In the wake of the Nobel for the search theory of unemployment, let’s talk about the search models that really matter: hooking up.
Everybody who reads this blog understands the Prisoner’s Dilemma. Play it just once and neither side will cooperate. So a simple theory of relationships is based on a repeated Prisoner’s Dilemma. When the relationship can potentially continue, there is now an incentive to cooperate today in order to maintain cooperation in the future. Put differently, the threat of a future breakdown of cooperation enforces cooperation today.
But things get interesting when we embed this into a search and matching model. Out of the large pool of the unmatched, two singles get “matched” and they start a relationship, i.e. a repeated prisoner’s dilemma. As long as the relationship continues each decides whether to cooperate or defect and at any stage either party can break-up the relationship and go find another match.
This possibility of breaking up the match adds a new friction to relationships. The threat of a breakdown in the current relationship is not enough anymore to incentivize cooperation because that threat can be avoided by leaving. And indeed, it’s not an equilibrium anymore for relationships to work efficiently because then any partner can cheat in his current relationship and then immediately go find another partner (who, expecting cooperation, is the next sucker, etc.)
Something has to give to maintain incentives. What’s the best way to make relationships just inefficient enough to keep as much cooperation as possible? A simple solution is to “start small:” At the beginning of any relationship there is a trial phase where the level of cooperation is purposefully low, and only after both partners remain in the relationship through the trial phase do they start to get-it-, er, cooperate.
This courtship ritual is privately wasteful but socially valuable. Once I am in a relationship I am willing to wait through the trial phase because the reward of cooperation is waiting for me at the end. And once the trial phase is over I have no incentive to cheat because then I would just have to go through the trial phase again with my new partner. Equilibrium is restored.
There are a number of different spins on this idea in the literature. There was an early series of papers by Joel Watson based on a model with incomplete information. I remember really liking this paper by Lindsey, Polak, and Zeckhauser on “Free Love, Fragile Fidelity, and Forgiveness.” And this quarter, we heard David McAdams with a new perspective on things, including some conditions under which courtship can be dispensed with altogether and partners can get right down to business.
Cheap Talk 
6 comments
Comments feed for this article
October 27, 2010 at 2:03 am
jasdeephundal
Two questions: How do individual preferences decide the pace of the ramp up of cooperation and how are matches selected in the first place? What kind of signalling is involved in the matchmaking, and why are nerds like myself, though clearly highly desirable mates, so bad at this game?
October 27, 2010 at 8:41 pm
jeff
the process which places pairs in matches is exogenous, so there is no signaling. that would indeed be an interesting extension for studying the stylized fact of unmatched nerds.
October 27, 2010 at 2:30 am
temnyalov
I’m wondering how to interpret this: “At the beginning of any relationship there is a trial phase where the level of cooperation is purposefully low”.
What do you have in mind when you say cooperation is low? That the agents are mixing with a smaller probability on Cooperate initially? Or that they are actually playing a different game, where the payoffs are smaller (in particular the gain from defecting is smaller)?
To me the latter seems like a much more intuitive model. Also, the game still has the essential structure of a repeated PD and courtship will still be socially valuable. But if you go with the former and don’t change the payoffs, then finding an equilibrium strategy with an increasing mixing probability over Cooperate may be ugly…
October 27, 2010 at 3:14 pm
Frank
@Tem: I was wondering the same thing. The players decide the stakes, and starting small is part of the equilibrium.
From Watson (either of the two papers): “The partners jointly determine the stakes of their relationship and individually decide whether to cooperate with or betray each other over time.” Also… “Both papers characterize equilibrium regimes in the partnership. An equilibrium regime is a specification of (a) how the stakes change over time and (b) an equilibrium in the players’ decisions to cooperate or betray. Both papers demonstrate that cooperation between high types is viable, regardless of the players’ initial beliefs about each other, as long as the relationship starts small enough.”
October 27, 2010 at 8:40 pm
jeff
what frank said.
October 29, 2010 at 7:49 am
Alicia
Well the cost to remove yourself from a relationshiop is low early on. Dumping someone is less of a hassle then say divorce. However, early on each is purposefully engageing in cheap talk. Attempting to provide flattering yet not accurate information. The makeup, cute dress and heels of the economic model.There is a lot of cheap talk trying to determine the true intentions and value of the other.