Abstract
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 econophysics. 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.
Reprinted from Evolutionary and Institutional Economics Review 2(2). Aruka, Y., An Evolutionary Theory of Economic Interaction: Introduction to Socio- and Econo-physics, 145–160 (2007). With kind permission from Japan Association for Evolutionary Economics, Tokyo.
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Notes
- 1.
- 2.
Bounded rationality may be given in view of the failure of estimation on the secondary effects. If we had some subpopulation which failed to catch up with the secondary effects of the interaction, the opponent subpopulation should rather utilize the failure of the former for its advantages.
- 3.
- 4.
This section is a concise version of Aruka and Mimkes (2005).
- 5.
S represents the different possibilities for production activities (processes). And we later find \( S = \ln P \). In a finite system of N elements the number of possibilities may be calculated by the law of combinations \( P = N!/N \).
- 6.
Aruka and Mimkes (2005), by the use of von Neumann-Sraffa model of production (von Neumann 1937, Sraffa 1960), attained to the next result:
Theorem 1. The probability of multiple truncations compatible with a given rate of interest r must be augmented if the number of truncations increases in the range of \( g \leq r \). Average welfare could then be risen by a hierarchical inclusion of a single process operation of higher profitability, i.e., by an increase of complexity.
- 7.
We can easily prove the next proposition: With groups of sizes \( {x_1},{x_2}, \cdots, {x_n} \) adding to \( G = \sum\nolimits_i^n {x_i} \), the average size is \( \frac{{{x_i}}}{G} \). The chance of an individual belonging to group \( 1\; is \;\frac{{{x_1}}}{G} \). The expected size of the group is \( E(x) = x_1\frac{{{x_1}}}{G} + \cdots + x_n\frac{x_n}{G} \). Hence it then holds that \( \sum\limits_{i = 1}^{n} \frac{{{x^2_i}}}{G} \ge \frac{G}{n}. \)
- 8.
Robert Frank loves to discuss plentiful discussions on this kind. See Frank (1988).
- 9.
Recently, “pessimistic subjectivity” is taken account of in the theory of expected utility theory. The theory of this type is called Choquet expected utility theory. But we rather are interested in the interaction of heterogeneous agents. See Bassett et al. (2004), for example.
- 10.
Finally, we must notice another point. Even in a society where there are only 24 persons, we always are faced with too many menu lists on type-size allocation when we must select. Suppose we always given an initial allocation of types. We can then always hold the initial allocation as a status quo(standstill) policy. In the case of Nash bargaining, the allocation is called the threat or impasse point.
- 11.
\( \frac{{\partial L}}{{\partial {N_i}}} = 0 \) implies \( {E_i} - T \left(\ln \frac{N}{{{N_i}}} - \ln \frac{{{V_i}}}{V}\right) = 0 \). Hence \( \ln \frac{N}{{{N_i}}}\frac{{{V_i}}}{V} = - \frac{{{E_i}}}{T} \).
References
Anderson P, Arrow K, Pines D (eds) (1988) The economy as an evolving complex system: studies in sciences of complexity. Addison-Wesley, Redwood, CA
Aruka Y (1996) Dictatorship, price hike like bubble and employment adjustment on the non-goldenpath of the von Neumann growth model with joint-production. In: Proceedings of econometric society Australasian meeting, vol 1. University of Western Australia, Perth, pp 475–504
Aruka Y, Mimkes J (2005) Complexity and interaction of productive sub-systems under thermodynamical viewpoints, systems under thermodynamical viewpoints. In: WEHIA2004: the 10th workshop on economics with heterogeneous interacting agents, University of Essex, UK, 13–15 June 2005
Bassett G, Koenker R, Kordas G (2004) Pessimistic portofolio allocation and choquet expected utility. CEMMAP Working Paper CWP09/04
Bellman R (1961) Adaptive control processes: a guided tour. Princeton University Press, Princeton, NJ
Bierlaire M (1997) Discrete choice models, mimeo
Frank RF (1988) Passions within reasons. The strategic roll of the emotions. W.W. Norton, New York (Paper edition 1989; German translation, Orednbourg 1992; Japanese translation, Saiensu-sha 1995; Greek translation, Kastoniosis 2000)
Hodgson GM (2003) The preface to Japanese version of “Economics and evolution: bringing life back into economics”. Polity, Cambridge
Holland JH (1992) Adaptation in natural and artificial systems. MIT Press, Cambridge, MA
Holland JH (1995) Hidden order: how adaptation builds complexity. Perseus Books, Reading, MA
Hoover KD (2001) The Methodology of empirical macroeconomics. Cambridge University Press, Cambridge, UK
Keynse JM (1972) The end of laissez-faire, The collected writings of John Maynard Keynse. IX Essays in Persuation. Macmillan, London
Luce R (1959) Individual choice behavior: a theoretical analysis. Wiley, New York
Mimkes J (2003) Thermodynamics of economic agent systems, Part III. University of Paderborn, Paderborn (mimeo)
Nash JF (1951) Noncooperative games. Ann Math 54:286–95
Schefold B (1989) Mr. Sraffa on joint production and other essays. Unwin Hyman, London
Sraffa P (1960) Production of commodities by means of commodities. Cambridge University Press, Cambridge, UK
Strang G (1991) Calculs. Wellesley-Cambridge Press, MA
von Neumann J (1937) Über ein Ökonomisches Gleichungssystem und eine Verallgemeinung des Brouwerschen Fixpunktsatzes, Ergebnisse eines Mathematischen Kolloquiums 8:73–83 (translated as “A model of general economic equilibirum.” Rev Econ Stud 13:1945–1946)
Weidlich W (2000) Sociodynamics: a systematic approach to mathematical modeling in the social sciences. Harwood Academic, London
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Aruka, Y., Mimkes, J. (2011). An Evolutionary Theory of Economic Interaction: Introduction to Socio- and Econo-Physics. In: Aruka, Y. (eds) Complexities of Production and Interacting Human Behaviour. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-2618-0_4
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