Emeritus Professor of
University College London, UK
Excerpt from Ken Binmore's
example(s) from your work (or the work of others)
illustrates the use of game theory for foundational studies
important application of game theory is to economics.
Economists only began to grasp its potential in the late
1970s and early 1980s, but it has now totally conquered
economic theory. Its most spectacular application within
economics has been to the design of auctions. My own
involvement came in 2000 when the British telecom auction I
was responsible for designing made a total of $35 billion.
After the auction, Newsweek magazine described me as
the “ruthless, poker-playing economist” who destroyed the
telecom industry, but I notice that the telecom industry
doesn’t seem to be destroyed at all.
design is a branch of the more general subject of mechanism
design. In this context, a mechanism refers to the rules of
a game invented by a government or other agency that has the
power to make sure that the rules are enforced. The problem
for a government is that the players in the game it invents
often know more about the world than the government itself.
For example, the companies who might buy licenses to operate
certain telecom frequencies are obviously in a better
position to value the licenses than the government who is
selling them. In such situations, the government needs to
delegate certain decisions to the players rather than to
take them itself. For example, the government will do better
by running some kind of auction than simply offering the
licenses for sale at a fixed price. But the problem in
delegating some decisions to the players is that the
players’ preferences are unlikely to coincide with the
objectives of the government. Mechanism design recognizes
this problem by first using the idea of a Nash equilibrium
to predict the outcome of all possible games that the
government might choose, and then singling out the game that
generates the outcome that comes closest to fulfilling the
I now have
quite a wide experience of applying the ideas of mechanism
design in practice, and I have no doubt that it
works---provided that one does not try to apply the theory
outside the domain within which its basic assumptions are
valid. It works in the sense that theoretical designs that
succeed in the laboratory can be relied on to work in the
field with reasonably high probability. It is therefore
frustrating to game theorists like myself that the
conservatism of most government departments should restrict
the areas in which we are allowed to operate so severely.
I want next
to mention applications of game theory to moral and
political science. The most important result in this context
is the folk theorem of repeated game theory, which roughly
says that any stable outcome a society can achieve with the
help of an external enforcement agency (like a King and his
army, or God) can also be achieved without any external
enforcement at all in a repeated game, provided the
players are sufficiently patient and have no secrets from
one another. Game theorists take the view that a
self-policing social system must be a Nash equilibrium in
which each player is simultaneously making a best reply to
the strategy choices of the other players. No single player
then needs to be coerced, because he is already doing as
well for himself as he can. We think that even authoritarian
governments need to operate a Nash equilibrium in the
repeated game of life played by the society they control if
they are to be stable, because popes, kings, dictators,
generals, judges, and the police themselves are all players
in the game of life, and so cannot be treated as external
enforcement agencies, but must be assigned roles that are
compatible with their incentives just like the meanest
citizen. In brief, the game theory answer to quis ipsos
custodes custodiet is that we must all guard each other.
To this insight, my own work
adds a game-theoretic approach to our understanding of
fairness norms (Binmore ). The folk theorem tells us
that there are many efficient Nash equilibria in the
repeated games of life played by human societies. This was
true in particular of prehuman hunter-gatherer societies.
Evolution therefore had an equilibrium selection problem to
solve. The members of such a foraging society needed to
coordinate on one of the many Nash equilibria in its game of
life---but which one? I believe that our sense of fairness
derives from evolution’s solution to this equilibrium
selection problem. That is to say, metaphysics has nothing
to do with fairness---if evolution had happened upon another
solution to the equilibrium selection problem, we would be
denouncing what we now call fair as unfair.
I go on to
argue that our sense of fairness is like language in having
a genetically determined deep structure that is common to
the whole human race. I then give reasons why one should
expect this deep structure to be captured by Rawls’ original
position. The question then arises as to whether Rawls
 or Harsanyi  are correct in their opposing
analyses of rational bargaining in the original position.
With the external enforcement assumed by both, the answer is
that Harsanyi’s utilitarian conclusion is correct.
Without external enforcement of any kind (so that there are
no Rawlsian “strains of commitment” at all), I come up with
something very close to Rawls’ egalitarian
conclusion. That is to say, although Harsanyi’s analysis was
better than Rawls’, but Rawls had the better intuition.
of our sense of fairness will doubtless be thought naïve by
future scholars, but it is hard to conceive of a future
approach that will not have a similar game-theoretic
want to observe that attempts to provide firm foundations
for game theory have profound implications for a whole range
of related disciplines. Such attempts fall broadly into two
classes, which I call eductive and evolutive.
game theory embraces all attempts to model players as
ideally rational agents. This approach has generated
numerous spin-offs, of which the most important is the
theory of common knowledge proposed by Aumann , who
was also a major contributor to the theory of repeated
My own attempts to make progress in this area center on how
to adapt theories of knowledge when the thinking processes
of the players are algorithmic---so that it is no longer
assumed that a rational player can decide the undecideable.
It is then no longer possible to speak of perfect
rationality as this term is currently understood. My most
recent paper on this subject is pure epistemology, and the
scope for making further progress in this direction seems to
me enormous. (Binmore ).
game theory includes all theories that model the players as
ideally rational entities who find their way to an
equilibrium by some process of trial-and-error adjustment.
This process may be involve individuals learning separately,
or it may be a cultural phenomenon in which imitation is the
most important factor, or it may be biological (in which
case one usually speaks of evolutionary game theory).
Evolutive game theory is too large a subject to assess here,
but it will perhaps be enough to draw attention to its huge
success in evolutionary biology since Maynard Smith’s 
ground-breaking Evolution and the Theory of Games.
248 pages / $26 / £16
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