Society has a way to break this Nash Equilibrium. It’s called marriage. Married couples do not obsess over each other 24×7.

As a matter of fact, if one is out in a restaurant and one sees various couples on various tables, one can tell if they are married or dating, based on the amount of words per minute they are using. The unmarried couples will usually talk more, unless the married couple is engaged in a fight.

Could the reduced effort a married relationship takes to maintain be an explanation for its evolution within societies?

I suggest that you split the post and separate the engine analogy and the Nash equilibrium. The Nash equilibrium conclusion is stud. The engine analogy is substandard.

Your table needs to be more rigorously defined. The quantity being represented is not readily apparent, and there’s room for confusion. Crucially, the necessary condition for Nash equilibrium, that one party can say “No matter what the other party does, I am better of doing X”, is not satisfied (in your table, a11 > a21, but a12 0)

Both taking the relationship for granted and remaining in full blast eventually lead to zero enjoyment. The first is the typical loveless (also hateless) marriage and the second is a boring “they grew old together” tale. The off-diagonals are interesting. If A doesn’t care but B dotes on A, A’s enjoyment increases, but only at a slow, decreasing rate with time. At max it saturates at 100*(1 + 1/alpha) (the alpha also takes care of the boundary condition at t=0). Even being doted on gets boring.

On the other hand, if A cares and B doesn’t, A’s life gets more hellish by the moment, and at an increasing rate to boot.

It would also be interesting to see how the table would vary in an iterated version. In fact, regular relationships are like that. One party devotes less to the relationship temporarily for some reason or the other – say work constraints or a hot secretary – but then he sees the error of his ways and comes back, and there’s a decision to be made again. We then need to start running a monte-carlo algorithm, but tit-for-tat-with-forgiveness has been found to be a reasonably consistent ‘good’ strategy for the classic iterated PD. “Be forgiving by know your limits” – Surprise surprise!
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Your table needs to be more rigorously defined. The quantity being represented is not readily apparent, and there’s room for confusion. Crucially, the necessary condition for Nash equilibrium, that one party can say “No matter what the other party does, I am better of doing X”, is not satisfied (in your table, a11 > a21, but a12 a21 and a12 > a22.

It is also interesting to think how this table varies with time. I think the dependence would be (with the same columns and rows) :

-50*exp(-t) 100*(1 + 1/alpha – 1/(t+alpha))
-100*exp(t) -10*exp(-t)

(alpha > 0)

Both taking the relationship for granted and remaining in full blast eventually lead to zero enjoyment. The first is the typical loveless (also hateless) marriage and the second is a boring “they grew old together” tale. The off-diagonals are interesting. If A doesn’t care but B dotes on A, A’s enjoyment increases, but only at a slow, decreasing rate with time. At max it saturates at 100*(1 + 1/alpha) (the alpha also takes care of the boundary condition at t=0). Even being doted on gets boring.

On the other hand, if A cares and B doesn’t, A’s life gets more hellish by the moment, and at an increasing rate to boot.

It would also be interesting to see how the table would vary in an iterated version. In fact, regular relationships are like that. One party devotes less to the relationship temporarily for some reason or the other – say work constraints or a hot secretary – but then he sees the error of his ways and comes back, and there’s a decision to be made again. We then need to start running a monte-carlo algorithm, but tit-for-tat-with-forgiveness has been found to be a reasonably consistent ‘good’ strategy for the classic iterated PD. “Be forgiving by know your limits” – Surprise surprise!

Also, both parties scaling down is less enjoyable but a compromise, in which case its payoff should be lesser than both parties scaling up.

You are assuming that scaling up = work = more effort = pointless = -ve payoff. This is suspect, because work in this case is not boring work, hence not painful.