**Parallelizing Neuro-fuzzy Economic Models in a GRID Environment**

**Horia-Nicolai TEODORESCU**, **Marius-Dan ZBANCIOC**, **Laura PISTOL**

Technical University of Iaşi

Institute for Theoretical Informatics of the Romanian Academy

Iaşi, Romania

**Abstract**: Modeling and simulating large economic systems, with hundreds of players, is a basic requirement for understanding economic processes even at the scale of a large town where tens of shops are competing. Based on fuzzy logic models, we parallelize computations with the purpose to make them affordable even when larger systems are simulated. After briefly introducing the basic models involving several strategies of the commercial players, we extend the models to group-based hierarchically organized players. The overall models are nonlinear, which favors a rich dynamic behavior. Then, we present the parallelizing procedure and simulation results. Special attention is paid to the dynamic behavior of the market, including transitory regimes, asymptotic stability, and periodicities.

**Keywords**: GRID computing, fuzzy systems, market model, economy, nonlinear dynamics.

**Horia-Nicolai L. Teodorescu** Dr. Dr.h.c., correspondent member of the Romanian Academy, is a Professor at the Technical University of Iasi and at the University Al.I. Cuza of Iasi; he is also Scientific Director at the Institute for Computer Science of the Romanian Academy. Prof. Teodorescu has published more than 30 books, about 300 papers and holds more than 20 patents worldwide.

**Marius Dan Zbancioc** Assistant Professor at the Technical University of Iasi and research assistant at the Institute for Computer Science of the Romanian Academy. He is co-author at 3 books and about 30 papers.

**Laura Pistol** M.S. in Informatics, Research Assistant at the Institute for Computer Science of the Romanian Academy, co-author at 2 papers.

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**CITE THIS PAPER AS**:

Horia-Nicolai TEODORESCU, Marius-Dan ZBANCIOC, Laura PISTOL, **Parallelizing Neuro-fuzzy Economic Models in a GRID Environment**, *Studies in Informatics and Control*, ISSN 1220-1766, vol. 17 (1), pp. 5-16, 2008.

**1. Introduction**

In this paper, we deal with models of the market involving essentially small companies that buy products from large manufacturers and distribute the products. The models dealt with are appropriate for small vendors (commercial agents) who sell common goods. For such agents, the buying price of the products they commercialize may be assumed constant in time and the same for all agents, as they all buy from essentially the same manufacturers or great distributors. Moreover, the products have similar quality and may be assumed identical in all respects. The models are therefore appropriate for agents like boutiques and small shops. Examples of such vendors are small shops selling general merchandise, shops in the street selling eatables, fashionable shops, boutique wineries, and over the counter drugstores. Subsequently, whenever confusion cannot arise, we name the small commercial agents companies, vendors, agents, or firms.

Markets composed of such vendors are often fluctuating widely and may show a large range of prices, not necessarily motivated by economic factors, but frequently motivated by the strategy subjectively adopted by the managers of the shops. To explain at least partly the behavior of these markets and to analyze the outcomes of the strategy adopted, in a certain context – represented by the other vendors – we have developed several models, involving various market strategies [16-19]. The strategies differ in the way the vendors change the price of the products depending on the prices their competition practices and on the profits that the vendors assume to obtain for a specified selling price. The computation of the profits involves reasoning based on fuzzy logic [6-8], [13-15].

The vendors’ strategies may vary from the reasonable seeking of profit maximization to the less reasonable seeking of a profit that is larger than that of the competition. Unreasonable behaviors of the economic agents are well documented in the literature [2-5], [9-11]. It may range from unreasonably hopeful to revenge- and hate-driven behaviors [16-19]. An unknown the vendors have to deal with regards the prices used by the competing agents; the vendors have to learn these prices. However, they do so after some delay. The values of the delays greatly influence the market dynamic behavior [9]. The dynamics is determined based on some arbitrary unit of time; that unit is equal to the time the agents are able to change their prices. We assume all vendors have the same time unit.

The simulation of the market dynamics requires the implementation of models with various strategies, possibly with associations of shops, coordinated by a “central” manager, as well as large number of agents. The use of fuzzy logic in modeling the decision making processes makes the model more appropriate to the qualitative manner the vendors reason, but increases the computation load in the simulations. As the individual decisions are based on the knowledge of the prices used by a large number of vendors, the complexity of the computations is quadratic. Even for medium markets, comprising a few tens of agents, the computation time on a PC becomes prohibitive (hours to tens of hours). For this reason, we developed GRID versions of the models [1], [21-22]. In this paper, we report on the GRID version of our models and on the results obtained by the implementation of the models with a few tens of agents.

In Section 2, we briefly overview the fuzzy models developed in previous papers [16-19]. In Section 3, we present hierarchical (group) models, involving a “main (central) manager and shop” and “dependent shops” that rely on the decisions made by the central manager. Section 2 is devoted to the analysis of the components of the economic fuzzy systems. A basic version of the parallelization of the algorithm is presented in Section 4, while in Section 5 we exemplify results related to the computation time. The final section is devoted to a discussion and to conclusions.

**6. Discussion and Conclusion**

We reported in this paper on the parallelization and computation in a distributed, GRID environment of several market models. Regarding the dynamic behavior of the larger systems simulated under GRID, we can conclude, based on the results, that the increase of the number of vendors in the model does not produce significant changes of the dynamics.

As expected, in markets where all vendors use the same strategy, the delays in the network largely decide the behavior, including the duration of the transitory regimes and the possibility of occurrence of periodic oscillations. Also expected, larger values of the increment – at least for reasonable values of the increment – tend to stabilize faster the behavior in the strategies using fixed increment. In case of markets with vendors that use different strategies (mixed strategies markets), one of the strategies might dominate the behavior, especially the length of the transitory regime.

Regarding the computation time, the use of a distributed environment reduces the computing time approximately by a factor of N, that is, decreases the perceived complexity from *O(N ^{~3})* to about

*O(N*. The complexity as obtained for relatively small numbers of agents (less than 100) appears to be

^{~2})*O(N*, while our theoretical estimation provides a complexity of order

^{~3})*O(N*. We do not have yet an explanation for this problem except that the overhead, for

^{2})*N*< 100, is still very important and simulations do not discern between overhead and the influence of N.

Further work is needed to implement variable price increments on a discrete scale, markets with more than two strategies. In addition, improved modes of distributing the computations must be developed, to reduce the communication time. Indeed, in the present version, the communication complexity is of the order of *O(N ^{2})*. One obvious way to reduce data transfers between nodes is to assign a whole group of vendors to a computing node; this distribution procedure is valid only for group (hierarchic) markets.

**Acknowledgement**

Notice. The contribution of the authors is as follows. Sections I to III, V, and VI have been written by the first author, with the consulting of the other authors. The second author, with consulting from the first author, has written section IV. The paper is based on the models proposed by the first author and presented in the papers [16-19], authored by the first two authors. The opinion of the first author is that a better parallelization could be obtained by assigning more nodes to a processor and fears that the parallelization proposed here is not very effective, due to large communication times. The second author, with some help from the first, wrote the FuzzyCLIPS code, moreover he wrote the C code for the applications. The third author has helped with obtaining the computation times and in the parallelization process.

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