Why Tinder doesn't work(*) - Part 1: Nash Equilibrium and Prisoner's Dilemma

(*) mathematically speaking

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Have you ever personally used Tinder or any similarly inclined dating app? Even if we pretend we haven't (hey I'm not judging :P) most of us probably are familiar with the concept of online dating regardless.
In any case maybe you have already realized by yourself that a lot of these programs rarely seem to be able to live up to their self-proclaimed ambitions and virtues. So while I'm not insinuating that these applications are useless by any means I can't deny the impression of Tinder & Co. collectively bringing out "the worst" of human nature in both genders.
Rather than facilitating genuine interaction it promotes more than anything a culture of superficiality and reduces the -admittedly difficult- search for the desired companion (may it be casual acquaintance or soulmate) to an anonymous slot machine generating 'matches'.
While this disparity certainly offers material for analysis from the perspective of several different fields of social, biological and psychological sciences, I would like to use this article to point out an inherent and fundamental mathematical flaw of the archetypical matching system perpetuated by Tinder (Yes, sometimes even math has real-life applications).

So first of all let me preface something. This first part will revolve around general mathematical concepts rather than featuring a discussion of the conceptual issues of Tinder, but will prove essential to the point I am going to elaborate on later. So feel free to skip or cross read this if the topic doesn't concern you that much and the next part is already out.

Game Theory

Oh, you're still here? In that case...
The topic I want to introdruce originates from a discipline called game theory which is a subfield of economics or discrete mathematics depending on who you ask. Game theory is called that way because it mathematically represents strategic interactions between several parties as a virtual game between the participants. This may range from discussing actual board or card games to modelling more seminal strategic decisions such as which countries might pursue nuclear militarization or who will strike the first blow in a global thermonuclear war.

In any typical game theoretic model there is a set of players each with a (maybe player-specific) set of possible actions and a framework of rules determining the interaction of the players's actions and their outcome.
Each player also has a clear measure to quantify the desirability of the global outcome for himself which he intends to maximize. This doesn't mean any player has to be 100% egoistic as you can include a 'grade of altruism' as an influence factor in this player's measure of desirability, but mathematically any player pursues the outcome most desirable for himself.
Furthermore any player is aware of the rules, strategic possibilites of every player and the respective global outcomes but chooses his own strategy secretly and independently. So while it is possible and advisable for one party to anticipate the other's action there is no definite knowledge of what the others will do in advance. With everyone having made their decision, all chosen strategies are finally revealed and the outcome determines the individual pay-off to any player.
A game is then constituted of one or more rounds of strategizing-decision-result but the ulterior motive of any player always remains to maximize his personal 'traget function' measuring the quality of his subjective outcome.

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Nash Equilibrium

Trying to anticipate 'likely' courses of the game invariably leads to the concept of the so-called Nash equilibrium named after US mathematician John Nash who was most prominently featured in the movie 'A beautiful mind'.
An ordered set of all parties' strategic decisions is said to be in Nash equilibrium if for any individual player there in no possibility to improve the subjective outcome of the game by altering his personal strategy while all other strategies remain unchanged. To paraphrase it differently, a Nash equilibrium is a configuration of strategies in which no player has an immediate incentive to change his own because he can not expect any improvement to his pay-off if he is the only one changing his strategy.
Nash equilibria are therefore very stable states of strategic decision and if any player anticipates the others' actions correctly the chosen strategies are likely to gravitate towards those equilibria.

But why am I telling you all of this?
See the first observation is that -mathematically speaking- dating apps behave very much like a game theoretic model with a lot of players and the strategic actions 'liking/swiping right' and 'not liking/swiping right'. Of course the desired outcome in that case would correspond to find love or a suitable companion for whatever.
The second observation applicable to many real-life instances is that Nash equilibria more often than not entail collectively horrible outcomes:

• If two people can betray each other without repercussions they will instead of trusting each other
• If two countries have access to nuclear weapons both will build up an arsenal instead of demilitarizing (see Cold War)
• If there is a distinct possibility of war it's better to eagerly declare it by yourself instead of attempting diplomacy (1st World War)
• ...

The Prisoner's Dilemma

A famous example epitomizing all of this is the prisoner's dilemma:

Imagine two criminals A and B have comitted a crime and are apprehended by the police. The police lacks sufficient evidence to convict them on a principal charge so both of them are separated and put into isolation. The prosecutors offer each one a deal. If they betray their partner by testifying that the other committed the crime they are offered their freedom in exchange. Although they don't communicate with each other both correctly guess that this deal is also offered to the respective other.

• If no one testifies the prosecutors can only convict them on a minor charge and each one serves 1 month in jail
• If one testifies the crime while the other does not, the betrayer goes free while the non-testifying criminal is the sole convict and has to serve 9 months in jail
• If both testify however the police will have evidence against both of them and both are convicted to serve 6 months in jail

Putting the expected sentences for A and B in a table yields something like this:

A\B's sentence in months	B remains silent	B betrays
A remains silent	1\1	9\0
A betrays	0\9	6\6

So collectively the wisest choice for the both of them would be to not testify with a total jail sentence of 1+1=2 months and both only being implicated for a minor offence.
But unluckily this is not the Nash equilibrium of the prisoner's dilemma. Irrespective of whether one expects to be betrayed by the other betraying their partner is always more favourable for them.

• If one is not betrayed he can lower his sentence from 1 month to 0 by betraying
• If one is betrayed he can still lower his sentence from 9 months to 6 by also betraying

The Nash equilibrium and likely result of the game (if both criminals are smart enough) is therefore given by the state 'A betrays B and B betrays A'. But as suggested this is the collectively worst state with 6+6=12 months of jail time and both of them convicted for a major crime.
See of course true cleverness would involve seeing the bigger picture and realizing that pursuing the best result for both involves implicitly trusting each other. But within the game theoretic model, the only subjectively rational decision is also the one making everything worse...

So what about Tinder?

Wait, are we still not there yet? Well I did warn you I was going to discuss mathematics...

I'll have to keep you waiting a little while longer though. The next time I am going to elaborate on which game theoretic analogy applies to Tinder and how a rather skewed Nash equilibrium exacerbates already pre-existing "bad" habits in both the male and female nature when it comes to dating. (And why the 'super-like' function and related concepts actually are a step in the right direction to tackle the problem)

See you next time and stay tuned ;)

Reference for further reading:

• Game Theory