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Starting from the principle that every action is always undertaken in view of a result, or in reply to an external stimulus, we are interested in the modeling of actions with retroactive effect (feedback).
We will propose then to characterize the global performance of an organization thanks to the measure of transaction frequencies at each hierarchical level.
|" Actor "(noted "A ") a subject who can be actor, observant as well as witness in a system or "acted " by the system, tossed by its environment. The term " Actor ", following our point of view is to emphasize the subject's will, whatever could be the type of action
undertaken by the Actor facing his environment: actions or / and observations, active or / and passive,
||"System "(noted" S ") is the Actor's vision of the environment in which
he evolves, his anthropocentric description of the World.|
The representation of a system is a "Model "created for needs of an "Observant". It can arrive that this "Observant " is the "Actor " engaged in the System observed.
To define the game of the "Actor " facing the "System", we assimilate each antagonist to a player.
In any game, each player try to maximize its gain hope and to minimize its loss risk (minimax rule) .
The theory of games schematizes this face to face situation by a matrix gains and losses matrix :
Each player is represented by the totality of states on which he can be. In our example, A can take n and S p different states.
We define in extension A and S by the totality of states that they are able to take.
|A = (a1,....,ap) the totality of actions retained by the Actor,
||S = (s1,....,sn) the totality of states of his relevant Environment, his target.
In the precedent matrix the progress of the transaction itself is not really shown.
But we research on the contrary a model that puts directly the accent on the progress of the transaction and non on the result (the gain).
It is precisely the object of our modelWhen the Actor A make a chose, to global transaction between A and S, including action and reaction, can be described by the following diagram:
A and S have formally the same status, so the reply of A to a solicitation of his environment would follow the same diagram.
Thereafter, we will adopt the here above terminology:
|A, S, ai & sj are called "poles" of the system.
||(A, ai) & (S, sj) are called "dipoles" of the system
It is possible to use our senaire in all cases of the theory of games.
For our purpose, retain simply that the game opposing A & S can necessitate non an alone, but a series of transactions.
This series can be statistically determined, as in the case of "mixed " strategies, or destined to test reactions of the adversary, as in the case of cooperative games.
Beyond this is a possible strategy of learning by "tests and errors".
When, due to a lack of information, the "Actor" can no longer define the matrix of the game, we can, in a first time, suppose that the "Actor" will try to avoid to put himself voluntarily in a state judged undesirable.
We can also suppose that, in order to avoid such situation, he has an idea of the states of the System to avoid.
In other words, we suppose our "Actor" able to realize a partition between the desirable and the undesirable.
This strategy, weaker than the "minimax" rule, is sufficient to allow us to give A & S a group structure.
Indeed, if we define an addition in A such as:exclusively
By definition of Å, it is impossible to choose ai or ai exclusively, so we have:
We define equally Å on S such as :
By defining a neutral element within A and S, a strategy weaker than the minimax rule would be, for the "Actor", to make correspond "impossible decisions" of A with undesirable states of S.
We will call such transactions taboos
When the list of states of S is defined, to look for information means to define the probability that S has to be in such or such state.
The essential point for our purpose is to note that the maximum of A uncertainty (that corresponds to a uniform probability of S state) is growing with the number of states p defining S.
One of preferential means of A to decrease his uncertainty is to "condense" or to "aggregate" the information; in other words to decrease the number of states describing "S.(see "Stability & Information").
To reply, the Actor has then to break the rules of the game, in other words to change, or modify the lists of states of A and S taken into account until this failure.To realize this "outage" of the System, the Actor have to change his description of his interactions with the System.
He has to situate himself and the System within a "meta-System".In others words, he has to develop his strategy on two different levels, which conduct him to a diachronic" analysis..
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