Relationships and Prisoner’s Dilemma

So I ws thinking about this car analogy for relationships. I was thinking about how when you start your car, you will need to drive in first gear, with full engine power, slowly releasing the clutch, using a lot of fuel. However, after you have gathered certain speed, it is wasteful and unstable to go on in first gear. It is time for you to take your foot off the gas pedal, hold down the clutch and change gears, and shift the car to lower engine power.

I think it is similar with romantic relationships. Once you’ve reached a certain level and gotten past the initial phase, it is wasteful to continue in the same full throttle. Once both of you understand that the other is firmly in the basket, there is no need to waste much time just assuring and reassuring each other of the other’s presence. It is simply a wastage of fuel. Also, if there is too much torque at too much speed, there is a good chance that the car will spin out of control, so that needs to be avoided.

A relationship is like a car with two control systems. It is important that both of you coordinate the gear change, else there is a danger that the axle might snap. Let us move out of the analogy for the rest of the post.

So there are two of you and both of you have the choice of whether to change gear or not. Now, the ideal thing to do would be to change gears together, since that will ensure the relationship is at the same level but you’ll both be spending lesser energy on it. The worst case is if exactly one of you changes gears. If one of you suddenly slows down while the other is still at full throttle, it is likely that the other will suddenly feel insecure that the one has stopped responding, and this is likely to lead to some sort of breakdown in the relationship, even if temporary. And in order to get things back on track, you’ll need to go full throttle, thus leading to wastage of energy.

So basically, exactly one party deciding to scale down can prove to be disastrous for both of them, because of which the dominant strategy is to stay where you are – at full power. Let me draw the 2 by 2.

———————————————————————

|                        |    Scale down           |  Remain at full blast     |

———————————————————————

| Scale down|    0                               |  -100                                  |

———————————————————————

|Remain at   |  – 100                         |  -50 |

| full blast     |                                      |                                              |

——————————————————————–

You will notice that the players start off at a Nash equilibrium! Of both of them remaining at full blast. And thus neither has the incentive to scale down, unless he/she is sure that the other will also scale down simultaneously! And if the couple is not communicative enough, they will continue in this suboptimal state for too long, and end up burning way too much energy and willpower, which could’ve been otherwise put to good use.

Hence it is important that the couple communicates about matters such as these, and coordinates the shift in gears, and saves valuable energy!

8 thoughts on “Relationships and Prisoner’s Dilemma”

  1. To extend the metaphor… some relationships are in cruise control for too long and suffer from the mediocrity of the routine too. Coordinated shifts in gears – even down-shifting sometimes – may be highly recommended! 😉

  2. Hmm. I get your overall point. However, ‘scaling up’ by both parties is also enjoyable, so I’m not sure why the payoff is -50. Its like doing enjoyable work, which can’t be called work anymore.

    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.

  3. 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 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!

  4. Here’s my full comment:

    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!

  5. Wimpy,

    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?

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