تحول معامله گران و مکتب کسب و کار با برنامه نویسی ژنتیکی: معماری جدید بازار سهام مصنوعی بنگاه مدار

In this paper, we propose a new architecture to study artificial stock markets. This architecture rests on a mechanism called ‘school’ which is a procedure to map the phenotype to the genotype or, in plain English, to uncover the secret of success. We propose an agent-based model of ‘school’, and consider school as an evolving population driven by single-population GP (SGP). The architecture also takes into consideration traders’ search behavior. By simulated annealing, traders’ search density can be connected to psychological factors, such as peer pressure or economic factors such as the standard of living. This market architecture was then implemented in a standard artificial stock market. Our econometric study of the resultant artificial time series evidences that the return series is independently and identically distributed (iid), and hence supports the efficient market hypothesis (EMH). What is interesting though is that this iid series was generated by traders, who do not believe in the EMH at all. In fact, our study indicates that many of our traders were able to find useful signals quite often from business school, even though these signals were short-lived.

Over the past few years, genetic algorithms (GAs) as well as genetic programming have gradually become a major tool in agent-based computational economics (ABCE). According to Holland and Miller (1991), there are two styles of GAs or GP in ABCE, namely, single-population GAs/GP (SGA/SGP) and multi-population GAs (GP) (MGA/MGP). SGA/SGP represents each agent as a chromosome or a tree, and the whole population of chromosomes and trees are treated as a society of market participants or game players. The evolution of this society can then be implemented by running canonical GAs/GP. Arifovic 1995 and Arifovic 1996, Miller (1996), Vila (1997), Arifovic et al. (1997), Bullard and Duffy 1998a, Bullard and Duffy 1998b and Bullard and Duffy 1999, Staudinger (1998) are examples of SGA, while Andrews and Prager (1994), Chen and Yeh 1996, Chen and Yeh 1997 and Chen and Yeh 1998, and Chen et al. (1996) are examples of SGP. MGA/MGP, in contrast, represents each agent as a society of minds ( Minsky, 1986). Therefore, GAs or GP is actually run inside each agent. Since, in most applications, direct conversations (imitations) among agents do not exist, this version of applications should not be mistaken as the applications of parallel and distributed GAs/GP, where communications among ‘islands’ do exist. Examples of MGA can be found in Palmer et al. (1994), Tayler (1995), Arthur et al. (1997), Price (1997), Heymann et al. (1998). While these two styles of GAs/GP may not be much different in engineering applications, they do answer differently for the fundamental issue: ‘who learns what from whom? ’ ( Herreiner, 1998). First, agents in the SGA/SGP architecture usually learn from other agents’ experiences, whereas agents in the MGA/MGP architecture only learn from their own experience. Second, agents’ interactions in the SGA/SGP architecture are direct and through imitation, while agents’ interactions in the MGA/MGP architecture are indirect and are mainly through meditation. It is due to this difference that SGA/SGP is also called social learning and MGA/MGP individual learning ( Vriend, 1998). At the current state, the SGA/SGP architecture is much more popular than the MGA/MGP architecture in ABCE. In addition to its easy implementation, the reason for the dominance of SGA/SGP in ABCE is that economists would like to see their genetic operators (reproduction, crossover, and mutation) implemented within a framework of social learning so that the population dynamics delivered by these genetic operators can be directly interpreted as market dynamics. In particular, some interesting processes, such as imitation, ‘following the herd’, rumors dissemination, can be more effectively encapsulated into the SGA/SGP architecture. However, it has been recently questioned by many economists whether SGA/SGP can represent a sensible learning process at all. One of the main criticisms is given by Harrald (1998), who pointed out the traditional distinction between the phenotype and genotype in biology and doubted whether the adaptation can be directly operated on the genotype via the phenotype in social processes. Back to Herreiner's issue, if we assume that agents only imitate others’ actions (phenotype) without adopting their strategies (genotype), then SGA/SGP may be immune from Harrald's criticism. However, imitating other agents’ actions are a very minor part of agents’ interactions. In many situations, such as financial markets and prisoners’ dilemma games, it would be hopeless to evolve any interesting agents if they are assumed to be able to learn only to ‘buy and hold’ or ‘cooperate and defect’. More importantly, what concerns us is how they learn the strategies behind these actions. But, unless we also assume that strategies are observable, it would be difficult to expect that they are imitable. Unfortunately, in reality, strategies are in general not observable. For instance, it is very difficult to know the forecasting models used by traders in financial markets. To some extent, they are secrets. What is observable is, instead, only a sequence of trading actions. Therefore, Harrald's criticism is in effect challenging all serious applications of SGA/SGP in ABCE. Although Harrald's criticism is well acknowledged, we have seen no solution proposed to tackle this issue yet. At this stage, the only alternative offered is MGA/MGP. In fact, it is interesting to note that many applications which heavily rely on evolution operated on the genotype (strategies) tend to use MGA/MGP. Modeling financial agents is a case in point. What is ironic is that this type of application is in essence dealing with human interaction and thus requires an explicit modeling of imitation, speculation and herd behavior. As a result, MGA/MGP is not really a satisfactory response to Harrald's criticism. In this paper, we plan to propose a new architecture and hence a solution to Harrald's criticism. This architecture rests on a missing mechanism, which we think is a key to Harrald's criticism. The missing mechanism is what we call ‘school’. Why ‘school’? To answer Harrald's criticism, one must resolve the issue ‘how can unobservable strategies be actually imitable’? The point is how. Therefore, by the question, what is missing in SGA/SGP is a function to show how, and that function is what we call ‘school’. Here, ‘school’ is treated as a procedure, a procedure to map the phenotype to the genotype, or in plain English, to uncover the secret of success. This notion of ‘school’ goes well with what school usually means in our mind. However, it covers more. It can be mass media, national library, information suppliers, and so on. Warren Buffett may not be generous enough to share his secrets of acquiring wealth, but there are hundreds of books and consultants that would be more than happy to do this for us. All these kinds of activities are called ‘schooling’. Therefore, if we supplement SGA/SGP with a function ‘school’, then Harrald's criticism can, in principle, be solved. Nevertheless, to add ‘school’ to an evolving population is not that obvious. Based on our earlier description, ‘school’ is expected to be a collection of most updated studies about the evolving population (evolving market participants). So, to achieve this goal, ‘school’ itself has to evolve. The question is how? In this paper, we propose an agent-based model of ‘school’. More precisely, we consider school as an evolving population driven by single-population GP (SGP). In other words, ‘school’ mainly consists of faculty members (agents) who are competing with each other to survive (get tenure or research grants), and hence the survival of the fittest principle is employed to drive the evolution of faculty the way it drives the evolution of market participants. To survive well, a faculty member must do her best to answer what is the key to success in the evolving market. Of course, as the market evolves, the answer also needs to be revised and updated. Once ‘school’ is constructed with the agent-based market, the SGP used to evolve the market is now also run in the context of school. The advantage of this setup is that, while the SGP used to evolve the market suffers from Harrald's criticism, the SGP used to evolve ‘school’ does not. The reason is simple. To be a successful member, one must publish as much as she knows and cannot keep anything secret. In this case, observability and imitability (replicatability) is not an assumption but a rule. In other words, there is no distinction between the genotype and phenotype in ‘school’. Hence, Harrald's criticism does not apply and SGP can be ‘safely’ used to evolve ‘school’. Now, what happens to the original SGP used to evolve the market? This brings up the second advantage of our approach. Since the function of school is to keep track of strategies (genotypes) of market participants and to continuously generate new and promising ones, any agent who has pressure to imitate other agents’ strategies or to look for even better strategies can now just consult ‘school’ and see whether she has any good luck to have a rewarding search. So, the original operation of SGP in the market can now be replaced by SGP in ‘school’ and a search procedure driven by the survival pressure of agents. Agents can still have interaction on the phenotype in the market, but their interaction on the genotype is now indirectly operated in ‘school’. An interesting aspect of this approach is to explicitly model the interaction between ‘school’ and the market by introducing a co-evolution model. To survive, school must adapt to market dynamics. On the other hand, market dynamics generate students for ‘school’ who, in turn, bring the knowledge learned from ‘school’ back to the market, and that knowledge may have further impact on market dynamics. While agent-based modeling is a bottom-up approach, one may use a system of two nonlinear difference equations, governing the dynamics of ‘school’ and the market, as a top-down ‘summary’. The difference between our proposed architecture and SGA/SGP and MGA/MGP is also illustrated in Fig. 1, Fig. 2 and Fig. 3.Fig. 1 depicts the market architecture represented by SGA/SGP. The top of Fig. 1 is the market as a single object, and the bottom is a population of directly interacting heterogeneous agents. The direct interaction is characterized by the symbol ‘↔’ among them. By this architecture, the information (knowledge) about the market is openly distributed among all agents. Nothing is kept secret. In between is a symbol ‘=’ (equivalent to), which means that market dynamics is equivalent to the evolution of this population of directly interacting agents. Full-size image (5 K) Fig. 1. The market architecture represented by single-population GAs/GP (SGA/SGP). Figure options Full-size image (10 K) Fig. 2. The market architecture represented by multi-population GAs/GP (MGA/MGP). Figure options Full-size image (12 K) Fig. 3. The market architecture represented by single-population GAs/GP with ‘School’. Figure options Fig. 2 gives the market architecture represented by multi-population GP. The market remains at the top, but there are two essential differences as opposed to the previous figure. First, the single symbol = is replaced by a series of ⇔s. Under these ⇔s is a population of indirectly interacting agents. By ‘indirectly’, we mean that these agents are interacting only through a bulletin board. Imagine that each agent sits in her office and watches the world from the web. They have no direct contact with one other, physically, and in some sense, mentally as well. The information (knowledge) about the market is now privately distributed among agents. Each agent has her own world and keeps her own secrets. The point here is that other agents’ minds are not directly observable, and hence not imitable. Within each agent's mind, there is a society of minds. The evolution of this society is driven by GP. Within this architecture, agents basically learn from her own experience, and not from other agents’ experiences. Thus, it is a typical model of individual learning. Fig. 3 represents the architecture of our proposed modification. Again, the market is placed at the top. At the bottom to the right, it is something between Fig. 1 and Fig. 2. In the phenotype, agents’ interaction is direct and identical to what Fig. 1 shows, whereas in the genotype, it looks something like Fig. 2, where there is no direct interaction. The original connection between markets and agents is now replaced by the connection between agents and school shown at the bottom to the left. Inside school, there is again a population of direct interacting agents (faculty), which is pretty much like Fig. 1. The key elements of our proposed architecture entitled ‘MS-GP’ (standing for GP implemented with ‘School’ in the Market) are the procedures ‘school’ and the search. We shall concretize these procedures with an application to the artificial stock market. The artificial stock market is a new but growing field. Some wonders and missions of this research area have been well documented by LeBaron (2000). In his article, LeBaron distinguishes the recent models of complex heterogeneity from those of simple heterogeneity. The use of heterogeneous agents is certainly not new to finance, and there is a long history to building heterogeneous agent rational expectations models. What is attempted in this set of computational frameworks is to attack the problem of very complex heterogeneity which leaves the boundary of what can be handled analytically. Traders are made up from a very diverse set of types and behaviors. To make the situation more complex the population of agent types, or the individual behaviors themselves, are allowed to change over time in response to past performance. (p.680) One of the missions of these agent-based computational models is to replicate time series features of real markets. While it will continue to be pursued, the focus of this paper will be much more fundamental. As calibration techniques advance, we may expect that sooner or later agent-based financial models will be so powerful that replicating time series features of real markets will not be that daunting. In fact, LeBaron himself has made the following observation: Validation remains a critical issue if artificial financial markets are going to prove successful in helping explain the dynamics of real markets. This remains a very weak area for the class of models described here. Further calibration techniques and tighter test will be necessary… . However, there are some key issues which affect these markets in particular. First, they are loaded with parameters which might be utilized to fit any feature that is desired in actual data… . ( Le Baron, 2000, pp. 698–699, Italics added). Judging from the results of recent progresses in the literature of artificial stock market, that moment will come in a couple of years. When that moment does come, one may start to question how these calibration techniques can be justified, which leads to the foundation of this research: can we regard GAs/GP as a suitable model of learning behavior within society?. The answer can hardly be positive or convincing if Harrald's criticism has not been well taken. We therefore consider this phase of research more fundamental. By saying that, this research tends to modify GP in a manner such that it has a closer connection with human learning and adaptation. MS-GP brings back search behavior, a subject which was once intensively studied in economics but has been largely ignored in the conventional GAs/GP economic literature. As we shall see later, through the idea of simulated annealing agents’ (traders’) search density can be connected to psychological factors, such as peer pressure or economic factors such as economic pressure. Furthermore, the built-in mechanism ‘school’ enables us to investigate the role of ‘school’ or the value of ‘education’ in the evolution of a very specific social process. The statistics generated from simulations, such as the time series of the number of ‘students’ registered, the number of ‘students’ who receives futile or fruitful lessons at ‘school’ can all help us understand how ‘school’, or information industry in general, coevolves with society. In Section 2, we shall present the analytical model on which our artificial market is constructed. In Section 3, a concrete application of the institutional GP to the artificial stock market is detailed. Section 4 provides the experimental design. Experiment results and econometric analysis of these designs are given in Section 5 followed by concluding remarks in Section 6.

The single experiment conducted here has demonstrated the rich dynamics that our artificial stock market can generate. We also show the relevance of this rich dynamics to financial econometrics and behavioral finance. For the latter, we address Peters’ criticism on the efficient market hypothesis as well as the survival test with our dynamics of microstructure. It is interesting to note that, while econometricians on the top may claim that our artificial market is efficient, our traders on the bottom do not act as if they believe in the efficient market hypothesis. This result seems to be consistent with our experience of the real world, and is one of the interesting features one may expect from the bottom-up approach.