture or because of historical contingency therefore, the normal thing for all people attracted to women is to like large breasts because then I’ve maximized how normal I am.
What is impressive is that despite ample evidence that the fetish for large breasts is not an innate trait of humans, the cultural norm that reinforces the fetish persists for generations. There are ways a culture maintains its norms but this is a very clear example of how effective they are. Not only does culture maintain the norm in this case but it also convinces a good majority of people that the cultural norm isn’t a cultural norm but instead instinctual behavior.
There is a cultural norm that men want nothing but sex and find marriage distasteful and that woman want nothing but marriage and find sex distasteful. However this absurd notion arose, once it has become popular it is difficult to dislodge completely. There are people who actively combat this notion and these people do valuable work but given how insidious cultural norms can sometimes be, it isn’t surprising that it persists.
Given that it persists, people will buy into it and will thus address the issue as if it were true. Even then a cooperative strategy is usually better than a competitive strategy but a simple analysis of a situation in which the false norm were true would lead one to the opposite conclusion (to reiterate: men and woman are trying to get something the other doesn’t want to give up, some sort of trickery or forcing is required). To see that the cooperative strategy is likely a better one requires a nuanced thinking. Someone having the ability to come to this conclusion would, before reaching it, likely reach the conclusion that the notion is absurd and is thus not likely to present any more thought to the notion beyond demonstrating is absurdness.
Because of this we are presented with the interesting situation. People who are more likely to adhere to the incorrect structure of reality are also more likely to deal with that false reality in a sub-optimal manner. As an outside observer it is entertaining but it also leads to another conclusion: there is correlation between those likely to date with a cooperative strategy and those who are likely to treat those they date as people rather than conquests.
I like this self-sorting mechanism and don’t mind that there are guides to how to win at the competition of dating. People who would take that advice aren’t the type of people I want to date and merely by taking a competitive stance with me, they would chase me away. I don’t spend much time with them (in the context of dating) and thus am better off.
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Yep. I want a lot of sex and a lot of marriage and I like large breasts, and so do the girls I end up dating.. But this is my blog so I get to declare that this is what’s normal :)
The bad news are: the internet is big, I can’t address everybody. The good news are: the internet is big, so there are a bunch of people out there who share my values and interests. My audience for this blog is 100,000 Jacobs.
Benjamin, I think you’re close to a very interesting model of a multi-polar game with different strategy-groups in equilibrium (scoundrels, talkers, cheaters etc.) I also like the fact about big boobs being a modern invention! I see that your blog isn’t super mathy and talks mostly about other subjects, but if you want to develop those ideas a bit more rigorously I’d be happy to publish it as a guest post!
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Jacob, I thank you for the invite. You audience may be 100,000 Jacobs but the audience I have for my blog is usually 1 Ben. If others get something out of what I write then that’s great and if no one else does then that’s great as well. I also have my style as you have yours.
As far as developing my thoughts more rigorously, I will keep that in mind but I don’t have any strong ideas right now that would be appropriate for me to take a sufficiently rigorous approach. I like mathematical rigor but others are often better then me at applying it. As far as fleshing out the ideas in my essay here, I suppose I would have to actually learn me some game theory…
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How do we read the protected blog posts?
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I apologize, I didn’t think the post would be even visible. I posted it as protected so that my friend could review it. A protected post means that it will be up soon and that I still can’t fully figure out the WordPress interface.
It’s up now!
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