Applications of the Von Neumannian Game

Even this very brief listing of some of the elements in Balinese ethos suffices to indicate theoretical problems of prime importance. Let us consider the matter in abstract terms. One of the hypotheses underlying most sociology is that the dynamics

38 Mead, "Public Opinion Mechanisms among Primitive Peoples," loc. cit., 1937.

39 Bateson and Mead, op. cit., pls. 17, 67, and 79.

43 At present it is not possible to make such a statement in sharply defined quantitative terms, the available judgments being subjective and Occidental.

of the social mechanism can be described by assuming that the individuals constituting that mechanism are motivated to maximize certain variables. In conventional economic theory it is assumed that the individuals will maximize value, while in schismogenic theory it was tacitly assumed that the individuals would maximize intangible but still simple variables such as prestige, self-esteem, or even submissiveness. The Balinese, however, do not maximize any such simple variables.

In order to define the sort of contrast which exists between the Balinese system and any competitive system, let us start by considering the premisses of a strictly competitive Von Neumannian game and proceed by considering what changes we must make in these premisses in order to approximate more closely to the Balinese system.

(1) The players in a Von Neumannian game are, by hypothesis, motivated only in terms of a single linear (sc. monetary) scale of value. Their strategies are determined: (a) by the rules of the hypothetical game; and (b) by their intelligence, which is, by hypothesis, sufficient to solve all problems presented by the game. Von Neumann shows that, under certain definable circumstances depending upon the number of players and upon the rules, coalitions of various sorts will be formed by the players, and in fact Von Neumann's analysis concentrates mainly upon the structure of these coalitions and the distribution of value among the members. In comparing these games with human societies we shall regard social organizations as analogous to coalition systems. 44

(2) Von Neumannian systems differ from human societies in the following respects:

(a) His "players" are from the start completely intelligent, whereas human beings learn. For human beings we must expect that the rules of the game and the conventions associated with any particular set of coalitions will become incorporated into the character structures of the individual players.

(b) The mammalian value scale is not simple and mono-tone, but may be exceedingly complex. We know, even at a physiological level, that calcium will not replace vitamins, nor will an amino acid replace oxygen. Further, we know that the animal does not strive to maximize its supply of any of these discrepant commodities, but rather is required to maintain the supply of each within tolerable limits. Too much may be as harmful as too little. It is also doubtful whether mammalian preference is always transitive.

(c) In the Von Neumannian system the number of moves in a given "play" of a game is assumed to be finite. The strategic problems of the individuals are soluble because the individual can operate within a limited time perspective. He need only look forward a finite distance to the end of the play when the gains and losses will be

44 Alternatively, we might handle the analogy in another way. A social system is, as Von Neumann and Morgenstern point out, comparable to a non-zero sum game in which one or more coalitions of people play against each other and against nature. The non-zero sum characteristic is based on the fact that value is continually extracted from the natural environment. Inasmuch as Balinese society exploits nature, the total entity, including both environment and people, is clearly comparable to a game requiring coalition between people. It is possible, however, that that subdivision of the total game comprising the people only might be such that the formation of coalitions within it would not be essential—that is, Balinese society may differ from most other societies in that the "rules" of the relationship between people de-fine a "game" of the type Von Neumann would call "non-essential." This possibility is not here examined. (See Von Neumann and Morgenstern, op. cit.)

paid up and every-thing will start again from a tabula rasa. In human society life is not punctuated in this way, and each individual faces a vista of unknowable factors whose number increases (probably exponentially) into the future.

(d) The Von Neumannian players are, by hypothesis, not susceptible either to economic death or to boredom. The losers can go on losing forever, and no player can withdraw from the game, even though the outcome of every play is definitely predictable in probability terms.

(3) Of these differences between Von Neumannian and human systems, only the differences in value scales and the possibility of "death" concern us here. For the sake of simplicity we shall assume that the other differences, though very profound, can for the moment be ignored.

(4) Curiously, we may note that, although men are mammals and therefore have a primary value system which is multidimensional and nonmaximizing, it is yet possible for these creatures to be put into contexts in which they will strive to maximize one or a few simple variables (money, prestige, power, etc.).

(5) Since the multidimensional value system is apparently primary, the problem presented by, for example, Iatmul social organization is not so much to account for the behavior of Iatmul individuals by invoking (or abstracting) their value system; we should also ask how that value system is imposed on the mammalian individuals by the social organization in which they find themselves. Conventionally in anthropology this question is attacked through genetic psychology. We endeavor to collect data to show how the value system implicit in the social prganization is built into the character structure of the individuals in their childhood. There is, however, an alternative approach which would momentarily ignore, as Von Neumann does, the phenomena of learning and consider merely the strategic implications of those contexts which must occur in accordance with the given "rules" and the coalition system. In this connection it is important to note that competitive contexts—provided the individuals can be made to recognize the contexts as competitive—inevitably reduce the complex gamut of values to very simple and even linear and monotone terms. 45 Considerations of this sort, plus descriptions of the regularities in the process of character formation, probably suffice to de-scribe how simple value scales are imposed upon mammalian individuals in competitive societies such as that of the Iatmul or twentieth-century America.

(6) In Balinese society, on the other hand, we find an. entirely different state of affairs. Neither the individual nor the village is concerned to maximize any simple variable. Rather, they would seem to be concerned to maximize some-thing which we may call stability, using this term perhaps in a highly metaphorical way. (There is, in fact, one simple quantitative variable which does appear to be maximized. This variable is the amount of any fine imposed by the village. When first imposed the fines are mostly very small, but if payment is delayed the amount of the fine is increased very steeply, and if there be any sign that the offender is refusing to pay— "opposing the village" —the fine is at once raised to an enormous sum and the offender is deprived of membership in the community until he is willing to give up his opposition. Then a part of the fine may be excused.)

(7) Let us now consider an hypothetical system consisting of a number of identical players, plus an umpire who is concerned with the maintenance of stability

45 L. K. Frank, "The Cost of Competition," Plan Age, 1940, vi : 314-24.

among the players. Let us further suppose that the players are liable to economic death, that our umpire is concerned to see that this shall not occur, and that the umpire has power to make certain alterations in the rules of the game or in the probabilities associated with chance moves. Clearly this umpire will be in more or less continual conflict with the players. He is striving to maintain a dynamic equilibrium or steady state, and this we may rephrase as the attempt to maximize the chances against the maximization of any single simple variable.

(8.) Ashby has pointed out in rigorous terms that the steady state and continued existence of complex interactive systems depend upon preventing the maximization of any variable, and that any continued increase in any variable will inevitably result in, and be limited by, irreversible changes in the system. He has also pointed out that in such systems it is very important to permit certain variables to alter.46 The steady state of an engine with a governor is unlikely to be maintained if the position of the balls of the governor is clamped. Similarly a tightrope walker with a balancing pole will not be able to maintain his balance except by varying the forces which he exerts upon the pole.

(9) Returning now to the conceptual model suggested in paragraph 7, let us take one further step toward making this model comparable with Balinese society. Let us substitute for the umpire a village council composed of all the players. We now have a system which presents a number of analogies to our balancing acrobat. When they speak as members of the village council, the players by hypothesis are interested in maintaining the steady state of the system—that is, in preventing the maximization of any simple variable the excessive increase of which would produce irreversible change. In their daily life, however, they are still engaged in simple competitive strategies.

(10) The next step toward making our model resemble Balinese society more closely is clearly to postulate in the character structure of the individuals and/or in the contexts of their daily life those factors which will motivate them toward maintenance of the steady state not only when they speak in council, but'also in their other interpersonal relations. These factors are in fact recognizable in Bali and have been enumerated above. In our analysis of why Balinese society is nonschismogenic, we noted that the Balinese child learns to avoid cumulative interaction, i.e., the maximization of certain simple variables, and that the social organization and contexts of daily life are so constructed as to preclude competitive interaction. Further, in our analysis of the Balinese ethos, we noted recurrent valuation: (a) of the clear and static definition of status and spatial orientation, and (b) of balance and such movement as will conduce to balance.

In sum it seems that the Balinese extend to human relationships attitudes based upon bodily balance, and that they generalize the idea that motion is essential to balance. This last point gives us, I believe, a partial answer to the question of why the society not only continues to function but functions rapidly and busily, continually undertaking ceremonial and artistic tasks which are not economically or competitively determined. This steady state is maintained by continual nonprogressive change.

46 W. R. Ashby, "Effect of Controls on Stability," Nature, clv, no. 3930, February 24, 1945, 242-43.

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