Why Tinder doesn't work(*) - Part 2: The Marriage Supermarket and opportunity costs

(*) mathematically speaking

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This is a continuation of Why Tinder doesn't work(*) - Part 1: Nash Equilibrium and Prisoner's Dilemma

I still owe you a mathematically inclined explanation of Tinder's inherent flaws and therefore we return to the subject of game theory once more. The last time I used some real world examples and the prisoner's dilemma to suggest why the so-called Nash equilibrium of player strategies more often than not entails a collectively bad outcome for everyone.

This heuristics is also present in our next example which directly relates to dating:

The Marriage Supermarket

So the marriage supermarket is a game theoretic analogy which is predominantly used in economics to illustrate how in a fair market the 'market power' tends to shift towards the party offering goods with the greater scarcity. As we will see however this result is even somewhat paradoxic in that it goes beyond the supply-demand principle and shows that the Nash equilibrium of market power comes out entirely one-sided even in a slightly skewed market balance.

Let's suppose there was a supermarket exclusively open to singles which is being very generous and has a unique policy. If by any chance a man and woman meet in the supermarket and agree to get married they are rewarded 200$ per couple which they are free to split amongst each pair.
Soon however not only people legitimately falling in love but all visitors of the supermarket begin to pair up systematically to take advantage of the 200$ incentive by marrying each other. The natural question arising in the context of game theory is how much of the 200$ reward can each man or woman succesfully demand from his/her parter for the marriage consent to maximize his monetary profit. What is the Nash equilibrium and what happens in that case?
I know, mankind is so heartless...

Suppose that 10 men and women each (or any balanced number) enter the supermarket. For symmetry reasons alone it then seems very reasonable and you can show that 10 couples will form and each person should recive the 'fair' share of 100$. With even numbers we end up with a symmetric and fair Nash equilibrium.

Now we only slightly perturb our initial state and consider 10 men and 9 women entering the market. The first observation is that only 9 couples can be formed now. You might say, well some unlucky guy will end up without a girl and money but there is no reason for the 9 couples not to share equally. But there is.
Being a player in the game, the one guy being left out may now approach any of the 9 already coupled up women and offer to lower his share so say 90$, offering the woman 110$. Since the woman is another rational player, she will take the offer, leaving her former mate fo the extra 10$. Now the recently left guy is in a bit of a situation but can apply the very same strategic shift and offer his marriage consent for a 90$ share and displacing a third guy. This can be iterated by the currently single players until every woman receives a 110$ share at which point the guys would have to lower themselves to say 80$ to remain competetive...

See where this is going? The only stable configuration in which no player has an incentive to change his strategy anymore -the Nash equilibrium- is given by the girls receiving 200$ each and the guys nothing (otherwise a guy can always offer to take an even lower share). What's worse, this didn't even eliminate the original problem of one unlucky person being left out! Now one person is still left out but the rewards are maximally unevenly distributed for everyone else...

The Dating Supermarket

All of this is very much reflected in dating in general. Our above example illustrates how a slight imbalance in gender distribution shifts the influence factor towards the scarcer or less active gender, which corresponds to empirics. Game theory is consistent with the observation that women evolutionarily speaking have to be more selective than men when looking for a mate and therefore collectively trust a more reserved approach which grants them more or 'freedom of choice' in who they date or not.
Conversely the male evolutionary strategy relies on making dating a numbers game - their freedom of choice is who and how many people they decide to approach in the first place and relying on stochastics to achieve one good match. Nature has so far obviously managed to balance things out quite nicely because it is much more complex system with more boundary conditions than our mathematical model. The problem is Tinder behaving less intricately than nature and more directly like our game theory model.

Applied to online dating the original issue lies both in numerics and behavioural psychology. Even without citing scientific publications I think we can agree that men tend to be more numerous and -importantly- more active in *dating initiative* in general and when it comes to online dating in particular. (If we do not want to accept this as a universal premise we can just treat it as a conditional one or reverse gender roles if needed. The abstract mathematics only requires any imbalance in gender activity, the specifics don't really matter.)
Being the 'less desired' and more active of the genders, men soon begin to adhere to their biological predisposition when tindering, i.e. making it a numbers game. Somewhat contrary to nature however, men have little incentive not to right swipe as many potential partners as humanly possible, it literally takes only a few seconds of their time each. While in real life you would be limited by opportunity costs and restrictions such as the time it takes you to meet a suitable girl by chance, approaching her in a somewhat original or imaginative way, the common courtesy of not proclaiming interest in x different girls at the same time etc., there are no opportunity costs in online dating apart from the seconds it takes to like someone.
Conversely female users have little incentive not to be *as selective as possible*, as they are statistically being liked by a large fraction of male users anyway and they don't have anything to lose by optimizing the quality of their matches.

'So what's the issue?' you might ask.
Well the point i am trying to make is the more according to game theory a system like Tinder behaves, the more the reality of online dating approaches a very asymmetric theoretic Nash equilibrium of the system - a state in which all male users match everyone while female users wait eternally for that one perfect match.
I'm aware that we have made some generalizations but in a simplified mathematical model that very undesirable state would be the asymptotic Nash equilibrium of Tinder. So disadvantageous in fact that each player's asymptotic strategies would render the app entirely unable to generate matches and therefore obsolete.

Another problem is given by the apparently disrespectful behaviour this entails even if it is only forced upon you by strategic necessity despite your intentions. Irrespective of your inital disposition would you not be annoyed by any guy caring so little about you as a person that he didn't even bother to read your profile and only matched you because he is chasing after every girl? Likewise as a guy wouldn't you be offended by every girl caring so litte about you as a person that she discards you just because you don't fulfil her impossibly high standards?
I have exaggerated of course, but you get my point. This is the behaviour a bad system of online dating facilitates in the mutual perception.

How does Superlike help?

So in case you don't know, 'superlike' is at first sight nothing than a more prominent and visible like that is also limited to a certain number per day.
The beauty of a 'superlike' function or corresponding designs in other apps is that it tackles the inherent flaw of the system by *reintroducing opportunity costs*. Its limitation makes the superlike more special and valuable than the usual one and therefore forces a well considered use. In some sense it brings back the reality to the space of online dating without compromising its ease of use.

While implementation and monetization of those functions is always debatable it is absolutely necessary to better emulate nature either by limiting likes, sophisticated matching algorithms etc. to meaningfully connect people. Because as we saw, without some humanity the anonymous slot machine of online dating will always remain quite literally a zero-sum game.
And the only winning strategy would be not to play.