Karthik Shashidar writes to us:
I am a regular reader of your blog, and like most of the stuff that you guys put there. Yesterday while blogging, I came across something which I thought might interest you people, hence I’m writing to you.
Recently my girlfriend and I realized that we were spending way too much time talking to and thinking about each other, and that we needed to scale down in order to give us time to do other things that we want to do. Both of us are in extremely busy jobs and hence time available for other things (including each other) is very limited, and hence the need to scale down.
I was wondering why this is not a widespread phenomenon and why more couples don’t do this “scaling down”
His analysis is here.
There is a natural force pushing couples toward too much engagement. Unilateral escalations make your partner feel good. Even if you internalize the long-run cost due to the inevitable following-suit, the slightest bit of discounting means that the equilibrium level will be above the social optimum. The usual dynamic game logic seems especially perverse here. If I am extra sweet to my sweet does she punish me for that? And what form does the punishment take, even further escalation?
Negotiating down from these heights is indeed tricky. Unilateral de-escalation is risky as Karthik discusses on his blog. The proposal could easily be read as a cold shoulder. Even assuming that both agree to scale down, how do you decide where to go? It is not easy to describe in words a precise level of interaction and this ambiguity leads to the potential for hurt feelings, if there is mis-coordination.
Some dimensions are easier to contract on. It’s easy to commit to go out only on Tuesday nights. However, text messages are impossible to count and the distortions due to overcompensation on these slippery-slope dimensions may turn out even worse than the original state of affairs.
But even setting aside all of these problems, what mechanism can you use to coordinate on a lower scale? If we both make offers and split-the-difference, then the one asking for a higher scale is going to feel hurt. Any mechanism has got to be noisy enough to hide such inequities without being totally random. The trick may be to short-circuit common knowledge. For example we could have a third party make a take-it-or-leave-it proposal and then the two partners secretly reject (if too low) or accept (if not.) The proposal is enacted only if both accept.
This ensures that when the offer is accepted, both parties learn only that each was willing to scale down to at least the same level. And when the offer is rejected, the one who was not willing to go that low will never know whether the other was, i.e. no hurt feelings.
(dinner conversation with Utku, Samson, and Hideo.)
Cheap Talk 
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November 12, 2009 at 11:29 am
Kevin Dick
There are two issues here. First, how do you scale down initially? Second, is there then a stable scaled down equilibrium? I think the first question is one of marketing.
In my experience, the utility function for romantic engagement differs over time scales. Some regions have decreasing marginal returns and others have increasing marginal returns. Moreover, the process has memory.
One could take advantage of this fact. The idea would be to simulate having to go away and reunite–like a business trip before the Internet. Many couples seem to do this fairly well.
So one partner would unilaterally proposes to “spice things up”. This signals that the partner is thinking about what is best for the relationship not to decrease overall engagement.
Some days will be “away” days where it is like the other person is far away. The only contact permitted is a good night phone call. But then other days are “reunion” days where there is, um, very concentrated contact. Alter the ratio to suit. Perhaps three away days, two reunion days, and two normal days for a few weeks. Then mix it up and have a longer away period followed by a longer reunion period.
November 16, 2009 at 7:39 pm
Relationships and the Prisoner’s Dilemma Part Deux | Pertinent Observations
[…] friends on GTalk will know that my earlier post on relationships and the prisoner’s dilemma got linked to from Cheap Talk, the only good Game Theory blog that I’m aware of. After I wrote that post, I […]
January 9, 2010 at 1:59 pm
Anonymous
Did you ever think about the following?
– There is a possibility of two types of scaling down in a relationship. The ‘physical scaling down’ which implies you scale down on the physical meetings or the ‘mental scaling down’ which implies you scale down on the cognitive or mental thinking about your partner. The discussion and analysis seems to talk about the former and completely overlook the latter which despite being intangible is more human resource consuming.
– The analysis doesn’t really substantiate relationships in the framework of a marriage or family, wherein the trade-offs, opportunity costs and decisions get much more complicated and there may be innumerable externalities acting on the decision making dynamics.