Game Theory inRelationship Dynamics
Two mathematicians built a compatibility test on John Nash's idea of equilibrium and a repeated version of the prisoner's dilemma. The math is old; what it says about texting is not.
Bever and Rowlett (2013) set out to build a compatibility test with actual mathematics behind it. They used two tools from game theory: Nash equilibrium, and a repeated prisoner's dilemma they call the iterated dating dilemma. Neither needs equations to be useful.
Key takeaways
- A Nash equilibrium is a stable arrangement: neither partner can do better by changing what they do alone. Stable is not the same as happy.
- The test is taken separately by each partner, which makes it hard for one person to steer the result. It measures balance of power and satisfaction, not love.
- In the iterated dating dilemma you can affect your partner's happiness by what you do, but you cannot unilaterally control your own. Mutual cooperation is the only strategy that wins over time.
- Recent history drives decisions more than the distant past. A bad month changes the game; a bad week usually does not.
Nash equilibrium, in plain words
A Nash equilibrium is a situation in which each person is doing the best they can given what the other is doing, so nobody gains by changing alone. A couple where one always texts first and the other always replies late is one. Neither can improve things by themselves: if the initiator stops, the conversation stops; if the responder speeds up, nothing else changes. It is stable, and it can still be miserable.
"We have created a compatibility test based on sound mathematical principles and John Nash's notion of equilibrium strategy. The test must be taken separately by both partners, making it difficult for either partner alone to control the outcome."— Bever & Rowlett, Love Games: A Game Theory Approach to Compatibility
The test asks each partner, separately, about the balance of power in the relationship and how satisfied they are with their life choices and activities together. Answering apart matters: it means neither partner can tune the result. The point is to find out whether the current arrangement is an equilibrium both people can live with, or a stable one that only one person chose.
The iterated dating dilemma
The second tool is a repeated prisoner's dilemma. In one round, each partner chooses whether to give (time, effort, a real reply) or hold back. Give when they hold back and you feel used; hold back when they give and you feel briefly in control; both hold back and the relationship goes quiet. The catch is repetition: you will play again tomorrow, and both of you remember.
Two results fall out. You can move your partner's happiness by what you choose, but you cannot unilaterally control your own; it depends on what they do. And because memory is finite and recent, the last few rounds weigh more than the whole history. Over many rounds, the only strategy that keeps both people's payoffs high is mutual cooperation.
What this looks like in a text thread
Initiation
Who starts conversations is the clearest equilibrium in most chats. If it is 80/20, ask whether that is a division of labour you both chose or one you drifted into. MosaicChats counts it for each person, which is more reliable than either partner's memory.
Effort matching
Reply length and question-asking are the give-and-take rounds. One-word replies to paragraphs are a hold-back move, and the other person will read them as one, whatever you meant.
Recent history
The model says the last few rounds dominate. So does experience: a bad week of terse replies during a work crunch is noise; a slow drift over two months is the game changing. A week-by-week tone timeline separates the two.
What to do with it
- Cooperate first, visibly. In a repeated game the way out of a hold-back equilibrium is one partner giving without being asked, and saying so.
- Do not keep a permanent ledger. Recent history matters more than the distant past, in the math and in practice. Relitigating last year's rounds does not change today's.
- Make the equilibrium explicit. "I notice I usually text first. Is that fine with you?" is the entire compatibility test in one sentence.
- Check the balance of power, not just the satisfaction. A relationship can score high on contentment and still have one person setting every term. The test measures both for a reason. Gottman's finding that accepting influence from a partner predicts stability is the same point from the other direction.
See who is carrying the conversation
MosaicChats shows who initiates, how reply lengths and times compare, and how the tone has moved week by week, so you can see the equilibrium you are actually in.
Analyze your chatFrequently asked questions
What does game theory have to do with relationships?
Game theory studies choices where your outcome depends on what someone else chooses, which describes every relationship. Bever and Rowlett (2013) used it to build a compatibility test based on Nash equilibrium and a repeated prisoner's dilemma they call the iterated dating dilemma.
What is a Nash equilibrium in a relationship?
An arrangement where neither partner can improve their situation by changing their behaviour alone. Always texting first while the other always replies late is one. It is stable, but stability is not the same as both people being happy.
Can a test really measure compatibility?
It can measure specific things: whether one partner dominates, and how satisfied each is with the life they share. Taking it separately stops either partner from steering the result. It does not measure attraction or love, and the authors do not claim it does.
Is keeping score in a relationship bad?
Keeping a permanent ledger is. The iterated dating dilemma shows recent rounds matter most and that mutual cooperation is the only strategy that keeps both partners' payoffs high. Noticing an imbalance and naming it is useful; holding last year against someone is not.
Related reading
References & Sources
- Bever, K., & Rowlett, J. (2013). Love games: A game theory approach to compatibility. arXiv, 1312.5483. Source