Cognitive Institutions as a co-ordination mechanism 
of the investment decisions

Stéphanie LAVIGNE

Ph-D Student in Economics

LEREPS (Laboratoire d’Etudes et de Recherches sur l’Economie, les Politiques et les Systèmes Sociaux)
Université des Sciences Sociales (Manufacture des Tabacs), Toulouse I
Tel : 05-61-12-87-19
Fax : 05-61-12-87-08
E-mail : lavigne@univ-tlse1.fr

Stéphane SANCHEZ

Ph-D Student in Informatics

IRIT (Institut de Recherche en Informatique de Toulouse)
Université Paul Sabatier, Toulouse III
Tel : 05-61-12-88-33
Fax : 05-61-12-88-32
E-mail : sanchez@irit.fr

Cognitive Institutions as a co-ordination mechanism of investment decisions.
A model of learning on an artificial stock market

Stéphanie LAVIGNE
Ph-D Student in economics, University of Toulouse I

Stéphane SANCHEZ
Ph-D Student in informatics, University of Toulouse I

Abstract

In this paper, an artificial financial stock market is presented. This market is composed of heterogeneous investors with learning capabilities. Those investors have an implicit objective in our model : they have to increase the value of their portfolios composed of stocks and liquid assets. We endow the investors with a target of satisficing and not with an objective of maximization. The model intends to analyze the decisions of investment of those agents and their direct interactions to understand the dynamic of the financial market. Our main purpose is in fact to explain the growth of the stock market capitalization recently observed on financial markets, and especially on the “New Economy” market. We analyze the price formation process while considering the markets dynamics as the result of direct interaction between investors.
In this paper, we attach a particular importance to the information published by rating agencies. We show that this information, considered as a cognitive institution, allows the coordination of the decision of investment.
In fact, we create two kinds of simulations: the first one in which investors can only observe the market price; the second one in which investors have access to an exogenous information: the information published by the rating agencies. The first kind of simulations shows that the market rapidly reaches an equilibrium state while the second kind is characterized by a speculative dynamic. We show that the exogenous information has an influence on the market dynamic: this information acts in favor of the instability of the market while driving the decision of the investors in the same direction, towards the same focal point.
The objective of the paper is, in fine, to demonstrate that the information published by rating agencies, that is to say exogenous signal, participate to generate speculative dynamics on financial markets.

Key Words: 
Cognitive Institutions, information, heterogeneous agents, interacting agents, learning, stock market, coordination, price formation process, speculative dynamics

Introduction 

The American Stock Market has been characterized by an increase without precedent of the capitalization of firms belonging to the sector called the “Net Economy” (Orléan, 1999). Parallel to this price dynamics, we must note the increasing presence of a particular category of investors on the American financial market: the Institutional Investors, among which pension funds, mutual funds or hedge funds. These actors hold today a significant fraction of the stocks quoted on the financial market and are considered as fundamental actors of the new model of capitalism: the fiduciary capitalism.

Our main purpose consists in justifying the market dynamics thanks to a detailed analysis of the process of investment of Institutional Investors. We intend to explain the global dynamic on the financial market, that is to say the financial bubble, as the aggregation of the decisions of the different investors.

We refer to a special definition of the financial market: we consider this market as a complex system in permanent evolution; as a system which the outcome is explained by the interaction processes between its components. We refer to the works that consider economy as “an evolving complex system” (Arthur, Durlauf, Lane, 1997), as “an adaptative nonlinear network” (Holland, 1988). The common point to these approaches is the stress laid on the dynamic and on the interactions between the heterogeneous agents that compose the system.

We are led to reject the fiction of the representative agent, even if it is very used in macroeconomic models (Malinvaud, 1995). Most of these models are based on the simplified assumption that the choice of an agent of a same category can be represented by the choice of a representative agent that maximizes his utility function. The dynamic of the system is thus considered as the result of the aggregation of the individual preferences through the figure of the representative agent (Kirman, 1992). While this fiction can be used to describe static states, it present some limits for our demonstration.  This fiction strengthens the hypothesis of homogeneity of the agents and denies for that reason one of the fundamental economic rule that justifies profit by the different preferences or expectations between the agents that constitute the market (Arrow, 1987). On the contrary, we consider that the market dynamics results of the confrontation of the opinion and of the evolution of heterogeneous agents (Kirman, 1992, 1998; Tordjman, 1997).

To study the process of investment of the agents and their opinions about the price dynamics, we build an artificial financial model using advanced software engineering techniques. The advantage of these techniques is that they enable us to understand the global dynamic as the outcome of the interactions between the investors composing the market. Our aim is to justify the investment decisions on the financial market and the behavior of investment of the agents.

We analyze investment decisions according to the information given to investors. We distinguish two kinds of information: an endogenous one representing information produced by the investors’ interaction; an exogenous one representing the information produced by financial intermediaries such as rating agencies or financial analysts (Tadjeddine, 2000). We carry out two kinds of simulation according to this distinction on the nature of the information. The first type is the one in which investors only have endogenous data, as the price of stocks or the historical data of prices on the financial market. The second type is the one in which investors have public information produced by financial analysts about the expectations of growth of stock prices.

We first show that investors manage to co-ordinate their investment decisions and that the market quickly reaches an equilibrium state. On the other hand, when they have exogenous information, we show that investors adopt mimetic behaviors because they follow this information: the market is characterized by a financial bubble.

This artificial model enables us to show the role of cognitive institutions in the market dynamics and most precisely their role in the co-ordination of the investment decisions. By cognitive institution, we mean “the institution that polarizes anticipations made by the agents with different representations of their environment”, (Walliser 2000). We show that cognitive institution – represented here by the exogenous information – play a role on the evolution of the system. Cognitive institutions guide the expectations of the investors towards the same focal point. Thus, the model is a modest contribution to the analysis of the financial market dynamics and most precisely of the financial bubble phases.

Before introducing the hypothesis of the model and the main results, we present the two thesis that can be opposed to justify the price formation mechanism on the financial market.

The first thesis rests on the efficiency hypothesis which stipulates that prices are perfect aggregator of the market information: they contain all available information on the market. Prices reflect the “intrinsic value” or “fundamental value” of the stocks (Fama, 1965). This first thesis, called “standard evaluation” or “fundamental evaluation”, means that the stock prices are the actualized sum of the future flow of earnings generated by the firm during its activity (Orléan, 1999). This first kind of evaluation supposes that investors maximize their utility function under financial constraints, make rational expectations and take their decisions without taking into an account the other agents. Under these conditions of efficient market and rational expectations, the financial market is characterized by an equilibrium state: stock prices reflect the “true” value of the firm. In these configurations, financial bubbles or crashes, defined as deviation with regard to the equilibrium state, are considered as exceptional situations on the market. These turbulences can be explained on the first hand as external shocks, on the other hand as irrational investment behaviors.

The second thesis, called the “non standard evaluation” or “speculative evaluation” (Orléan, 1999), brings a different representation of the market dynamics. According to this approach, prices do not only reflect the fundamental value but also integrate the expectations of the agents about the system dynamics. Stock prices are apprehended as the result of the investment decisions: they represent the agreement of the financial community because they are an aggregator of the average behavior of the agents. “The financial market organizes the confrontation between personal opinions to produce a judgment which have a reference value”, (Orléan, 1999, p 32). This approach does not mean that prices are only determined by the behaviors of the investors. It means that investors take account of the other agents and most precisely of their environment which moves under their own actions. This approach allows us to justify turbulences on financial market as financial bubbles. Turbulences can be explained by the auto-referential process that characterized the investment decisions. Indeed, while trying to discover the average opinion on the market, investors can lead prices to excessive levels in comparison with the real economic data. Prices on financial market emerge not because they reveal the “true” value of the firm but “because (they) express the major opinion of the financial community”, (Orléan, 1999, p 57).

1- FOR A JUSTIFICATION OF THE ARTIFICIAL MODEL

The artificial model, that we present, is built thanks to advanced software engineering techniques and more precisely to the classifiers systems. Which are the advantages of those systems to deal with the mechanisms of price dynamics?

Classifiers systems are instruments particularly well adapted to the analysis of the emergence of a complex dynamic, like the phenomenon of bubble on the financial markets. They are well adapted to study a global dynamic resulting from the interactions between the different agents composing the system. On a theoretical level, those systems belong to the works that search microeconomics bases to macroeconomics since they explain an emergent global dynamic as the consequence of the individual behaviors - knowing that the environment exerts an influence on the decision process - (Paulré, 2000). We especially mobilize classifiers systems for these tools make it possible to analyze the decision process in a context of uncertain and evolutionary future. Classifiers systems allow to analyze the emergence of beliefs and the emergence of rules of investment, knowing that these rules are not fixed ex-ante but result from the many processes of interaction. It should be considered that each simulation carried out provides an exploration of the possible dynamics of the financial market: “each simulation giving the idea of one of the possible behaviors of the system”, (Tordjman, 1997, p 878).

The recourse of classifiers systems supposes a particular theoretical posture, that of the evolutionary research program and overall the program of Cognitive Economy (Walliser, 2000). This posture recognizes the importance of the investors’ cognition to explain their behaviors and the dynamic of the market which result from it. It is a question of considering that agents are endowed with beliefs on their environment, with capabilities of learning and adaptation in an evolutionary environment. The beliefs of the agents are not fixed but evolve in the course of time. Financial markets are thus characterized by evolutionary dynamics: the model is not referring to a static state but rather to a permanent innovation introduced into the system. Investors are modeled by classifiers systems which permit to analyze the evolution of the rules of investment in a context of dynamic environment.

If we refer to the cognitive approaches, it is especially because they grant a central place to the process of learning by regarding it as the driving principle of the evolution of the system. In our model, learning results from the evolution of investors beliefs and more precisely of the evolution of their rules of decision. We consider learning as an adaptative and a path-dependent phenomenon because its direction is function of the past experiences and the knowledge accumulated by investors (David, 1985, Arthur, 1992, Tordjman, 1997). Learning operates by induction in the model: at the start, each investor is unaware of the profit associated with each possible action, the result of each action being dependent on the actions of the other participants. Investors only observe the sequence of the actions and the past rules of decisions to try to find some regularities. The process of learning is characterized by an alternation of phases during which each investors try to select the “good” rules, that is to say rules that generate profit. We can consider two phases in the learning process: the first one is called the “exploration phase” and consists in discovering the profiles of profit; the second one is called the “exploitation phase” and consists in playing again the best actions, i.e those which generate profit. We consider that the investors’ rationality enables them to summarize the past profits and to create an index of profit for each activated rule, knowing that investors tend to reinforce the rules which generate profit. 

But which kind of rationality do we mobilize to characterize investors?
Investors are endowed with bounded rationality in the sense that 1) each agent does not know the whole options that are offered to him : one speaks in this case about informational limits ; 2) each agent is not able to evaluate all the consequences of its choices : one speaks in this case about computational limits. Investors are not perfect calculators because they are neither able to solve maximization program, nor able to evaluate the effect of each decisions (Simon, 1979). This form of rationality could be interpreted as a weak one but we interpret it, on the contrary, as a form of completed rationality which recognizes the real limits in the means of choices of investors (Mongin, 1984).

Bounded rationality supposes the introduction of a new concept: the concept of satisficing. It does not mean that agent do not choose the best action. Agents select a satisfactory action whose evaluation is higher than the threshold of aspiration fixed initially. In our model, the objective of investors is not to determine the rules of investment that maximize the portfolio value but the rules which make it possible to increase this value. Bounded rationality supposes cognitive capacities less demanding than the ones required by the maximization program: investors do not need nor to consider the whole scenarios, nor to evaluate the exact maximum value of the portfolio.

The rationality which we mobilize is situated in the sense that agents must adapt their choice to the concrete problem which they are confronted: the object is to take a decision in a dynamic environment and to generate an increase of the portfolio value. Rationality is situated in the sense that agents take account of the resources of the environment to make their decisions of investment: the environment provides resources which facilitate their actions (Laville, 2000). Lastly we consider that the rationality is cognitive in that agents must carry out the adequacy between their personal information and their expectations about the system (Walliser, 2000).

2 - MICROSTRUCTURE OF THE MARKET

We propose to analyze the price dynamics on the financial markets starting from the assumption according to which prices are determined by the “confrontation between the personal opinions of the investors”, (Orléan, 1999, p 32). We analyze, through several simulations, the price dynamics generated by the interaction of heterogeneous and adaptative agents.

2-1: Investors

At each period, investors must take a decision of investment in a dynamic environment. They can take four types of decisions:  purchase, sell, ignore or conserve stocks.
Investors are heterogeneous in the sense that they manage portfolios of different amount, and although they have theoretically access to the same information, they do not use it in an identical way to take their decisions. Portfolios managed by investors are composed of stocks and liquidities, the latter representing a random percentage of the amount of stock and being not able, by convention, to exceed 100 % of the total amount of the stocks.

Investors have an implicit objective through the system of remuneration of rules that we have created: it is an objective of profit in accordance with the principle of satisficing and not an objective of maximization. The investment rules mobilized by investors are rewarded when they generate an increase of the portfolio value and penalized when they lead to losses. According to the functioning of classifiers system, a rule is reinforced if it generates profit. So, the system is likely to generate an increase in the portfolio value as well as speculative dynamics on the financial market.

Investors take their decisions under budgetary constraints, transactions being impossible when they do not have sufficient liquidities. No purchase order can be executed if investors miss liquidities. Thus, investors can be constrained to sell stocks to get liquidities in order to by new stocks.

Investors are endowed with capacities of learning. At t=1, they take a decision and analyze the result of their decisions at t=2. They readjust their rules of investment according to profits or losses that incurred and they select the rules which generate profits in the system.

Investors’ rationality can be described as limited and adaptative rationality. Investors have limited cognitive and computational capacities in the sense that 1) they are unable to test all the possible strategies, 2) they build procedural knowledge to modify their behavior of investment according to the evolution of their environment and according to the behavior of the other agents.

2 – 2: The market 

The market is composed of twenty investors who must distribute their portfolio on ten firms. If investors are heterogeneous agents, firms are also entities with different characteristics. Firms are different by their capitalization since the number of stocks and the price of stocks are different for each firm. It is advisable to specify that in our artificial model, there is neither creation, nor destruction of stocks during the 4000 periods over which the various simulations are carried out.

At t=0, the market is created in a random way: stock prices and the distribution of the investors’ portfolio are generated in a random way.

We create an indicator to characterize each firm: this indicator can be compared to a classification of firms produced by a rating agency or by financial analysts. We call this indicator “Expectated Percentage of Growth” (EPG). It attests the potentialities of growth for the firm because it reveals the expected percentage of growth for the stock price. We propose a classification of the firms according to this criterion, knowing that this indicator can take values between – 10 % and + 10 %. Negative values attest unfavorable prospects for a potential increase of the stock prices. On the contrary, positive values attest of favorable prospects. It should be noted that the values of EPG are generated in a random way. The EPG indicator enables to highlight the role of the beliefs and the expectations of the investors: do they integrate the information provided by the EPG criterion in their decision of investment?

We must specify that the EPG indicator announces expectations of growth of the stock prices for the following period. We make the simplify assumption that the prospect for growth announced by the rating agency are correct. Thus we create a system of remuneration that tends to support the rules of investment which are in agreement with the expectations announced by the agency. The object of this system of remuneration is to show the influence that the EPG indicator can exert on the beliefs and expectations of the investors and in fine on the market dynamics.

We create an institutional rule on the market, this rule having for vocation to avoid the tendency to speculation. Thus investors can only propose a purchase price ranging between 0 % and 10 % of the current price: they can only propose a selling price ranging between 0% and – 10 % of the current price. This rule demonstrates the organizing function of the market since we postulate that institutional rules are a framework for individual action (Lesourne, 1991).

We finally make the simplifying assumption that there is no cost of transaction on this market and that information is free and accessible to all investors without discrimination.

2 – 3 : Informational signals on the financial market

One of the essential tasks of the model maker is to specify the information at the disposal of the various investors. Investors receive two kind of information: exogenous signals which indicate the information produced outside the financial sphere and endogenous signals which represent the information produced by the investors on the market (Tadjeddine, 2000).

Exogenous signals design information produced outside the financial market: it is represented, in our model, by the number of firms, the number of stocks on the market, the number of stocks that can be bought by investors according to their liquidities, the initial price of the stocks and the classification of the firms according to the EPG indicator.

Endogenous signals represent information which results from the confrontation of the investors’ opinions: they are signals on the investors intentions revealed through the stocks price. Among these signals are 1) the current price of the different stocks, 2) the historical data for the stocks price over the twenty, the ten and the last two periods, 3) the configuration of the stock : does the stock has a tendency to the purchase or the sale ? The historical data on the financial market enables us to postulate the existence of chartist investors as well as the role of the memory in the decisions of investment. Do investors hold account of the past data to take their decisions? Do they have a short term or a long term memory?

2 – 4:  Orders on the financial market: the role of the auctioneer

We reproduce the functioning of the pre-opening of the Stock Exchange: investors take their decisions in a simultaneous way and transmit their sale and purchase orders for each firm to the auctioneer. The latter treats the orders firm by firm, the order of treatment of firms being carried out in a random way.
Purchase orders are accepted by the auctioneer if investors have sufficient liquidities to buy stocks. A purchase order will have priority on the others if it proposes the highest purchase price. Conversely, a sale order will have priority if it proposes the weakest selling price.

All orders can not be carried out: certain investors can be rationed if they do not have sufficient liquidities or if they do no find a sufficient counterpart. But at the beginning of each period, orders systematically reset to zero.

2 - 5: The unit of selection :

The unit of selection is not the investor or the firm but the rule of investment mobilized by the agent. At t=0, the model is composed of 4000 rules of investment which have all the same weight. At t=1, the rule selected by each investor results from a random choice. By a process of induction, investors analyze the outcome of their investments decisions and replay the rule according to the profit obtained. We create a double system of remuneration: a first one related to the stock prices differences between two periods; a second one related to the fact that investors take account or not of the information produced by the rating agency (see Appendix).

Each investor evaluates the consequences of his decisions of investment by the following procedure: he creates a rule of reinforcement which supports the advantageous actions. The process of learning is path-dependant for it depends on the past profits; it is also inductive for the investors make inferences starting from the profits and losses observed. In our model, there is neither creation, nor destruction of rules but simply adaptation of the strategies of investment mobilized by investors in a dynamic environment. This it is not of a purely evolutionary model creating a variety of rules in the system, but a model of learning since investors continuously adapt to their environment.

III – Results:  

We present the results of two types of models : the first one in which investors only have endogenous signals, and in particular historical data of prices ; the second one in which agents take their decisions starting from the exogenous information produced by the rating agency.
In each simulation, one analyzes the market dynamics by building a stock index to study the evolution of the firms’ capitalizations. Our objective is to evaluate the total performance of the market and the positioning of the various firms compared to the index. 
We also build a typology of investors according to their performances of investment, i.e. according to the increase or decrease of the portfolio value. This typology enables us to inform the determinants of the investment on the financial markets and to analyze the performances of the portfolios compared to the stock index. Do the investors reproduce the performances of the market, under-perform or out-perform the market? 

Each simulation is carried out over 4000 periods, one period being able to be theoretically comparable to one day of pre-opening to the Stock Exchange.  

3 - 1:  Coordination of the investment decisions: towards an equilibrium 

3-1-1:  The dynamics of market: an equilibrium state 

The analysis of the stock index shows that it grows on average of 90 % on the period, and this in all simulations carried out. This progression of the stock index is not continuous : the market always goes through a phase of strong growth (bubble), then through a decrease of firms capitalizations (crash), to finally stabilize itself after the period of learning  More than to stabilize itself, the market balances between t=2000 and t=3000 for the whole simulations carried out. Investors manage to co-ordinate their behaviors of investment without having a reference of equilibrium identical for all at beginning of the play, reference on which they could have a priori coordinated each other. How is it possible to justify such a co-ordination?  

We cannot explain it by the fact that investors have an identical idea of the equilibrium market price for there is any reference, neither precedent nor convention at the beginning of the simulation. Thus, we are led to propose an explanation concerning the remuneration of the rules of investment. At the beginning, the rules of investment are mobilized in a random way. Let us imagine that the first rules are remunerated in a positive way, having generated the realization of appreciations and thus an increase in portfolios value. Our structure of remuneration encourages agents to repeat decisions which generate profit, decisions that can be described as “good” actions, and not to repeat decisions which lead to losses. 
In other words, if the first emergent rules lead to profit, these rules have a strong probability of being selected again. The investor is likely not to explore the whole possible alternatives because of his limited computational capabilities. And if all the investors act in the same way, each one persisting in the exploitation of the first emergent rules, they can succeed in coordinating each other and the price stabilize after the learning period. 
Because there are no fundamental variables and because only the actions of the other agents count, the place where the price stabilizes is random: it depends on the direction obtained by the first “good” rules which emerge (Tordjman, 1997, p 891). 

We show that a common characteristic to all investors is that they do not take account of the historical data on the financial market to take their decisions of investment. Investors evaluate the result of their actions on an extremely limited horizon: in all simulations carried out, they only take account of the historical data over the two last periods to take their decision. This observation can make it possible to confirm the thesis according to which the dynamic of financial market is exposed to the short termism of the investors.
"Rare must be the fields of the human behavior where the history counts as little as in the financial universe ", Galbraith (1992), p 20.  

3-1-2: For a typology of the Investors  

In this first type of model, we observe speculative behaviors that are extremely reactive behaviors to the recent movements of prices. 
Despite the common points previously drawn up, that is to say co-ordination of the investment decisions and short term memory of investors, the detailed analysis of the strategies of investment and the evolution of the investors’ portfolios reveal three recurring kind of behaviors of investment on the financial market.  

Type 1 includes the investors whose performances of management are weak and negative, although these investors are those which manage the largest portfolios at the beginning. These investors have a very aggressive behavior of investment on the market: at the start, they follow an important policy of purchase until exhaustion of their liquidities, and then they massively sell their stocks before managing to stabilize their portfolios at the end of the simulation. These investors buy whatever the configuration of the stocks on the market and propose sale and purchase prices so that their orders are treated in priority. The rule of investment which generates the highest profit consists in buying a stock whatever its configuration. These investors are speculators without precise strategy in relation to the prices, nor to the other agents. They behave as isolated calculators and seek short-term profits by adopting very aggressive behaviors of investment. 

Type 2 includes the investors whose performance of management is positive while remaining lower than the progression of the stock index. These investors are also speculators since the sale and purchasing orders are very frequent on all the stocks. This group of investors is different from type 1 by the adoption of principles of investment: these investors always speculate in small quantities for the purchase and they sell in a more massive way; they generally buy when the stock has a tendency to be sold – in other words when there is a potential offer - and they sell whatever the configuration of the stock is. Thus, these investors do not behave as isolated calculators but take account of the other agents to make their decision of investment and in particular for their decisions of purchase. 

Finally type 3 gathers the investors whose performances of management are positive and higher than the progression of the stock index. We underline the strong growth of the stocks composing the portfolios of these investors. These agents buy when the stock has a tendency to be sold, that is to say when there is a potential offer, and they sell whatever the configuration of the stock is. Contrary to the investors of the type 2, they are characterized by positions of investment very targeted on certain firms, i.e. by a strong concentration of the portfolios on a reduced number of stocks. Thus their portfolios are not distributed in an identical way on all the stocks: one can speak about targeted strategy. 

The rule that generate the highest profit for this group of investors is the one which consists in preserving stocks whatever their configuration on the market. Thus, these investors practice a management combining short-term positions characterized by movements of purchases and sales on certain firms, and “medium-term” positions because of their stable holdings on a targeted number of firms. As the horizon of these investors is not only the short term, we qualify them of prudent investors, their targeted and stable holdings certainly representing a form of risk aversion.

This first type of model, in which investors have only endogenous signals, enables us to find the stylized facts observed on financial markets, namely 1) speculators who are not averse to risk and who behave as isolated calculators, 2) speculators taking account of the other agents, that is to say strategic calculators, 3) careful investors adopting mixed strategies characterized by an alliance of stable holdings in certain firms and frequent movements of purchases and sales on others. 
3 –2:  Exogenous information like focal point in the co-ordination of the investment decision: a speculative market

In this second type of model, investors can use an exogenous information which is the EPG to take their decision of investment. This indicator is comparable to an information on the fundamental value of the firm, in other words on its real expectations of growth. It enables us to postulate that investors form expectations or representations starting from this exogenous information. Above all, it especially makes it possible to predict dynamics more complex than those revealed in the first type of model. What is the potential impact of the information provided by the rating agency on the evolution of the system? 

3-2-1: The market dynamics: a financial bubble  

Stock index

0

100

200

300

400

500

600

700

800

1

166

331

496

661

826

991

1156

1321

1486

1651

1816

1981

2146

2311

2476

2641

2806

2971

3136

3301

3466

3631

3796

Periods

The analysis of the stock index shows that it grows on average of 600 % over the period for the whole simulations carried out. The market dynamics is open-ended and one observes a continuous growth of the stock prices, that is to say a phase of financial bubble. We do not observe a stabilization of the market, i.e. no co-ordination on a particular equilibrium in this second type of model.

Our analyses show that firms whose EPG indicator is negative or null are those which carry out the worst performances of management. Investors have short term holdings on these firms since the orders of purchases and sales are very frequent. This behavior enables us to advance the assumption according to which investors do not have overall confidence in the prospects of firms with negative or null EPG. On the other hand, the analyses reveal that the firms whose EPG indicator is positive are those which obtain the best performances of management and the three firms with the strongest EPG are those which obtain higher performances than the progression of the stock index. Investors have long-term holdings in those firms. Thus we formulate that investors have confidence in the announced prospect of growth since they have stable holdings on these firms. 

These analyses on the impact of the EPG criterion on investment decisions and market dynamics are reinforced by the fact that investors who follow the recommendations of the rating agency, in other words those who invest in the firms with the strongest EPG, are those which carry out the best performances of management.

These results lead us to highlight the role of focal point played by the EPG indicator. The information published by the rating agency has a real capacity on the orientation and the evolution of the system by allowing the co-ordination of the investment decisions on certain firms, and more precisely those recommended by the rating agency. But how can we justify this mechanism of coordination?

To take their decisions of investment, investors formed representations which they test successively. They also have the EPG indicator allowing them to forge expectations on the prospects of growth of stocks. If all investors take account of the EPG signal, they will all decide to invest in the firms recommended, in other words in the firms having positive EPG, which will mechanically cause a rise of prices since the offer of stocks becomes higher than the demand. Carrying out profits on the firms with a strong EPG thanks to the realization of prices appreciations, the rule of investment will be remunerated and regarded as a “good rule ". Investors will continue to mobilize this rule by a process of self-reinforcement, which will generate a new rise of prices. Finally, there is a self-realization of the expectations of growth announced by the rating agency, in the sense that agents follow the exogenous information and invest in the firms recommended. The consequence of this process is an increase of the capitalization of those firms. The market dynamics which results from this process of learning by self-reinforcement of the “good” rules is not characterized by a co-ordination of the investment decisions, but by a dynamic of financial bubble.

3-2-2:  Typology of the Investors  

The analysis of the rules of investment and the evolution of the investors’ portfolios reveal again three kinds of investors, whose common point is their short-term memory. It arises that investors do not take account of the historical data to take their decisions of investment. Investors only consider the two last periods to decide to invest in firms.  
Like previously type 1 includes investors who manage the largest portfolios at the beginning of the simulation and whose performances of management are weak and negative. These investors speculate in all the stocks and do not have any stable behavior of investment. We cannot advance any particular factor to determine their strategy of investment: these investors do not take account of the configuration of the stocks on the market, nor of the trend of the stock price, nor of the EPG indicator. Concerning the EPG criterion, one even notes a tendency to buy stocks whose EPG value is negative or null, but in a general way, the EPG criterion is not a deciding factor for the investment decisions. Finally, these investors are short-sighted speculators, acting as isolated calculators, without any directing principle relating to the decision of investment. Their purchases and sales are massive and frequent on all firms.

Type 2 includes all the investors whose performances of management are positive while remaining lower than the progression of stock index. Contrary to the preceding group of investors, it is possible to highlight particular criteria of investment for type 2. The EPG criterion is a determining factor for purchase and sale orders: investors have stable holdings in firms with positive EPG and speculate in a permanent way in firms whose EPG is negative or null. At the beginning, these investors adopt a short-term strategy. After the period of learning, they adopt a “medium-term” horizon as their stable holdings in the firms recommended by the rating agency prove it. The rule of investment which generates the highest profit is the one which consists in preserving stocks whose EPG is positive. 
These investors buy when stocks have a either a tendency to be sold or to be purchased: their behaviors of investment are a function of the existence of a potential offer at the preceding period. So these investors do not act as isolated calculators but take into account all the agents on the financial market. They adopt stable behaviors of investment on the firms recommended by the rating agency. 

Type 3 includes the investors whose portfolios growth is higher than that of the stock index. For this group of investors, the EPG criterion is a determining factor in the decision of investment. These investors have very stable holdings – and even behaviors of quasi-monopoly - in firms with positive EPG. They also behave very aggressively on firms with negative or null EPG. In other words, these investors adopt a “long-term” strategy on firms recommended by the rating agency, and a short-term behavior on firms with the worse prospects for growth. In a very clear way and concerning their decision of investment on the firms with negative EPG, investors of type 2 buy when the price increases, sell when the price drops and conserve stocks when the price is stable: this behavior corresponds to the principle of destabilizing speculation. This group of investors generally proposes a very high purchase price - near to 10 % - so that their orders are treated in a priority way. 
Lastly, the rule which generates the highest profit after the period of learning is the decision to preserve stocks whose EPG is positive. 

This group of investors manage to out out-perform the market by adopting a complex strategy: 1) they take into account the other agents on the market, i.e. the existence of a potential offer on the market; 2) they take into account the EPG criterion to decide to invest in such or such firm; 3) they adopt long-term strategy that can be described as prudent because it consists in preserving stocks whose EPG is positive, i.e. stocks " recommended " by the rating agency. 

IV–Conclusion  

The interest of our model is to register the dynamic on the financial markets from the point of view of a cognitive perspective, perspective that grants a central role to the beliefs of the agents and their processes of interaction on the market. It is a question of analyzing the decision process of investors in a situation of uncertainty through the formation of expectations. It is especially a question of explaining the emergence of a global dynamic on the financial market starting from the interaction of investors endowed with capabilities of learning, i.e. able to adapt to the evolution of their environment which evolves under the effect of their own actions of investment.

The model makes it possible to highlight several elements as for the possible dynamics of the financial markets and makes it possible to find stylized facts that exist on financial markets.

The model initially enables us to give up the fiction of the representative agent, agent designed like an isolated calculator maximizing its utility function (Kirman, 1992). On the contrary, we consider heterogeneous agents, acting in parallel and taking account of the other agents, i.e. of the collective opinion, to form their decisions of investment. Market dynamics is largely based on an auto-referential conception of the prices formation which underlies that prices are the product of the investor’s interaction. Prices are the result of the opinions of the community of the investors (Keynes, 1936; Orléan, 1999).

The model exhibits a feature characteristic of the decisions of investment in an uncertain environment: the short-term horizon of investors. Indeed various simulations show that investors do not take account of the historical data of prices on the 20 and 10 last periods for their decisions of purchase or sale. They only take into account the historical data over the two last periods to take their decisions of investment. This result consolidates in particular the analyses on the financial speculation showing the euphoric and short-sighted character of investors during the phases of strong growth of the Stock Exchanges (Kindleberger, 1989, Galbraith, 1992)

Our model also makes it possible to bring lightings on the question of the co-ordination of the decentralized decisions of heterogeneous agents. Indeed, it allows answering partly to an old question: how can an economic order emerge from the interactions of agents motivated by the search for their personal interests? We show that when investors have only endogenous signals which are the result of their interactions they succeed in coordinating each other on a stable state of the market. This result is all the more surprising that there is not any precedent or a common reference enabling them to co-ordinate quickly (Schelling, 1980). We explained this result by the structure of remuneration of the rules: the first emergent rules, if they generate increases in portfolios value will be remunerated in a positive way. Classifiers systems make that these rules will be mechanically replayed. If all investors do the same, in other words if all replay the first emergent rules, the system is likely to converge towards an inert or equilibrium state (Tordjman, 1997). 

Finally, the artificial model makes it possible to show the role of cognitive institutions – here the information produced by the rating agency - in the dynamic of the financial markets. Exogenous information relates to the prospects for growth of the stocks prices and makes it possible to direct the representations of investors in the same direction. The rating agency has a real capacity of influence on the orientation of the system and contributes to generate a speculative dynamics. We showed that the EPG criterion makes it possible for the agents to forge representations on the prospects of growth of the firms. When they take account of this criterion and invest in the "recommended" firms, investors cause mechanically, by their actions of investment, a rise of stocks price: there is a self-realization of the expectations of growth generated by investors.

This model finally enables us to postulate that cognitive institutions, as exogenous information on financial markets, have a real capacity of influence on the evolution of the system. They are in particular a generating factor of instability on the financial market, the market dynamics being characterized by an important financial bubble. 

We specify that the object of the model does not consist in giving an opinion on the utility of the rating agency or on the utility of financial analysts on financial market. Rather it is to underline the influence that can exert exogenous information on the investors’ expectations and the market dynamics.  

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APPENDIX

Remuneration of rules of investment

One considers the following variables for one period of simulation Pi and for one firm:

pi1: stock price at t1 before the transaction (i.e. price at the moment of the decision)
pi2: stock price at t2 after the transaction (i.e. new stock price)
Gi: remuneration of the rule involved in the action of investment for period Pi
Gij: remuneration of the rule from period Pi to period Pj
NbSf: number of stocks of the firm
NbSpi: number of stocks purchased at period Pi
NbSoi: number of stocks owned at period Pi
NbSsi: number of stocks sold at period Pi.

1 – Remuneration of rules in simulations without EPG:

For this kind of simulation, remuneration of a rule of investment is calculated only considering gains or losses that it generates.

1-1- Remuneration of classifier system PURCHASE/IGNORE:

IGNORE:

PURCHASE:

The rule that generates a purchase order is never remunerated at the moment of the transaction (period Pi) for when one buys a title one only transforms liquidities into stocks. But it is remunerated by gains or losses that the acquired stocks generate from the period of purchase: in fact, a purchase rule is remunerated as long as the investor possesses the stocks.
So, if Pi is the period when the investor purchases stocks of a particular firm and Pj the current period, the remuneration of the rule will be:

1-2 Remuneration of classifier system SELL/CONSERVE:

SELL:

CONSERVE:

2 – Remuneration of rules in simulations with EPG:

For this kind of simulation, remuneration of a rule of investment is function of expectation on new stock prices calculated considering the information given by EPG (Expected Percentage of Growth of stock price) and of gains or losses that it generates.

One considers that EPGi represents the EPG for the period Pi.

2-1- Remuneration of classifier system PURCHASE/IGNORE:

IGNORE:

PURCHASE:

The rule that generates a purchase order is, at the moment of the transaction (period Pi), only remunerated according to the EPG rating. Then it is remunerated by gains or losses that the acquired stocks generate and by expected gain according to EPG.

 
2-2- Remuneration of classifier system SELL/CONSERVE:

SELL:

CONSERVE: