KEN BINMORE

Emeritus Professor of Economics
Economics Department

University College London, UK


Excerpt from Ken Binmore's interview:
2. What example(s) from your work (or the work of others) illustrates the use of game theory for foundational studies and/or applications?

The most 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.

Auction 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 government’s objectives.

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 [2005]). 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 [1972] or Harsanyi [1977] 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.

My analysis 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 foundation.

Finally, I 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.

Eductive 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 [1976], who was also a major contributor to the theory of repeated games.[1] 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 [2006]).

Evolutive 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 [1982] ground-breaking Evolution and the Theory of Games.


 

[1] Philosophers think Aumann’s credit should be shared with David Lewis [1969], but Lewis’s failure to produce an operationally useful definition of common knowledge is evident in the fact that the claims he makes about what needs to be common knowledge for a convention to work are mistaken.

Read the remaining part of Ken Binmore's interview in Game Theory: 5 Questions, edited by Vincent F. Hendricks and Pelle Guldborg Hansen. The book is released in April 2007 by Automatic Press / VIP.

ISBN 87-991013-4-3
(paperback)
248 pages / $26 / £16

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