Acteristics of living organisms are simply the strategies that have
Been found satisfactory over centuries of competition, and built
Into the young animal so as to be ready for use at the first demand.
Just as many players have found “P— Q4” a good way of opening
The game of Chess, so have many species found “Grow teeth” to
Be a good way of opening the Battle of Life.
The relation between the theory of games and the subjects
Treated in this book can be shown precisely.
The first fact is that the basic formulation of S.11/4— the Table of
Outcomes, on which the theory of regulation and control has been
Based— is identical with the “Pay-off matrix” that is fundamental in
The theory of games. By using this common concept, the two theories
Can readily be made to show their exact relation in special cases.
The second fact is that the theory of games, as formulated by
Von Neumann and Morgenstern, is isomorphic with that of certain
Machines with input. Let us consider the machine that is equiva-
Lent to his generalised game (Fig. 12/22/1). (In the Figure, the let-
241
GA M ES AN D STR A TE GIE S
The subjects of regulation and control are extremely exten-
Sive, and what has been said so far only begins to open up the sub-
Ject. Another large branch of the subject arises when D and R are
Vectors, and when the compounding that leads eventually to the
Outcome in T or E is so distributed in time that the components of
D and R occur alternately. In this case the whole disturbance pre-
Sented and the whole response evoked each consists of a sequence
Of sub-disturbances and sub- responses.
240
A N I N T R O D UC T I O N T O C Y B E R NE T I C S
TH E ERR O R- CO N TR O LLED REG U LA TO R
Ters correspond with those by von Neumann in his Chapter 2,
Which should be consulted; his T’s do not correspond to the usage
In this book.)
There is a machine M with input. Its internal structure (its
Transformations) is known to the players Ti It has three types of
input: Γ , V, and T. A parameter Γ , a witch perhaps, determines
Which structure it shall have, i.e. which game is to be played.
Other inputs Vi allow random moves to be made (e.g. effects
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From a roulette wheel or pack of shuffled cards to be injected; cf.
S.12/15). Each player, Ti, is a determinate dynamic system, cou-
Pled to M both ways. He receives information from M by speci-
Retain their values and his strategy will be unchanged; but if dis-
Satisfied (i.e. if the payment falls below some critical value) the
Step-functions will change value, and the loser, at the next play,
Will use a new strategy.
A related subject is the theory of military codings and de-cod-
Ings. Shannon’s Communication theory of secrecy systems has
Shown how intimately related are these various subjects. Almost
Any advance in our knowledge of one throws light on the others.
More than this cannot be said at present, for the relationships
Have yet to be explored and developed. It seems to be clear that the
Theory of regulation (which includes many of the outstanding prob-
Lems of organisation in brain and society) and the theory of games
Will have much to learn from each other. If the reader feels that
These studies are somewhat abstract and devoid of applications, he
Should reflect on the fact that the theories of games and cybernetics
Are simply the foundations of the theory of How to get your Own
Way. Few subjects can be richer in applications than that!
We are now at the end of the chapter, and the biologist may
Feel somewhat dissatisfied, for this chapter has treated only of sys-
Tems that were sufficiently small and manageable to be understood.
What happens, he may ask, when regulation and control are
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