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.

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