Yuji Aruka

Avatamsaka Game Structure and Experiment on the Web

Avatamsaka is a well known Mahayana Buddhist Sutra. A Japanese professor, working in the field of Buddhist philosophy, skillfully illustrated the situation of heaven and hell in terms of the Avatamsaka (Kamata 1988 pp. 167–168). Suppose that two people sit down at a table, across from each other. They are bound with rope so that one arm only is free, and are then each given a very long spoon. This spoon is so long that they cannot feed themselves with it. There is enough food for both of them on the table. If they cooperate and feed each other, they will both be happy. This is defined as heaven. However, if the first is kind enough to provide the second with a meal, but the second does not feel cooperative, then only the second gains. This must give rise to a feeling of hate in the first. This situation denotes hell. The gain structure does not only depend on an altruistic willingness to cooperate. On an individual level, there is no difference between cooperation and refusal, and the same is true for risk taking. A situation of expected maximization of utility gives infinite equilibria. Our interest is to find a way to heaven from the other possible situations. This chapters is concerned with how an actual player would react in such experiments.

Avatamsaka Game Experiment as a Nonlinear Polya Urn Process

We imagine “driving a car” in a busy place. When we wish to enter into a main street from a side road or a parking area along the road, it must be much better for us that someone can give way for us although someone cannot gain any more by giving us whom someone might never meet. This kindness done by someone implies our gain. A symmetrical situation in replacing someone with us holds the same relation. Anybody who gives a kind arrangement to someone, can never be guaranteed to gain from another. If nobody never gave way for someone, the whole welfare on the roads should be extremely worsen. We call such a situation Avatamsaka Situation in the sense of the footnote.1 The Original Source: Avatamsaka is a well-known one of the Mahayana Buddhist Sutras. Shigeto Kamata, Professor Emeritus, the University of Tokyo, who is working under the field of Buddhists philosophy, he skillfully illustrated the situation of Heaven and Hell in view of Avatamsaka. See Kamata (1988, pp. 167–168). Suppose that two men vis a vis sat down at the table, across from each other. They however are tied with rope except for one arm only, then given each a too long spoon. Own selves cannot serve them by the use of a too long spoon. There are meals enough for them on the table. If they cooperate in concert to provide each other with meal, they can all be happy. This defines the Heaven or Paradise. Otherwise, one will be so kind to provide the other with meal but the other might not have a feeling of cooperation. This case however pays the other. This must give rise a feeling of hate for the other. This describes a situation enough to note the Hell. The gain structure will not essentially depend on the altruistic willingness to cooperate. The model after synchronizing our original setting albeit a vulgar conversion can be written down as a variant of coordination games, although the model can then provide with infinite equilibria in view of individualistic expected utility maximization. A profile of strategic deployments on a set of \( \{ cooperation,defection\} \) may be argued in a repeated form. Thus one way to look for an eventual end point in our repeated game is to formulate the model in terms of evolutionary game of a simultaneous differential equations system (Aruka 2000, 2001). On the other hand, this paper will deal with a stochastic aspect of this evolutionary process. Finally, it is noted that we have internationally achieved Avatamsaka Game Experiment on the Web by my original program by he use of File Maker Pro’s web companion.2We have already had experiments for several times at Chuo University, Japan, Frankfurt University, Germany, and Maquette University, USA.

How to measure social interactions via group selection?: Cultural group selection, coevolutionary processes, and large-scale cooperation: a comment

It is interesting to know that Henrich’s skillful challenge of the Price equation of biology in Price [Nature 227 (1970) 520; Annals of Human Genetics 35 (1972) 485] to locate large-scale cooperation of human beings certainly gives a straight way to argue social interactive mechanism in economic theory. In fact, Glaeser and Scheinkman [E.L. Glaeser, J.A. Scheinkman, Measuring social interactions, in: S.N. Durlauf, H.P. Young (Eds.), Social Dynamics, Brooking Institute, Washington, DC, 2001, pp. 83–131] exhibits a limited form of the Price equation in economic theory without any explicit reference to it. This suggests a common analytical way to measure interactive effects of between-groups and within-group whether in biology or economics. This way however is to be accompanied by some difficulties. Some overarching mechanism between between-groups and within-group will be necessary to establish a definite direction of group selection. The idea of Hildenbrand [W. Hildenbrand, Market Demand, Princeton University Press, Princeton 1994] may be helpful to do this, although his trial has been done in a qualitatively different field.

The Law of Consumer Demand in Japan: A Macroscopic Microeconomic View

In economics, there have been found few fundamental theories as complying with statistical laws, really examined by observation. Econometrics still clings to a very special structure, patronized with favoritism by the traditional economic theory. In 1990s, Hidenbrand, Grandmont, Grodal and others have tried to formulate consumer demand by a procedure definitely different from the traditional way of using an individualistic utility function. An alternative approach is to make assumptions on the population of the households as a whole – the macroscopic microeconomic approach. If the households’ demand functions are not identical then one needs a certain form of heterogeneity of the population of households. This approach really also requires the empirical tests. The method of nonparametric test on income distribution to estimate covariances on the households spending may be applied. In this article, Japanese Family Expenditure Data is used for estimation. The law of consumer demand is one of the most important topics since a birth of economics. Our statistical economics should, first of all, demand innovation in this area.

A Macroscopic Order of Consumer Demand Due to Heterogenous Consumer Behaviors on Japanese Household Demand Tested by the Random Matrix Theory

So far the consumer theory was microscopically too restrictive to overlook many important scenes of the whole consumption activities. This view is deliberately dropping the inter-correlated factors between different income classes and household demands. The household demands must have a certain bias toward either common or different directions among different income classes. In some sense, the traditionally narrow interest may be dangerous because other decisive factors contributing to the consumption activities may be missed. This article argued to choose a particular scene where some natural or social correlative relations i.e., some dominant forces, may work in the consumption activities over the different income classes. By introducing the different income classes, we can just analyze a new facet of interactive correlations among the heterogeneous consumers. Here we can find any correlative relation, irrespective of price variations. Such a way of thinking may lead us observing another hidden force of the consumption activities.

Evolution of Reciprocal Cooperation in the Avatamsaka Game

The Avatamsaka game is investigated both analytically and using computer simulations. The Avatamsaka game is a dependent game in which each agent’s payoff depends completely not on her own decision but on the other players’. Consequently, any combination of mixed strategies is a Nash equilibrium.

An Evolutionary Theory of Economic Interaction: Introduction to Socio- and Econo-Physics

We try to construct an evolutionary theory of economic and social interaction of heterogeneous agents. Modern physics is helpful for such an attempt, as the recent flourishing of econophysics exemplifies. In this article, we are interested in a specific or more fundamental use of physics rather than in the recent researches of econo-physics. In the first part of this article, we mainly focus on the traditional von Neumann-Sraffa model of production as complex adaptive system and examine the measure of complexity on this model in view of thermodynamical ideas. We then suggest the idea of hierarchical inclusion on this model to define complexity of production. In the latter part, we try to construct an elementary theory of social interaction of heterogeneous agents in view of statistical mechanics.

Exploring the Limitations of Utilitarian Epistemology to Economic Science in View of Interacting Heterogeneity

The principles of political economy born before utilitarianism seized power in economics were entirely irrelevant to the kind of utility maximization. Utilitarianism made economists share a unique definite purpose for the art of life, thus becoming to play the crucial role in arguing economics almost everywhere. We can easily find our main prototype of modern economic ideas from the classical source of literatures of utilitarianism, in particular, James Mill who suggested the “Art of Life”, whose ultimate end is happiness in the society. Put another way, utilitarianism is a kind of art which has ultimately recourse to the sole value judgment on happiness either personally or interpersonally.

The Historic Design of the Demand Law and Its Reconstruction

The historical development of economic theories suggests that the most essential constituents of economics are the demand law, the utility function, the production function, and general equilibrium. These issues were argued professionally from the 1930s to the 1950s, mainly by mathematicians and physicists. The most fundamental of these seems to be the demand law. Many economists have been unable to find a consistently self-contained model either by any kind of individual utility formulation or the revealed preference axiom. This problem was solved by Hildenbrand (Market demand, Princeton University Press, Princeton, 1994), taking into account macroscopic order. Even the consumer theory was too restrictive to encompass many important aspects of consumption activities. In this sense, the traditionally narrow interest may be dangerous because other decisive factors contributing to consumption activities may be missed. There are many aspects to consider, including the inter-connected factors between different income classes and household demands. Household demand includes some items that are so indispensable that demand for them is unaffected by price. Ignoring price levels, people would choose items to meet their desire for both luxury and sophistication. This chapter argues a particular scenario where different forces may apply to consumption activities in different income classes. By focusing on a self-organizing pattern of consumption, we analyze a new facet of interactive correlations among heterogeneous consumers. This may lead us to observe another hidden force driving consumption. Before discussing the detail, I consider the basic structure of traditional theories of static and random preference.

Possibility Theorems on Reswitching of Techniques and the Related Issues of Price Variations

Aftermath to a great debate called capital controversy over three decades ago, several seemingly useful results on production theory so far became familiar with us as given by Diewert (1982), Newman (1987), and others: GNP functions, Hotelling’s lemma and Shepard’s lemma. Intermediate microeconomic textbooks usually collect the topics, although these results would virtually be invalid in front of a combination of the use of intermediate goods like in the Sraffa–Leontief system and an introduction of joint-outputs, even if the neoclassical distribution principle were employed. Exception for the case is only a kind of the factor price equalisation theorems, as Woodland (1982) showed. Many economists, however, do not feel serious about those limitations of neoclassical production theory. We may wonder whether they have given up working with those subjects or discarded a theory of production.