Josip Stepanic Jr.1,*, Igor Bertovic2, Josip Kasac3
1 Department of Quality, Faculty of Mech. Eng. and Naval Arch. - University of Zagreb,
I. Lucica 1, HR - 10000 Zagreb, Croatia
2 Department of Physics, Faculty of Science - University of Zagreb,
P.O.Box 331, HR - 10002, Zagreb, Croatia,
[email protected]
3 Department of Control Engineering, Faculty of Mech. Eng. and Naval Arch. - University of Zagreb,
I. Lucica 1, HR - 10000 Zagreb, Croatia,
[email protected]
* Author to whom corresponence should be addressed;
E-mail: [email protected]
Received: 6 May 2002 / Accepted: 7 February 2003 / Published: 11 June 2003
Abstract: Economic interactions are conducted between economic agents - individuals and collectives, through exchange of natural or artificial entities - goods, services and money, in a myriad of combinations. In this article we adopt a microscopic point of view, concentrate on the exchanged entities, and extract their relevant attributes as seen from structurally simple economic processes. Following that, we approach the interpretation of the economic interactions with their mediated character emphasized. Mediators of the interaction are locally available environment units. They are locally recognized and appropriately interpreted in a given value set as goods and money. The overall intensity of economic interactions considered is related to mediators' spatial and temporal characteristics. Extracted characteristics of mediators and economic processes are compacted in the set of formal rules. The approach is connected with similar approaches in economy and physics.
Keywords: economic processes, economic interactions, mediators, agents.
There have been many realizations of money throughout history [1]. Moreover,
the development of appropriate form of money is still unfinished. A large number
of types of objects and artifacts that have served as money share several
functions: (i) a transaction function, (ii) a value storage function, and (iii)
function of a common measure of value [1,
2]. If one concentrates on the
transaction function, money belongs to a class of means for realization of a
particular mode of communication among agents, and an established scale for
measuring agents' wills to communicate in that way. This interpretation brings
about the idea to look at money and its functioning in a society from the point
of view of communications. For example, if money is considered as a
representation of trust [2], then it enables a pair of humans to communicate
with a level of trust that would not exist otherwise.
Starting point regarding that approach, which is adopted here, is to look at
money, other means of exchange and exchanged goods as means for mediating a
specific type of communication between agents, which is conventionally known as
economic process. The valid communication includes mutual understanding and
relationship. The former means that the communication be comprehensible and
true, and the later that agents consider it as trustworthy and appropriate,
respectively [3]. The mutual understanding further implies that communication's
relevant characteristics are manifest in the very communicative action, while
the relationship indicates that the communication is conducted following the
widely accepted rules. The exchanged goods are considered as mediators within
the economic system. The approach to description of economic interactions, in
which the attributes of goods exchanged are considered explicitly, is regarded
as mediated economic interaction (MEI). If the restriction to economic system is
released, then one encounters the general human interaction, in which a large
number of mediator types is involved. Mediators in such an approach are
generally exchangeable structures. The corresponding approach to description of
human interaction as a set of processes including all available exchangeable
structures is referred to as mediated human interaction [4].
The interpretation of economic processes as considered here has similarities
with the praxeological analysis of economic processes [5], as the individual
characteristics are manifestly crucial. However, while in the praxeology the
emphasis is put on the analysis of an individual's behavior in the economic
context, in MEI the emphasis is put on the very mediator attributes, i.e. the
way they influence individual behavior. The specifics of individual behavior are
included at the beginning, and at the end the individual behavior is analyzed as
influenced by the mediators. Between these two points, as stated, mediator
attributes are considered, and are interpreted in the rather formal categories
existing in the physical description of mediated interactions [6].
Mediator is a term used already in different fields [6 - 9]. In all fields
where it is encountered it is a structure connecting two other structures, like
two physical entities [6], bacteria [7],
two humans in a triad, other groups of humans, animals, or general agents [8],
or a human and a machine [9]. Depending
on the context, mediators are given different attributes. Notion of mediators
used here follows closely notion of mediators in theoretical physics [6]. There,
fundamental interactions among elementary particles are described as conducted
through a set of mediators. For example, from the point of view of mediator
exchange, electrons interact through exchange of virtual photons, the quantized
excitations of vacuum. This similarity is to be taken with some caution, as
formalism of physics is highly developed consequence of a natural sciences' positivistism.
To the contrary, positivistic elements in economics are not
accompanied with correspondingly developed formalism, thus only a part of
existing physics formalism is expected to have readily extractable counterparts
in economy. Realizations of mediators in different, yet similar, descriptions of
complex phenomena are given [10]. The approaches to social, political, economic
or other human systems, and other natural realizations of complex systems with a
reference to formalism from physics and chemistry are numerous [11 - 18]. The
microscopic approaches [11,
12] and approach of mediators are rather similar.
While seemingly the macroscopic approaches are not related to it, their broad
field of applications [13 - 18],
and in particular global character [12,
13, 18]
provide one with a basis for inference about microscopic origin of phenomena
encountered, of which mediators are one example.
The concept underlying this article - the concept of mediated human interaction
[4] in the economic context - is developed through a constructive procedure, in
which a part of existing economical description [5], and a part of existing
physical description [6] are used in formulating more formalized interpretation
of economic terms. Such an approach is needed in order to obtain a basis
sufficiently precise for development of analogue of theoretical physics concept
of mediated interaction. The conceptual character is clearly seen from the text,
because the similarities and differences of underlying structures are analyzed.
The specific applications of the concept are money and the description of
structurally simple economic interactions. Money is interpreted as a mediator
that is used only as an exchangeable in economic interactions. In many cases
money is not present naturally, i.e. spontaneously, in agent environment, what
is more pronounced in technologically more developed human systems. Agents are
individuals or economically active organizations. Structurally simple economic
interactions are those that involve few mediators. The structural simplicity
does not mean that MEI is not applicable otherwise. This simplification is
introduced in order to add to understandability of the formalism presented in
the text.
The structure of the article is a series of combinations of a well-known
economic fact and its interpretation using terms developed originally within the
theoretical physics. In particular, the very economic interaction is interpreted
as a mediated interaction between two agents. Following that, some regularly
encountered attributes of mediators in economic interactions, e.g. the mediator
energy, mass and duration, are related to the physical characteristics of
regularly encountered mediators in physics.
The outline of the paper is as follows. In the second section auxiliary terms
used to clarify notion of mediators are introduced and described. They are
described here in order for the article to be self-contained, while more
detailed description is given elsewhere [4]. In the third section similar
approach is undertaken for exchangeables in economic processes. In that section,
quantitative description of elementary economic processes is given, and
illustrative results obtained. The central quantity is a measure of economic
process intensity. In the fourth section as an example, a qualitative comparison
of barter and monetary processes is presented.
An environment excitation is a part of environment of an agent system, which
is in some value set attributed different characteristics from the rest of
environment. Using that notion, the environment is represented as a set of
environment excitations, with the number of their types depending on the
relevant value set. This notion includes both of the traditional attributes:
"natural" and "artificial". Moreover, the ways of obtaining some structure do
not preclude its naming as an environment excitation.
Only a small part of possible environment excitations is used significantly in a
particular agent system. Because of that, a notion of environment excitation is
not very useful in the analysis of the connections between the agents' value set
and the plurality of environment excitations used in regular agent dynamics.
Some of the environment excitations are recognized in a local agent system. The
recognition denotes that their existence and functioning is represented in the
local value set. An elementary excitation which is attributed a specific
function in a given value set, is called the elementary environment excitation (EEE)
within that value set.
The very adjective elementary means that excitations are attributed established
functions in a local agent system, and points to their recognition. For example,
a wheel is an EEE in many societies since several thousand years. It is
furthermore an EEE that is traditionally considered artificial, in that only its
raw materials and not the total construction occur spontaneously in human
environment. There are many other examples of elementary environment
excitations: food, furniture, weapons, buildings, words, news, newspapers,
Internet, stories, proverbs, songs, ... in fact all structures which we consider
part of our environment. The adjective elementary is to be interpreted strictly
in connection with the referent value set of an agent system. It includes the
existence of a function attributed only to that EEE. However, the very presence
of a function does not mean that the corresponding part of environment is the
least part of environment which is used in performing that function in the agent
system. Therefore, the notion elementary in EEE is needed. Furthermore, the
convention that value set which is relevant for some system is the functional
value set for that system is adopted. Such a convention then, is valid for parts
of the value set, in particular EEEs, and need not be further emphasized once
the EEE's definition is known. For example, a function of a wheel is to
transform the periodic motion into aperiodic. It is the least part of a system
which performs such a transformation. Half of a wheel, spokes, possibly included
rubber or wooden parts of a wheel separately are not considered as periodic-to-aperiodic
motion transformers. Motors, shafts and other similar structures are capable of
such a transformation, but are more complex than a wheel. Their additional
attributes are responsible for other, more complex functions they are linked to.
The word elementary as related to a value set is somewhat inconvenient if one
adopts the theoretical physics point of view in which elementary attributes are
valid throughout the known universe. That inconvenience is consequence of too
strict reference to analogue notions in theoretical physics, which is to be
taken with caution. In other words, every value set is a universe of its own,
and along with its dynamics, the notions of EEEs change. Certainly, such changes
are seen only relatively, in comparison with earlier, or in other ways different
value sets.
The relation of EEE and elementary excitations needs more clarification. In
particular, the point to be emphasized is that only one value set figures in
definition of EEE while two value sets figure in definition of elementary
excitations. In other words, within one agent system, to which we will refer as
the primary for the moment, if there is a recognized part of environment it is
an EEE. Let as assume that there is another agent system, referred to here as
the secondary, the value set of which does not include that part of environment.
For the secondary system the considered part of environment is environment
excitation, but not EEE. As an illustration to that, wheels were not EEEs in old
enough societies, although then wheels were still possible environment
excitations, as we can conclude from our point of view.
The EEEs are characterized with a value in a local agent system. Value, denoted
as V, is considered here to be a scalar quantity. The EEEs have set of
attributes uniquely determining them, denoted as {a}. Value is influenced with
several factors: availability and cost of components, cost of agent labor,
durability, possibility of different usage and demand for it. One type of EEE
includes sets of attributes with different vales, e.g. wheel can be wooden,
metallic, combined, or produced from different materials, or their more complex
combinations. Between the listed factors influencing an EEE's value, durability,
denoted as D, has somewhat different meaning, as it measures the EEE's
degradation in time. It is regarded here as imaginary counterpart of real value.
Hence, total value of an EEE is
| Va + iDa | (1) |
|
|
(2) |
where V is auxiliary value variable, mathematically real quantity. The meaning of propagators will be clear after processes involving mediators are described in some detail. For the moment, it is to be emphasized that the value of Pa(V) diverges if auxiliary value V approaches the total mediator value.
State of an agent in reciprocal space is represented as a collection of values of EEEs which are considered as belonging to the agent. Agent dynamics in the reciprocal space is described as time dependent collection of values. Time dependence is introduced through degradation of an EEE, possibly through its consumption by an agent, or exchange of EEEs among agents. The functioning of EEEs as means for interaction between agents is one possible EEEs function. The EEEs which are regularly used in performing an interaction between the agents are called mediators.
Characteristics of EEEs are suitably collected in their graphical representation, Figure 1a. In it, additional structure is representation of relevant agent states, Figure 1b, i.e. representation of values of states (i - initial and f - final) which are significantly changed in interaction with EEEs. In Figure 1, time axis makes possible putting the agent-EEE interaction into a sequence. Explicit attributes of a particular state, like set of EEE's attributes are assumed, and are not shown in order to simplify the representation. Agent states are represented using full lines, and EEE's states using dashed lines. Among all the EEEs only those changing agent states are considered, hence the elementary agent-EEE process is represented in Figure 2.
 |
| Figure 1. a) Graphical representation of an EEE, b) relation of the EEE with agent states. |
 |
| Figure 2. Elementary agent-EEE interaction processes. |
A connection of two lines representing different agent states with a line representing a mediator is represented as a circle, and is called a vertex. Vertices are functions of attributes of the joined states, which expresses the probability of occurrence of a particular combination of joined states. As an illustration of these elementary processes, if the agent is a baker, and the EEE is a loaf of bread, then interaction of these two will not change the agents knowledge about automobiles, the very automobile owned etc., thus these characteristics will not be mentioned in the set of agent states. If, in some other case, the agent is a mechanical engineering student, then knowledge about automobiles is one relevant agent state, while the automobiles owned or a number of loaves of bread are not. Assume the EEE to be a book about automobiles, Let us describe processes shown on Figure 2 in more detail. Process on Figure 2a describes a situation in which an EEE is emitted from some agent. That emission can be a formation of the EEE which did not exist before, or a release of the EEE which existed before when it was conventionally described as agent's property or responsibility. As an example of the former type let us consider bread which a baker bakes. Bread is the EEE and the baker is the agent. Bread is formed in a process starting with heat, wheat and some other EEEs, summarily known as baking. An example of the later type of EEE emission is a student with a textbook. The student carrying the book is interpretable as an agent whose present state includes one EEE. The student may leave the book in the room, return it to the library, or in some other ways come in the state without the book which then becomes an independent EEE. These two, and a myriad of similar processes, are represented as shown on Figure 2a. On Figure 2b the converse processes are represented; collection or destruction of an EEE. In order to simplify the description, the processes on Figure 2a, and Figure 2b are considered as emission and absorption of an EEE, respectively.
However, the economic processes are not included in the representation on Figure 2.
From these elementary processes one step further is needed to obtain a
representation of an elementary economic process here considered as the
elementary transaction. This is so because in the economic processes changes of
quantities of agents' assets are considered, realized as the mutual exchange of
assets. The asset could be a material one, or not. Information is an example of
an asset traditionally considered non-material.
Considering the world-wide identity of elementary economic processes observed
throughout the history periods, it is opportune to consider as an inherent
property of agents the following fact: a change of an agent state induced with
only emission of one EEE is considered highly unwanted when economic processes
are considered. The usual economic description involves a utility function of an
agent, which is a scalar function referring to the combination of attributes the
agents tend to augment. In economic interactions with a single EEE emission the
value of utility function is considered too large to be acceptable. The larger
the deviation of a final state in a process from some referent state, the
smaller its probability. The utility function represents the local value set.
Graphically, Figure 3 depicts favoring of two-mediator process using the sketch
of some utility function. In Figure 3a the value of utility function is shown as
a function of resource change, caused by mediator emission (negative changes) or
absorption (positive changes). Having in mind that what is emission for one
agent is the
 |
| Figure 3. a) Individual agent utility function, and b) utility function of two economically interacting agents. The utility functions are shown as functions of the agents' resource changes. |
absorption for the other, the graph of combined change of utility functions for both interacting agents shown on Figure 3b is obtained. Because of a qualitative character of this graph, the maximum of the combined change is centered at zero net resource change. The precise form of the optimal combined utility function change is a separate, thoroughly examined problem; it is recognized as Nash equilibrium in game theory on the one hand, and as the Luhmann's contingency problem on the other hand. As that is out of the scope of this article, we will not analyze furthermore the precise form of the combined utility function change, i.e. the influence of both vertices. Further in the text we use a utility function as a functional representation of a vertex. Therefore, every vertex combining agent states i and f with corresponding resources ri and rf, respectively, is in the reciprocal space represented as
 |
(3) |
 |
| Figure 4. One example of elementary transaction seen as agent-agent interaction realized through exchange of two EEEs. |
The stochastic character of the concept of mediated economic interactions is
clearly seen if one recognizes that the exchange described in general is
repeated perpetually among all agents in the system. That is not the only source
of stochasticity, because one expects the stochastic elements in internal agent
dynamics. However, its explicit taking into account occurs when macroscopic
quantities are derived through suitable averaging of the set of elementary
transactions.
Formal representation of elementary economic interaction processes, the example
of which is shown on Figure 4, contains several appropriately connected
elements: mediator propagators and vertices. Representations of processes on
Figure 5a and 5b, denoted as Ma and Mb, respectively, are
 |
(4) |
 |
(5) |
 |
(6) |
 |
(7) |
Expressions (5) and (7) equally contribute. In (5) and (7) Da =
a4 - a2. On
Figure 5 the meaning of indices encountered in (4 - 7) is explained. As mediator
transfers a finite value, relations V1 =
a1 - ai =
a4 - aj for one mediator, and
V2 = a3 -
ai = a2 -
aj for the other mediator, hold for process on Figure 5a,
thus agents' intermediate states are known. Mediator auxiliary values are
assumed equal to differences in agent's values connected in a vertex, i.e. they
are also known. Similarly, in case of a process shown on Figure 5b relations V1
= a1 - ai =
aj - a2 for one, and
V2 = a3 -
ai = aj -
a4 for the other mediator
hold. Integrals and sums in (4 - 7) are put in order to take into account that
in general there can be more than one type of mediators with a given value,
hence their duration may differ. The sign ` in summation over mediator indices
points to the fact that signs of values Va and
Vb are equal. A complete
representation of a process is
| M = Ma + Mb = 2Ma = 2Mb. | (8) |
 |
| Figure 5. Elementary economic processes occurring in (4 - 7). |
Generally, values of M are larger for more pronounced augmentation of combined utility function, and in cases when mediator values match values which are attributed to mediators by agents, as seen from their intermediate states, i.e. when V1 = |Va + iDa| and V2 = |Vb + iDa|. Furthermore, values of M are larger if mediators are more durable, i.e. for lower Da, b. Following that, one can interpret M as the indicator of economic activity - the larger its value, the more probable economic interaction. Strictly, this interpretation is valid for an elementary process between two agents. In order to obtain measure of a probability of process between two agents in specific states a1, 2 one needs to sum (4 - 7) over possible final agent states a3, 4. Such a summation is formal representation of Luhmann's contingency problem. Furthermore, a system indicator which measures intensity of agents' economic interactions is obtained after additional averaging over all possible initial agents' states. Structure of a system is then explicitly taken into account.
Further characteristics of an elementary transaction are seen clearly in case
of a process with two agents and two EEEs. Let us emphasize here that the
availability of an EEE, linking given initial with a particular final state, is
connected with the probability of a change of a state. If the EEE needed is
available, the probability of a process is non-zero. However, if the EEE needed
is unavailable, the probability of a process is zero. On average, in a
collection of agents, the average number of realizations of a particular process
involves the quantity of available EEEs needed for that process. The very
availability is a function of local characteristics. It is changed with the
number of agents providing or needing some EEE. In case when there is small
number of types of EEEs, it is simple to find a pair of agents such that their
surpluses and lacks of EEEs are aligned, and to connect them, i.e. to perform an
elementary transaction. In case when there is large number of types of EEEs, it
is still formally simple to find such a pair of agents. However, practically it
may become rather improbable for particular agents to realize such a pair,
considering the probability of interaction, range of interaction, time available
for interaction, screening of the two agents which tend to interact mutually by
other agents, etc. The screening means that effective values of parameters of
interaction differ from cases in which there are only two agents in environment.
The situation changes significantly in case when there is a single EEE that is
in a particular way equivalent to all other EEEs. The equivalence is such that
there is a definite and widely accepted exchange ratio for expressing value of
different types of EEEs. The very existence of that ratio is consequence of
effective space and time invariance of set of values. In that case, for the
realization of an exchange process it is needed to form a pair of agents with
interests in exchanging a single general and the universally accepted EEEs. On
average this is simpler to realize than the earlier case. Such a universally
accepted EEE we denote as a global exchangeable (GE), and in further text EEE
means additionally non-GE. A GE has several attributes. Primarily, it should be
a sufficient substitute for a variety of EEEs, including slowly consumed ones.
Hence, it should be durable. More formally, durability means that accompanied Da
is negligible compared to values of EEEs' Da. The GE should be available in
large enough quantity for the very transaction including it be possible. The
availability includes technical aspects, e.g. relatively simple transport. On
the other hand, good transportability further implies relatively large range of
interaction or, more precisely, relatively large space region around one agent
in which the probability of interaction with another agent does not depend on
the time connected with the GE transport. The ending recognition is that GEs
have relatively low economic inertia, introduced here as the analogue of
physical inertia, i.e. mass of an object. Economic inertia is a measure showing
how large efforts are needed in order to change a state of some EEE. Between two
EEEs, the one requiring larger amount of efforts for the equivalent transfer is
attributed larger economic inertia. The origins of economic inertia are in the
existing formal (e.g. laws about GE transfer between two regions) and informal
rules (e.g. a possibility of robberies during transport tend to reduce somewhat
the rate of GE transported. This is overcome by making larger the number of
required actions of agents, of which one consequence is enlargement of the
quantity of energy required). Generally, in one system there may exist more than
one type of GE. Universal acceptance means further that GE forms naturally a
scale of value, i.e. it figures also as a measure of value. But, these several
attributes are the functions of money stated in the introductory section of this
article. Hence there is equivalence between the notion of money and the notion
of GE.
Simple forms of exchange processes involving (i) two EEEs, (ii) one EEE and one
GE are known as barter and monetary transaction. Such recognition contributes to
realizing further characteristics of elementary transactions.
A) Barter
In elementary barter, each of two types of EEEs is needed by one of two
interacting agents. Additionally, EEEs used in barter are of variable, generally
finite, duration. Because of that, they are needed when prolongation of internal
agent's dynamics requires so, and are henceforth soon transformed appropriately,
e.g. food is consumed, building material included in houses built. This also
reduces barter duration, hence it is localized in time. Its additional
characteristic is relatively small probability of finding two agents with such a
combination of initially owned resources, i.e. EEEs, that after mutual exchange
they achieve more wanted final states. Hence, in the barter based economy, (i)
economic processes are localized in time and space, (ii) overall activity
depends crucially on the probability of agent-agent interaction. Interpretation
using terms from theoretical physics includes statements that mediators involved
are of relatively large economic inertia, hence are short-ranged. The changes in
assets caused by emission or absorption of one EEE with a large economic inertia
are considered relatively large (but that does not mean that accompanied utility
function changes significantly, cf. Figure 3), hence are instantaneous.
Formal representation of that process is given with (8). Practical
simplifications, which are consequences of the very barter characteristics, are
that Va and Da are relatively large in comparison with achievable V, thus in a
barter M simplifies into
 |
(9) |
 |
(10) |
 |
| Figure 6. Graph of f(Da) defined in (10). |
 |
(11) |
The approach to elementary agent interaction with other agents and
environment in terms of exchanged elementary environment excitations is
described. It is applied onto description of elementary transactions as exchange
of two elementary environment excitations, and to description and comparison of
barter and monetary economy. It is argued that attributes of mediators used in
economic context are one part of the influences on the duration and range of an
elementary exchange process. Because of the perpetual repetition of exchange
processes, these attributes are implicitly found in the averaged economic
dynamics. The other part of the influences is the influences intrinsic to
agents, which are parameterized, e.g. using individual agent utility function.
The attributes involved are interpreted using terms originating in the
theoretical physics description of mediated interactions, which provides one
with a number of possible parallels.
Formal description of elementary economic processes is given, starting with
appropriate scheme. Non-trivial elements in the scheme: mediator lines and
circles for vertices have mathematical counterparts given by (2) and (3),
respectively. Integration is assumed for all variables of states other than
final or initial: values of agents' resources and auxiliary value of mediator .
Summation is assumed for all mediator indices. Quantity thereby obtained, M,
measures the intensity of economic interaction. It is mentioned how M is used as
a starting point toward obtaining measures of economic activity valid for total
system. Agent intermediate states are treated in a rather simple form.
The concept developed here opens in two different directions. Firstly,
similarity with the concept of mediators as developed within theoretical physics
here is only tackled. If one would like to set the limits of the analogies, then
introduction of some new concepts, e.g. Hamiltonian or Lagrangian function,
should be analyzed. Secondly, the functions encountered in the article, e.g.
form of a vertex as described in (3), point to the necessity for application of
the MEI onto realistic cases.