THE ERROR-CONTROLLED REGULATOR 12/22 



This, for instance, may be the case in wild hfe when a prey 

 attempts to regulate against an attack by a predator, when the 

 whole struggle progresses through alternating stages of threat and 

 parry. Here the predator's whole attack consists of a sequence of 

 actions Dj, D2, D^ . . ., each of which evokes a response, so that 

 the whole response is also a sequence, Ri, Rj, R2, . . . . The whole 

 struggle thus consists of the double sequence 



Di, Ri, D2, i?2» ^3» ^3j • • • 



The outcome will depend on some relation between the predator's 

 whole attack and the prey's whole response. 



We are now considering an even more complex interpretation of 

 the basic formulation of S.11/4. It is common enough in the bio- 

 logical world however. In its real form it is the Battle of Life; in 

 its mathematical form it is the Theory of Games and Strategies. 

 Thus in a game of chess the outcome depends on what particular 

 sequence of moves by White and Black 



W„ Bi, W2, B2, Wi, 53, . . . 



has been produced. (What was called a "move" in S.11/4 corres- 

 ponds, of course, to a play here.) 



This theory, well founded by von Neumann in the '30s, though 

 not yet fully developed, is already too extensive for more than 

 mention here. We should, however, take care to notice its close 

 and exact relation to the subject in this book. It will undoubtedly 

 be of great scientific importance in biology; for the inborn character- 

 istics 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.l 1/4 — 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 

 thetheory 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 equivalent 

 to his generahsed game (Fig. 12/22/1). (In the Figure, the letters 



16 241 



