Научная статья на тему 'Imitation in economics and management. Part II: imitation in economics'

Imitation in economics and management. Part II: imitation in economics Текст научной статьи по специальности «Математика»

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Ключевые слова
ЭКОНОМИКА / УПРАВЛЕНИЕ / ИМИТАЦИОННОЕ ПОВЕДЕНИЕ / ЭКОНОМИКО-МАТЕМАТИЧЕСКИЕ МОДЕЛИ / ECONOMY / MANAGEMENT / IMITATION BEHAVIOR / FORMAL MODELS

Аннотация научной статьи по математике, автор научной работы — Sanditov Bulat Dambayevich, Mantatova Aryunavalerianovna

This is the second part of a review of imitation and social learning in economics and management. While the first part is primarily concerned with evidence and modeling of imitative strategies from the point of view of organization theory; in this paper we focus on formal models of imitation in economics.

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Текст научной работы на тему «Imitation in economics and management. Part II: imitation in economics»

8. Нусратуллин В.К. Неравновесная экономика. Изд. 2-е, допол. (электронный вариант). - М.: Компания Спутник, 2006.

9. Радаев В.В. Важные условия развития экономической теории // Вестник Московского университета. Сер. 6. Экономика. - 2004. - № 3. - С. 31.

10. Роббинс Л. Предмет экономической науки // THESIS. -1993. - Вып.1.

11. Рузавин Г.И. Концепция современного естествознания: учебник. - М.: Культура и спорт, ЮНИТИ, 1999.

Бартунаев Лазарь Романович, доктор экономических наук, профессор кафедры «Экономическая теория», Бурятский государственный университет. Адрес: 670042, г. Улан-Удэ, ул. Калашникова 18-32. E-mail: grigrass@mail.ru, т. 45-47-70

Bartunaev Lazar Romanovich, Doctor of Economic Scinces, Professor at Economic Theory Chair, Buryat State University. Address: 670042, Ulan-Ude, Kalashnikova St., 18-32. E-mail: grigrass@mail.ru. Tel: 45-47-70

Желаева Светлана Эдуардовна, кандидат экономических наук, доцент кафедры «Экономическая теория, национальная и мировая экономика», Восточно-Сибирский государственный университет технологий и управления. Адрес:670000, ул. Димитрова 4а-23. E-mail: zhelay@yandex.ru, т. 89516230683.

Zhelaeva Svetlana Eduardovna, Candidate of Economic Sciences, Senior lecturer at Economic Theory, National and World Economy Chair, East-Siberian State University of Technologies and Management. Address:670000, Dimitrova St. 4а-23.E-mail: zhelay@yandex.ru. Tel: 89516230683.

УДК 33:005 © B.D. Sanditov, A.V. Mantatova

IMITATION IN ECONOMICS AND MANAGEMENT. PART II: IMITATION IN ECONOMICS

This is the second part of a review of imitation and social learning in economics and management. While the first part is primarily concerned with evidence and modeling of imitative strategies from the point of view of organization theory; in this paper we focus on formal models of imitation in economics.

Keywords: economy, management, imitation behavior, formal models.

Б.Д. Сандитов, А.В. Мантатова

ЭКОНОМИЧЕСКИЕ НАУКИ ОБ ИМИТАЦИОННОМ ПОВЕДЕНИИ: ИМИТАЦИОННЫЕ СТРАТЕГИИ В ЭКОНОМИЧЕСКИХ МОДЕЛЯХ

В продолжение обзора экономических аспектов поведенческих стратегий основанных на имитации и social learning, опубликованном в предыдущем выпуске журнала (Мантатова, Сандитов 2012), в статье обсуждаются подходы к описанию имитационного поведения в экономико-математических моделях.

Ключевые слова: экономика, управление, имитационное поведение, экономико-математические модели.

1. Imitation in Economics

Although historically mainstream economic theory with its focus on formal market mechanisms of exchange and emphasis on perfectly rational individual agents largely ignored non-market mechanisms, last two decades have seen growing recognition of the importance that non-price interactions play in economic activities. As a result there is an increasing number of works that seek to fit social interactions in general and imitation mechanisms in particular into the world of formal economic models.

Homo economicus

The economic model of human behaviour known as homo economicus is very distinct from the models of individual behaviour developed in other behavioural sciences. She is an amazing creature in all ways. Her raison d'etre is to maximize her utility at all times. For that, in addition to a comprehensive and coherent set of preferences, she possesses brain power exceeding all imaginable

limits, and never hesitates to apply it in any circumstances. Organizations consisting of many homo economicus together share most features with individual homo economicus: omniscient rationality and greediness.

What is a reason for perfectly rational individuals or organizations to copy behaviour of other individuals? While other behavioural models reviewed in the previous section consider the tendency to imitate as “hardwired” in boundly rational individuals and organizations in the course of evolution, this cannot be the case with perfectly rational homo economicus: she must be sure that she is better off with copied behaviour than any other alternative. Therefore, observed imitative behaviour should be explained in terms of individual (expected) payoff from copying behaviour of the others.

Before we start reviewing economic models of imitation, we shall note that economists are cautious

not to interpret every process concerning diffusion of a novel behavioural pattern (e.g. adoption of technology) as driven by imitation. Many economic models allow for alternative explanations for observed correlations in the timing of adoption by different economic agents (famous S-shape diffusion curves) (1). Still, other models consider the diffusion process as driven by imitative behaviour. We can divide them into models with direct payoff externalities, where imitative behaviour is driven by innate preferences for being similar to one's reference group (2), and models with indirect payoff externalities, where agents have no innate preference for being conformists, but choose to imitate others for some other reason. The indirect externalities may arise for a variety of reasons: they may be a result of certain institutional arrangement as in the case of social norms (Elster 1989), competition for social status (Frank 1985), or, what deserves special attention in the light of social learning theory, informational externalities such as in informational cascades (Bikhchandani et al. 1992; Banerjee 1992).

Direct payoff externalities

Gary Becker (1991) in his treatment of restaurant pricing describes an observation made at a popular seafood restaurant in Palo Alto, California: [Restaurant] does not take reservations, and every day it has long queues for tables during prime hours. Almost directly across the street is another seafood restaurant with comparable food, slightly higher prices, and similar service and other amenities. Yet this restaurant has many empty seats most of the time. [... ] The same phenomenon is found in the pricing of successful sportive events, such as World Series and Super Bowls, and the related way in the pricing of best-selling books.

He notices that consumption of certain goods has not only private value, but also social meaning

[A] consumer's demand for some goods depends on the demands by other consumers. The motivation for this approach is the recognition that restaurant eating, watching a game or play, attending a concert, or talking about books are all social activities in which people consume a product or service together and partly in public. [ ... ] pleasure from a good is greater when many people want to consume it, perhaps because a person does not want to be out of step with what is popular or because confidence in the quality of the food, writing, or performance is greater when a restaurant, book, or theater is more popular.

He proposes to make individual demand dependent of the aggregate demand (according to the neoclassical consumer theory it suggests that utility

of consuming “social good” depends on consumption choices of the others).

Becker is not the first economist to seek explanation for some anomalies in consumption of goods with social meaning by making the assumption of interdependence between individuals' demand schedules. Leibenstein (1950) employed a similar approach to formalize the verbal treatments of interdependencies in consumer choice due to Veblen and his theory of the leisure class (Veblen 1991), but also due to earlier writers such as John Rae, and Pigou. He examined three types of effects interdependencies that consumer choices have on individual demand: a bandwagon effect is an increase in individual demand due to popularity of the good, a snob effect is exactly the opposite, i.e. decrease in demand due to adoption of the good by other consumers, and the Veblen effect captures conspicuous consumption, an increase in demand for a good due to an increase in its price. He found that bandwagon and snob effects change the price elasticity of aggregate demand (with respect to individual demand), while Veblen effects may result in upward sloped parts of aggregate demand (3).

Extensive treatment of direct payoff externalities can be found in the literature on industrial organization, where they are referred as “network externalities” (Arthur 1989, Farrell and Saloner 1986). This kind of externality often appears in the context of a competition between different technical standards. Consider two standards (technologies) A and B, which are mutually incompatible. At each moment in time one potential adopter has to make his choice between the standards. Because of the incompatibility, a user of standard A is better off when he is surrounded by users of the same standard, A. Let the payoff to agent i from adopting a standard be the sum of the gains due to the technical efficiency of the standard and the gain due to compatibility with other users of the standard. We assume that the latter increases with the number of the users of the same standard. Suppose that ceteris paribus the standard B is more efficient then A.

Consider a situation where the difference in the numbers of users happens to be such that the gain due to the larger installed base offsets the loss from adoption of a technically inferior standard A. In such a situation a potential adopter should choose inferior standard A, thereby increasing the instalment base of standard A, and subsequently increasing the gain from adopting standard A even further. As a result, the next adopter will also choose A, and so on: the system locks in an inferior (with respect to social welfare) state.

Examples of lock-ins to technically inferior standards are well known in the economics of technical change. Initial advantage of an inferior standard/technology that leads to suboptimal lock-in may arise for a variety of reasons. One such a reason often mentioned in the literature is related to first-mover advantage, and the most famous example of it is story of QWERTY vs. Dvorjak keyboard (David 1985). Another factor that may cause an early lock-in to an inferior standard is related to sponsorship of a particular technology (Cowan 1990).

Payoff externalities may give rise to informal conventions. Consider right- vs. left- hand traffic. Once most drivers choose one of the alternatives, a driver would pay a dear price for choosing the alternative. As a result all drivers are better off taking the same side, even if for whatever reason some of them have intrinsic preferences for doing it the other way. Therefore we can say that one of the alternatives will be chosen by all drivers, and no driver would like to change her choice while others stick to theirs. The two choices correspond to two stable equilibria of a coordination game among perfectly rational individualistic agents. The problem of coordination can be solved by some informal agreement (Farrell and Saloner 1986).

Indirect Payoff Externalities

Inserting externalities directly into the payoff (utility) function is a straightforward way to take into account social interactions and it allows for some insights into behaviour of a system with interdependencies between agents' choices. Nevertheless, one might feel uncomfortable about approaching to the problem this way, because the question of why do agents imitate others has an extremely simple answer - they have preferences to do so! In some applications, e.g. competition of standards mentioned above, the origin of such preferences is transparent (whenever compatibility with other users is an advantage, it is better to adopt a popular standard) and the straightforwardness of the answer is well justified. In other applications, however, it is not clear how such preferences come about and further explanations are needed.

Payoff externalities may arise due to asymmetric information. For instance, Scharfstein and Stein (1990) explain mimetic isomorphism of new institutional theory mentioned earlier in a principal-agent framework. They examine a model with a population of investment funds managers of two types: “smart” ones who observe a signal correlated with the state of the market, and “dumb” managers who observe uncorrelated noise. The labour market can judge a manager only on the basis of information

which consists of (a) profitability of investment, and (b) whether the investment behaviour of the manager is similar to behaviour of his peers.

Notice, that in the absence of (b) smart managers' decisions would be correlated (since their signals are correlated with the state of market), while dumb managers would invest at random. However, under (b) “herding” arises due to a “sharing-the-blame” effect: a manager who mimics the investment decisions of his peers is less likely to be blamed because then his decision is correlated with the decision of the others and this suggests to the labour market that he is likely to be smart. As a result even if a manager receives a negative signal about the market he may still decide to invest following the crowd to avoid being punished by the labour market. In Keynes's words “Worldly wisdom teaches that it is better for reputation to fail conventionally than to succeed unconventionally”.

As has been mentioned above, direct payoff externalities may result in the emergence of informal agreements (4). However many social norms are individually costly, and self-interested perfectly rational agents should not comply with such norms. For instance, consider racial (gender, cast etc.) discrimination. If, say, employers have positive taste for racial discrimination then they deliberately reduce the pool of potential employees and therefore an employer without racial prejudice should have competitive advantage (Becker 1976). In the long-run, in principle discrimination should disappear as a social norm even if no government/civil actions against racial discrimination are taken. Nevertheless, racial discrimination does exist, as do many other individually costly norms.

Another example of individually costly social norm is a code of vengeance. Under certain circumstances (e.g. where corresponding formal institutions are weak or absent) the code may be socially beneficial, as it might work as a barrier to unlawful violence toward others. However punishing disobedience also involves costs: complying with a vengeance code a member of a family (clan, tribe etc.) has to take revenge, which means putting himself at risk. If this is the case, the party that is supposed to punish the deviator is better not doing it. Hence a rational decision is to leave it. Knowing this, rational agents would not follow the norm. But if everybody feels the same then revenge is not a credible threat, and vengeance cannot prevent violence. Nevertheless, a social norm that is individually costly may still be sustained if it is enforced by another norm.

Akerlof (1976) explained how such norms may be supported on the example of discrimination in Indian caste system. While earlier analysis would conclude that discrimination disappears in the long-run due to room for arbitrage (Becker 1976), Aker-lof showed that even individually costly customs may support themselves when not only breaking a norm is subject to penalty, but not punishing a rule-breaker is also punishable. He examined a simple model of a labour market under a caste system, in which employers have a choice between hiring labour according to caste codes with wage differentials, or according to output maximization regardless of caste. In addition, he assumes that a consumer who decides to buy goods from companies not using labour according to the caste code will be punished and become an outcast. He showed that the model has two equilibria: “low-trap” caste equilibrium, and no-caste optimal equilibrium. Once the system is trapped in the caste equilibrium, it may get out of it only if a significant share of agents decides to break the rules at the same time.

Notice that in this model the tendency to copy behaviour of others to comply with the socially imposed behavioural norm is not a part of innate preferences. Instead payoff externalities are introduced into the model in an indirect way via the institutional set up.

Although we examined only two economic contexts where payoff externalities arise even though not explicitly present in agents' preferences, there are many other instances where it happens as well (e.g. bank runs or financial crises). Now we proceed to a particular type of models with indirect payoff externalities inspired by the literature on social learning.

Informational externalities

Social learning theory outlined in section general emphasizes “reciprocal determinism”: environment via learning causes individual behaviour, but the individual behaviour, in turn, causes the environment. In the process of acquiring novel behaviour some knowledge is produced. It spills over to other agents and may induce some of them to copy the new mode of behaviour. This, in turn, also produces knowledge and enhances (or inhibits) the process of adoption. In contrast with the other models mentioned above, the process of adoption of a technology is driven solely by information externalities: agents' payoffs do not depend on the actions taken by others.

Bala and Goyal (1994) study a model of entry into a new market with unknown stochastic demand. They consider a pool of entrepreneurs who

face a choice whether to enter the market of abstain from the entry. Decisions are made in sequential order, so that later entrepreneurs may observe the experience of their predecessors. They found that, first, if the pool consists of one entrepreneur, then with non-zero probability a market may disappear even if it is viable. They also explore the role of heterogeneity in entrepreneurs' beliefs: if beliefs are not heterogeneous enough then similarly to the case of single entrepreneur a viable market may be abandoned, while if the population is characterised by significant heterogeneity even non-viable markets never cease.

Caplin and Leahy (1994) examine a model of market crashes with firms trying to extract information about market viability from decisions made by other firms in this market. In their model entry into a market is two-staged: initial investment allows a firm to gather information about the state of final demand and on this basis it decides whether to make additional investment and enter the market or abandon the project. Information gathered by a firm is private, however its decision (to entry into the market or cancel the project) is publicly observed. The information structure of the model implies that as far as the firms continue with their projects the knowledge of the market accumulated by firms is effectively “trapped” in private hands: there is no way to distinguish between the behaviour of a firm that has received good news and a firm that has received negative information. The situation changes dramatically when some firms decide to suspend their projects. Suspensions release negative information and the market suddenly crushes.

Bolton and Harris (1999) examined a model of social learning based on a game of strategic experimentation. Their model is an extension of the well-known two-arm bandit problem. One of the bandit arms (the “safe” arm) provides some known payoff, the other generates random payoff with unknown distribution (the “risky” arm). The bandit problem is a classic example of the trade-off between experimentation and exploitation. While usually bandit models examine a player who makes his decision in isolation based on information from his own experience with the machine, Bolton and Harris (1999) consider a population of players each of whom face the same choice between “safe” technology with known payoff and “risky” technology with unknown payoff. Time is continuous and switching between technologies is costless. Players dynamically allocate their time between the technologies. Payoffs are publicly observable.

They prove existence of symmetric equilibrium and prove that its uniqueness (5). They show the presence of two motives in agent's behaviour working in opposite directions. First, there is free-rider effect: a player may be tempted to devote time to the known technology, in the hope of free-riding on the experimentation performed by others. Second, there is “encouragement effect”: a player may choose to experiment, in order to encourage experimentation with the risky technology by others, in order to benefit from the induced positive informational externality.

Informational cascades

Informational cascades represent a particular case of models for social learning that became popular among economists after the seminal works of Baner-jee (1992), Bikhchandani et al. (1992) (BHW henceforth), and Welch (1992). Let us follow the presentation of BHW model given in Bikhchandani et al. (1998). Consider a population of agents presented with a choice between two actions. In the context of technology adoption it may be Adopt the technology or Decline. The payoff to adoption is either +1 or -1 depending on the state of the technology: “High” or “Low” respectively. Without any further information both states of the technology have equal probabilities (i.e. prior probabilities are '/2 for both “High” and “Low” states of the technology).

Agents make their decisions in sequence; the order in which agents decide is exogenous and known to all agents. Information about a technology comes to an agent from two sources: a private signal and information about actions of her predecessors. Private signals are conditionally independent and may be of two types “High” and “Low”. Probabilities to receive a particular type of signal depends on the state of the technology, when in the favourable state of the technology the probability to receive “High” (p) is higher than the probability to receive “Low” (1 - p), while when the state of the technology is “Low” the probability of a “Low” signal is higher then the probability of a “High” signal. For simplicity we assume that the precision of a correct signal is the same for “High” and “Low” states of the technology. Table 1 presents conditional probabilities for the signals. Notice, that if agents' decisions were based solely on private information, then agent's optimal strategy is to “follow the signal” i.e. to adopt if the signal is favourable, otherwise reject the technology.

The other source of information is the history of adoption. Had all agents followed their signals, agents' private information would be revealed to the public. However it is not always individually op-

timal to follow one's own signal. At certain point positive (negative) public information exceeds a threshold and starts to outweigh private signals, then instead of taking action in accordance with private information the agent should “follow the herd”, and adopt (reject) the technology regardless to his private information. An informational cascade is said to occur if an agent's action does not depend on her private signal (Bikhchandani et al. 1992).

Once an informational cascade started actions of all further agents become uninformative. Indeed, after the numbers of adopters and non-adopters are such that agent i has to follow the herd, the next agent, (i + 1) must infer that i discarded private information. Hence i's action reveal no new information to (i +1). As a result, (i +1) finds herself in the same situation as i, and therefore must ignore her private information as did i, and so does (i +2) and so on. Once an informational cascade starts accumulation of public information ceases and conformity arises.

Several features of the model are worth mentioning here. First, notice that similar to other models with lock-in, an action widely adopted does not have to be the “correct” one. Indeed, even if the state of the technology is “High”, an unlucky chain of events (negative signals) might result in widespread rejection of the technology (and vice versa an informational cascade might lead to adoption of a mediocre technology). Second, notice that were agents able to observe signals rather than actions of their predecessors the true state of technology would be figured out with probability 1. Existence of suboptimal lock-ins in the model is due to the restrictions on publicly available information. Third, cascades are “fragile” (6): the arrival of better informed individuals, the release of new public information, or changes of the underlying value of adoption could dislodge an informational cascade. A cascade emerges when agents acting in selfinterest find it optimal to follow the herd and do not reveal their private information. If, however, in the course of the process an agent decides to follow the signal and in contravention to popular behaviour, then her action would reveal her private information and unlock the cascade. Bernardo and Welch (2001) have shown that irrationally overconfident entrepreneurs who overweight their private signals with respect to signals of the others enhance social welfare (7).

Bounded rationality

Although the assumption of perfect rationality of human beings has allowed economists to build par-

simonious yet self-coherent models of individual behaviour, it is obviously in odds with reality. To address the problem a variety of models that account for bounded rationality of individuals have been proposed. It is impossible to give any complete review of them in a short space; instead here we focus on several key references on social learning with bounded rational individuals.

Kirman's (1993) work on “ants, rationality, and recruitment” seeks to explain the asymmetric behaviour of market participants in an apparently symmetric situation by analogy with the process of the recruiting behaviour of ants. In an experiment by entomologists a colony of ants was allowed to feed on two identical sources of food. Interestingly they documented that the pattern of exploitation of these sources was highly asymmetric: while intuitively one might expect that in the long run ants would be split in half between the sources, if fact they stabilized with 80 percent at one source, and the rest 20 percent at the other. Moreover, from time to time “flips” occur between the concentrations at the two sources, i.e. a source that was exploited by some 80 percent of ants before the “flip”, attracts 20 percent after the “flip”. An analogy with traders' behaviour is obvious.

Kirman formulated a simple model of such asymmetric behaviour based on a particular form of a Markov chain similar to Polya urn processes. Consider two kinds of stocks (8) available at the market, say stocks A and B. Some traders prefer to hold stock A, while others prefer B. The state of the system can be characterized by the “market shares” of the stocks.

Each period a trader meets another trader chosen at random from the population. With some probability the first trader adjusts his preference to the preference of the second (due to the symmetry it makes no difference who is the first and who is the second), i.e. changes his preference, if the other one has different preference, or keeps her view if the second trader is of the same type. There is also a small probability e that the first trader changes his view independent of meeting the “model”. In the real world it might happen, for instance, due to arrival of exogenous “news”, or replacement of the existing trader by a new one with the different view.

Depending on the parameters of the model the equilibrium distribution of A and B shares, the fraction of the time the system spends in each of its states (particular splits of the market), is U-shaped, flat, or inverted U-shaped.

Asymmetric equilibrium distribution (U-shape form) that corresponds to the observed pattern of

ants' (and stock market) behaviour arises when parameter e is small enough, i.e. the effect of social interaction overwhelms exogenous influence. In this case the system spends most of the time near one of the boundaries, i.e. when the one of the stocks is much more “popular” then the other, with occasional “flips” in traders' preferences.

Several features of the model are particularly interesting in our context. First, there is a sharp contrast between the complex dynamics of the system (resembling stock market “sunspot” investment targets), and yet the very simple behaviour of agents. It highlights the importance of social interactions that have to be taken into consideration if one is to build any realistic model of human (and apparently ant) behaviour:

the behaviour of the group as a whole cannot be inferred from analysing one of the identical individuals in isolation. Without taking explicit account of interaction between individuals, the group behaviour ... cannot be explained.

(Kirman 1993, p. 137)

Second, although the process of decision making is not explicitly specified in the model (hardly any economist would claim to know ants' map of preference), the behavioural rule is consistent with the social learning theory (Bandura 1977). Indeed, the second trader can be considered as a “model” for the first one. Through observational modelling the first trader may adopt the behaviour of the “model” and, in turn, pass it to another trader and so on and as a result a new pattern may arise.

The paper does not explicitly discuss the implications of imitative behaviour for overall social welfare. For that let us assume that underlying agents' behaviour rule there are some (perceived) payoffs and those payoffs are different for different actions, say, stock A has higher returns than stock B, and they are reflected in the probabilities of “conversion”, i.e. preference for stock A is more likely to be “imitated” than preference for stock B. This difference in transition probabilities would bias the equilibrium distribution toward stock A. However, the general feature of the distribution, its U-shape, would still hold. Therefore, even though the system would spend more time in the socially optimal state (with most agents holding stock A), there still would be non-zero probability of a temporary “madness of the crowd”, when all of a sudden the system will get stuck in sub-optimal state.

Also notice that in the model the “society” is not structured: agents meet each other at random (9). At the same time, in many situations the structure of contacts in the population is highly relevant for un-

derstanding the dynamics of the process. An obvious example is the spatial dimensions of the process. If interactions between agents have a local nature, we are likely to see localized emergence of behavioural patterns, which may differ from place to place (e.g. consider left- and right- hand traffic).

Ellison and Fudenberg (1993) examined “rules of thumb” in social learning. As well as Kirman (1993) in their model(s) agents follow some fixed behavioural rules (“rules of thumb”). The rules of thumb they study try to capture the process of social learning through “popularity weighting”: agents (individual or firm) incline to use technology that did best in the previous period. Drawing an analogy with imitation studies in organization theory one might say that the model blends frequency-based imitation mode as reflected by popularity weighting, and outcome-based imitation driven by current payoff difference.

The structure of the simple model with a homogeneous population is as follows. There is a continuum of agents who can (and must) choose between two technologies. Each period only fraction of the population can rethink their choices. The difference in payoffs to adopting technologies at time t is a random variable that is a sum of some unknown constant and a random shock. An agent can observes adoption decisions and payoffs associated with the decisions. The agents' decision rule, the rule of thumb, is based on “popularity weighting”: an agent chosen to revise her technology choice at time t take into account both current payoffs (realization of payoffs in the previous round), and popularities of the technologies. The rule of thumb is characterized by a parameter that describes “popularity weight” vs. current payoffs difference in the decision making.

Ellison and Fudenberg (1993) examined a particular case where random shocks are distributed uniformly, and they asked whether the system converges to one of its boundary states (i.e. when one of the technology dies out), and under which parameters.

They find that depending on the weighting parameter, three possible situations may arise. First, there may be “optimum” weighting when for any initial condition the system converges with probability one to the better technology.

Second, there may be “overweighting” when the system always converges to a steady state. However in contrast with the case of “optimum” weighting, whether the better technology will be selected depends on the payoff difference and the initial shares of the technologies. When expected payoff differ-

ence is high, then with probability one the better technology will be selected, regardless of the initial condition (i.e. the behaviour of the system is very similar to “optimum” weighting case). When the difference is not high enough to ensure convergence to the better technology, then all depends on the initial conditions: if the initial share of a technology is high the system converges to the technology that was more popular at the beginning of the process (path-dependency), otherwise one cannot say in advance which of the two technologies will prevail in the long run (both steady states have positive probability).

Finally, the third case when agent's decision is based predominantly on the current payoffs (the value of the weighting parameter is low) is the situation of “underweighting”. In this case the system may not converge at all. Similarly to the case of “overweighting” the difference in expected payoffs is crucial for prediction of long run behaviour of the system. If the difference in expected payoffs is high enough, then with probability one the better technology will be selected regardless of the initial condition. Otherwise the system has a nondegenerate invariant distribution.

Taking a broader perspective we can draw parallels with the organization theory literature on imitation and make conjectures about diffusion path of competing technologies in relation to organizations' strategies/“behavioural traits”. In the environment where agents put enough weight on the most popular choice (frequency-based imitation) the process of social learning always leads to conformity. On the contrary, when the decision about technological choice is heavily affected by (contemporary) performance of the technologies (outcome-based imitation) the system never settles down and both technologies will be in use at any time (on management fashion cycles see a model by Strang and Still (2004)). Moreover a large enough payoff difference ensures that the system converges to better technology no matter where it starts. In the situation when popularity weighting is overwhelming (“overweighting”) but the difference in the payoffs is moderate, the system may converge to a suboptimal steady state.

Speed of diffusion of a new superior technology in their model depends on the payoff difference. This result is consistent with empirical findings from diffusion research. Indeed, according to empirical evidence on the diffusion of innovations profitability of an innovation increases the speed of its adoption (Griliches 1957, Mansfield 1961). Another interesting finding is that for a fixed payoff differ-

ence, the speed of convergence decreases as the magnitude of the random shock is increasing. Haun-schild and Miner (1997) examined the decision of hiring of an investment banker to advise an acquiring firm on an acquisition, and found that uncertainty is likely to increase the probability of frequency-and trait- based imitation, while decrease the probability of outcome-based imitation.

Ellison and Fudenberg (1995) modeled social learning in an environment where information spread via “word-of-mouth”. Similarly to Ellison and Fudenberg (1993) there are two technologies with unknown payoffs, and each period only a part of the population may reconsider their choices. Payoffs to adoption of the technologies are subject to two kinds of shocks: common shocks shared by all agents and idiosyncratic ones specific for each of the agent. ‘Word-of-mouth” is introduced into the model through random sampling of the population: an individual who is to reconsider her choice makes a random sample of N (exogenous) people and adopt the technology with the highest payoff. The main focus of the study is to find the conditions under which the system exhibits conformity and under which it is characterised by diversity.

First, they find that conformity is achieved if there is not too much communication. Furthermore, socially efficient outcomes, i.e. convergence toward the technology that does better on average, can be achieved only when there is very little communication. That might seem to be somewhat surprising, especially if compare it with the results of their previous model discussed above. Indeed, while the “rule of thumb” model says that lock in to one technology (conformity) is impossible without sufficient social learning expressed in popularity weighting, the “word-of-mouth” model suggests that social learning tends to push the system away from a lock-in.

The reason that social learning has to be restricted in order to let the system settle down is the “must-see” condition in the later model: an agent can adopt a technology only if she sees it in her sample. With this condition unpopular technologies might die out: if the size of agents' samples is relatively small the unpopular technology will not be present in the samples of many thus its share will decrease over time until it will eventually disappear.

On the contrary, if the size of the sample is not small even the unpopular technology will end up in the samples of many and under some realization of random shocks it might have a dramatic comeback.

The second result is related to the efficiency of the social learning: for convergence to the better

technology the intensity of “word-of-mouth” (sample size) has to be small, but not too small. Indeed, as we know when the size of the sample is not small enough, the system never settles. If however the sample is too small the system has excessive inertia such that an unlucky realization of random shocks might lock the system into the suboptimal choice. In the middle there is a region of sample sizes where the system on the one hand may settle down, but on the other, due to the fact that on average one technology is better than the other, it avoids the suboptimal lock-in.

2. Summary

From more general perspective imitation is a mechanism of evolutionary selection relevant understanding behavior of individuals (be they animals or humans), groups of individuals (such as organizations), and aggregate collective dynamics. In this paper we reviewed literature on imitation and social learning in economics and organization theory.

Organization theory acknowledges that the task-performing rules by which organizations (and individuals within organizations) operate have evolutionary nature and arise in the process of boundedly rational search. In this respect imitation and learning from observing the others are the key mechanisms through which successful routines are transmitted within and between organizations. Research in this field mostly concerns with identifying instances, describing and classifying different types of imitation, and to less extent with the motivation of imitating agents and analysis of the effects on the collective dynamics.

In (mainstream) economics, which takes as a model of agents’ behavior perfectly rational optimizing agents, the motivation for copying behaviour of others traditionally has been assigned to direct or indirect payoff externalities. In the past decade, economists turned their attention to boundedly rational behavior and developed a number of models to analyse properties of an economic system where agents imitate behavior of each other. Most of such models however have to rely on rather simple (and often ad hoc) assumptions about agents’ behaviour to match the sophisticated organizational routines studied in organization theory. In this respect, convergence of the two field (economics and organization theory) remains the challenge for future research.

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Примечание

1. For example, consider probit diffusion model of Davies (1979). In this model adoption of new technology happens without imitation. Actions of others have no effect on an agent. In fact, he even does not need to know what others are doing, because the only information he cares about is the threshold value.

2. In the case of adoption by a firm, profit from adopting a technology might depend on the compatibilities between competing technical standards (Farrell and Saloner 1986).

3. Bandwagon, snob, and Veblen effects may have important consequences for the dynamics of adoption of consumer goods innovations (Cowan et al. 1997; Reinstaller and San-ditov 2005)

4. In the context of imitative behaviour, social norms are interesting for two reasons. First, as is discussed above, social norms provide incentives to behave “as others do”. Second, one of the main channels for diffusion of social norms is imitation.

5. Although other non-symmetric equilibria might exist.

6. This feature makes them different from other models with positive feedback.

7. They examine an evolutionary group selection model and found that groups with overconfident entrepreneurs have higher chances to survive.

8. The exact number of alternative stocks is not important.

9. It corresponds to fully-mixed approximation in epidemiologic models of contagion.

Сандитов Булат Дамбаевич, кандидат технических наук, Школа Бизнеса ТЕЛЕКОМ (Франция)

Sanditov Bulat Dambayevich, PhD in Technical Sciences, TELECOM School of Management, Mines-Telecom Institute, France

Мантатова Арюна Валериановна, кандидат географических наук, старший преподаватель, Бурятский государственный университет.

Mantatova AryunaValerianovna, Candidate of Science in Geography, senior lecturer, Buryat State University, Russia

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