Complex Decision-Making in Economy and Finance. Pierre Massotte
of actions and interactions that are propagated in the network and, after a certain number of steps, it will gradually stabilize in a stable state.
– Finally, this situation to which we have converged will lead to a consolidation of the system’s structures, a strengthening of some of its components such as intrinsic functions at the level of agents or interactions. This phase of capitalization or adaptation will include activities such as configuration adjustment, learning, formalization of certain mechanisms, acquisition of know-how, etc. Thus, the second principle of thermodynamics is not enough if it is applied alone. Many complex systems tend towards order and not disorder. When a system is stable, an action can change it, destabilize it and turn it into disorder, but in fact such a system is placed on a new trajectory that converges towards a new order. In industry, this phase is called the structuring or self-organization phase. Thus, everything begins and ends with the organization.
The difficulty is therefore to know how an order is established in a complex structure. Everything depends of course on the behavior of nonlinear dynamic systems. Two theories are then evoked:
– Catastrophe Theory: as previously mentioned, it was developed by the French mathematician René Thom. In the 1960s, Thom showed how some nonlinear systems could “catastrophically” switch from one state to another. It is actually a jump in the trajectory. However, this very attractive approach is very limited. Indeed, in practice, the mathematical models we had developed were too “reduced” and could never be applied in practice. This is an excellent qualitative approach that allows us to imagine and describe some complex behaviors, but not to predict them. Hence, a limited industrial interest.
– Deterministic Chaos Theory: this is in fact very closely linked to and consistent with the catastrophe theory; it complements it with much greater success. Indeed, in industry, physics or biology, the description of the behavior of an elementary cell or agent can often depend on very few parameters which lead to models that are fairly close to reality, and in this case, it is possible to have a much more precise technique. This has allowed us to show, in the semiconductor manufacturing lines of the IBM Factory in Corbeil-Essonnes, how and when deterministic chaos could appear. And in the 1980s, we were able to develop innovative production management methods to better control its behavior, particularly in an area of low chaos.
2.1.6. How and where do structures emerge?
Complexity theory has a certain universality in that, in Nature, we are surrounded by complex systems with nonlinear functions and interactions. Such systems have the property of evolving in a divergent way, but in a limited space. For example, the number of states that a chaotic system can achieve may or may not be limited, but the extreme values are in a limited space. Similarly, a fractal structure has a dimension represented by a real number, but this is within certain limits. For example, a quasi-volume has a real dimension between integers 2 and 3.
In all complex systems, there is a powerful intrinsic dynamic. The objective is to migrate a system to the border of chaos to turn it upside down and acquire new properties, which we have also called orders. Indeed, these systems evolve according to an internal dynamic in an unpredictable way (because they cannot be calculated) and converge towards an emerging global structure. These considerations therefore lead us to define the following schema of principle in which two totally different approaches to complex system management are included.
Figure 2.1. Two approaches to managing complex systems (from Pierre Massotte – HDR thesis, 1995)
These are in fact two visions of the world and two ways of understanding it:
– on the left side of the figure, we find the Vitalist point of view, which is representative of the conventional approach to the processing of complex systems. A process is analyzed in a global and exhaustive way. By applying the principle of decomposition, the main, or global, tasks are divided into more elementary tasks and so on. The process is therefore modeled through a sequence of transformation functions. It is a static evolution model; by applying a stimulus, we observe and measure results. When the correct control parameters are adjusted, after a number of iterations or calculations, the real system can then be adjusted. We are in the old conception of a state of equilibrium dominated by the concept of action-reaction and predictability. In this static and top-down approach, we generally take the opportunity to simplify the so-called “complex” system or its process; it then becomes possible to automate it using computers. To solve a problem, many functions must be performed in parallel. The difficulty is only related to the performance of the calculation means, and it will always be possible, with appropriate time and investment, to find the right solution;
– the right side of the figure represents the point of view of Mechanists and Connectionists. This is a dynamic, interaction-based approach, which we will call a bottom-up approach. Based on the principles just described, it is a question of generating a global function or of creating a structure or configuration based on the interactions existing in the interconnected network. This makes it possible to obtain a complex system (in the sense of behavior) from a great underlying simplicity (in terms of elementary functions and interactions). The implementation of such advanced concepts still raises many related problems nowadays, not to the performance of the calculation means, but to the overall performance of the emerging order (coherent with an overall objective). This requires an analysis of three points:- the exploitation of instabilities and low chaos to achieve optimal flexibility and responsiveness,- the definition of new associated methods for managing complex systems in order to better control them,- the development of new approaches and simulation tools to validate action plans to be applied to complex systems.
In practice, it would be a mistake to apply only one of the approaches described above. These complement each other and highlight a feedback loop that operates accurately and continuously. The above diagram taken as a whole (right and left sides) forms a dynamic structural whole: one the left, being reductionist, the diversity of the system is reduced while defining strategies and tactics (optimal action plans), while one the right, concerning new forms, configurations and orders are generated. The dynamic is therefore intrinsic and comes from the internal evolution of the whole.
2.2. The implementation conditions for self-organization
To study the self-organization mechanism, we consider systems whose purpose is not known a priori. More specifically, the notion of chance is integrated into the system, and disruption is part of the system’s constraints. The basic principle is that agents, or elements of the system, do not self-organize to ensure that a particular result is achieved, but only to adapt to external disturbances and to facilitate the achievement of an overall objective at the system-wide level. The elements that make up the system pursue an individual, not a global, objective. Cooperation between these elements provides an overall result that can be judged by an observer outside the system who knows the reasons why the system was designed. These lead to the development of robust, adaptive and tolerant systems.
Before analyzing the properties related to self-organization, it is necessary to recall notions related to its usefulness:
– self-organization is a necessary skill in applications where you want to have high responsiveness, high fault tolerance (e.g. computer or machine failure), consideration of a disruption or stimulus or when the system is very complex;
– the objective of self-organization is to allow the dynamic evolution of an existing system, depending on the context, in order to ensure its viability. It allows the entities composing the system to adapt to their environment either by specializing functions (learning) or by modifying the topology of the group and the corresponding interactions. This gives rise to a new organizational model.
2.2.1. Emergence of self-organized patterns
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