INTERVIEW WITH ROBERT AUMANN
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did you vote? Ninety percent of the people in the sample said yes; in fact, only
sixty-eight percent of the electorate voted.
H: It calls into question what we learn from polls.
A: It sheds a tremendous amount of doubt; and it shows something even more
basic. Namely, that when people answer questions in a poll, they try to guess what
it is that the questioner wants to hear. They give that answer rather than the true
answer; and again, this is not something that they do consciously.
That is another example of rule rationality. I am not saying that people do this
because there is something in it for them. They do it because they have a general
rule: try to please the people to whom you are talking; usually they can help you. If
you are unpleasant to them it is usually not to your good. So people subconsciously
develop tools to be pleasant and being pleasant means giving the answer that’s
expected.
H: What you are saying is that one should evaluate actions not on a decision-
by-decision basis, but over the long run. Also, one has to take into account that
we cannot make precise computations and evaluate every decision. We need to
develop rules that are relatively simple and applicable in many situations. Once
we take into account this cost of computation, it is clear that a rule that is relatively
simple, but gives a good answer in many situations, is better than a rule that
requires you to go to extreme lengths to find the right answer for every decision.
A: That’s the reason for it. You are giving the fundamental reason why people
develop rules rather than optimize each act. It is simply too expensive.
H: Kahneman and Tversky say that there are a lot of heuristics that people use,
and biases, and that these biases are not random, but systematic. What you are
saying is, yes, systematic biases occur because if you look at the level of the rule,
rules indeed are systematic; they lead to biases since they are not optimal for each
individual act. Systematic biases fit rule rationality very well.
A: That’s a good way of putting it. If you look at those systematic biases
carefully you may well find that they are rule optimal. In most situations that
people encounter, those systematic biases are a short way of doing the right thing.
H: This connects to another area in which you are involved quite a lot lately,
namely, biology and evolutionary ecology. Do you want to say something about
that?
A: The connection of evolution to game theory has been one of the most
profound developments of the last thirty or forty years. It is one of the major de-
velopments since the big economic contributions of the sixties, which were mainly
in cooperative game theory. It actually predates the explosion of noncooperative
game theory of the eighties and nineties.
It turns out that there is a very, very strong connection between population
equilibrium and Nash equilibrium—strategic equilibrium—in games. The same
mathematical formulae appear in both contexts, but they have totally different
interpretations. In the strategic, game-theoretic interpretation there are players
and strategies, pure and mixed. In the two-player case, for every pair of strategies,
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each player has a payoff, and there is a strategic equilibrium. In the evolutionary
context, the players are replaced by populations, the strategies by genes, the
probabilities in the mixed strategies by population proportions, and the payoffs by
what is called fitness, which is a propensity to have offspring. You could have a
population of flowers and a population of bees. There could be a gene for having
a long nectar tube in the flowers and a gene for a long proboscis in the bees.
Then, when those two meet, it is good for the flower and good for the bee. The
bee is able to drink the nectar and so flits from flower to flower and pollinates
them.
What does that mean, “good”? It means that both the flowers and the bees will
have more offspring. The situation is in equilibrium if the proportions of genes of
each kind in both populations are maintained. This turns out to be formally the
same as strategic equilibrium in the corresponding game.
This development has had a tremendous influence on game theory, on biology,
and on economic theory. It’s a way of thinking of games that transcends biology;
it’s a way of thinking of what people do as traits of behavior, which survive, or get
wiped out, just like in biology. It’s not a question of conscious choice. Whereas
the usual, older interpretation of Nash equilibrium is one of conscious choice,
conscious maximization. This ties in with what we were saying before, about
rule rationality being a better interpretation of game-theoretic concepts than act
rationality.
H: Perhaps it is time now to ask, what is game theory?
A: Game theory is the study of interactions from a rational viewpoint. Even
though the rationality does not have to be conscious, it is still there in the back-
ground. So we are interpreting what we see in the world from a rational viewpoint.
In other words, we ask, what is best for people to do when there are other
people, other decision makers, other entities who also optimize their decisions?
Game theory is optimal decision making in the presence of others with different
objectives.
H: And where everyone’s decision influences everyone’s outcomes. One takes
into account that everyone is doing his own optimization and everyone is trying
to advance his own objectives.
Game theory started formally with the von Neumann and Morgenstern book
in the 1940s. Probably the war had a lot to do with the fact that many people
got interested. Just to see how it developed, in the first international game theory
workshop in 1965 in Jerusalem there were seventeen people.
A: There were three conferences on game theory in Princeton in the fifties: ’53,
’55, and ’57. Those were attended by more than seventeen people. The seventeen
people in 1965 were seventeen selected people.
H: The discipline has really grown—from a few dozen people in the fifties and
sixties, to more than six hundred at the last game theory congress in Marseille.
This is a good point to discuss the universality of game theory. In the Preface to
the first volume of the Handbook of Game Theory [iv] we wrote that game theory
may be viewed as a sort of umbrella or unified field theory.