Two Person Cooperation With Repeat Play
Hume’s example  opportunity for cooperation between 2 farmers involves working
jointly to drain a marsh
Opportunity for a net benefit for each exists only if the two cooperate  there is a
cooperation dividend to be had in this two-person society if they can sructure
relationships appropriately to capture it.
Were this the entirety of the relationship between Farmer A and Farmer B, the
cooperation dividend would remain uncaptured and life for each would be slightly more
impoverished than it might have been.
Hume’s example is a self-contained situation in which there is the prospect of a
cooperation dividend in this one circumstance – one-shot deal.
Most societies  more enduring
They usually do not materialize for that one opportunity of securing a cooperation
dividend; nor do they immediately disintegrate thereafter.
This week  marsh needs draining
Next week  common fence needs patching
Week after that  2-man job of replacing a roof on one farmer’s barn
Week after that  the other’s pond needs to be selaed
Point: Most societies consist of a series of repeated (or even continuous) encounters, not
one-shot plays of a game
Fact of repetition changes things dramatically, but only if some other conditions are met
Imagine the strategic interaction in Display 1 is played not once, but twice – exactly
twice – and both farmers know it
Each farmer will know that the second play will be the last – it will be a one-shot affair
So each will play his non-cooperative strategy
Backing up to the first play then, each will realize that the first play is, in effect, the last
play, since the second play will be non-cooperative, no matter what happens in the first
So, again, each will rationally play his non-cooperative strategy
More generally, if the number of repeat plays is finite and commonly known to the
members of the society, then each encounter will be played out as though it were a oneshot affair
Repetition (in this instance) is no more than a string of one-shot games and the
cooperation dividend is lost in each case.
The idea of a known finite number of repetitions, however, is almost as artificial as the
one-shot example that we began with.
Societies are on-going and continuous  Farmers A and B may not live forever, but they
don’t know when their micro-society will come to an end.
They don’t know when the last play for a cooperation dividend will arise.
Consequently, they might as well proceed as if their society is unending.
It is this form of repeat play that allows for the capture of cooperation
dividends….sometimes.
If each assumes the string of opportunities for cooperation will be very long, each may be
willing on the first occasion to take a chance.
Worst case scenario  he gets burned, learns his lesson, and refuses to cooperate
subsequently
Given the symmetry of the situation, both may take a chance in the first encounter,
resulting in the outcome in top left cell of Display 1 – a payoff of (1,1)
Next occasion, each will remember the cooperation dividend, encouraging each to try it
again.
In short, positive reinforcement  set them on a “cooperation path” for some time
It’s the prospect for cooperation dividends (not just now) but over the long haul, that
makes cooperation moves look very attractive
This strategy of “being nice” the first time….then on each succeeding occasion doing
what the other guy did the time before is what Robert Axelrod calls the “tit-for-tat”
strategy
First time cooperate  next time cooperate if your counterpart cooperated the first time,
but don’t cooperate if he didn’t last time, and don’t cooperate again until he changes his
wicked ways.
In other words, cooperate conditionally after the first play of the game.
Only the tiniest of baby steps from observing each farmer play his tit-for-tat strategy in
the repeat play of Hume’s marsh draining game to claim the norm of reciprocity exists in
this society.
They have not internalized a moral principle (i.e., the Golden Rule), although their
behavior seems to exhibit it
Nor is the heavy hand of government making them cooperate
Instead, each of these two ruggedly individualistic, rational egoists has, by virtue of being
embedded in an on-going social relationship, found it in his self-interest to cooperate with
his counterpart.
Before we get too happy and break out the champagne  note that there is an “evil twin”
to the norm of reciprocal cooperation
If the relationship had gotten off to a bad start – one or both not being “nice” at the outset
– then tit-for-tat would echo this misfortune
At each play, each farmer will “punish” the other for failing to cooperate the time before
This social interaction would look more like a blood feud or a civil war  surely the
world is full of ethnic, tribal, racial, and interpersonal hostilities that look like tit-for-tat
gone mad!
Happier point  demonstrate that cooperation dividends may be captured as a sensible
and rational response by individuals to the circumstances in which they find themselves.
Religious or philosophical dogma, not to mention external enforcers, may well reinforce
this sort of behavior.
I believe they would have a much harder time, however, if they could not rely on the selfinterest of the cooperators.
All we (Hume) have shown is that there are circumstances in which this self-interest
exists.
Alternative Mechanisms: Inducing Cooperation
As strongly as I believe that rational responses to ongoing relationships ae responsible for
quite a lot of the cooperative dividends most of us realize I every day life, clearly there
are other alternatives  examine two briefly.
People do, in fact, internalize values that dispose them to cooperate, if only to cause them
to “be nice” in the first place so that the norm of reciprocity might develop
I don’t have much to say about why one set of moral or religious principles rather than
another is internalized by any individual
I will, however, comment, in a superficial sort of way, about the mechanism by which
such internalized principles might operate.