Interactions between Market Barriers and Communication  Networks in Marketing Systems  Ian N. Durbach  Department of Statistical Sciences  University of Cape Town  Rondebosch 7701, South Africa  ian.durbach@uct.ac.za  Jan H. Hofmeyr  Synovate Brand and Communications Practice  Alphen Business Park  Constantia 7800, South Africa  jn.hofmeyr@iafrica.com  ABSTRACT  We investigate a framework where agents search for   satisfying products by using referrals from other agents. Our  model of a mechanism for transmitting word-of-mouth and  the resulting behavioural effects is based on integrating a  module governing the local behaviour of agents with a   module governing the structure and function of the underlying  network of agents. Local behaviour incorporates a   satisficing model of choice, a set of rules governing the   interactions between agents, including learning about the   trustworthiness of other agents over time, and external constraints  on behaviour that may be imposed by market barriers or  switching costs. Local behaviour takes place on a network  substrate across which agents exchange positive and   negative information about products. We use various degree  distributions dictating the extent of connectivity, and   incorporate both small-world effects and the notion of preferential  attachment in our network models. We compare the   effectiveness of referral systems over various network structures  for easy and hard choice tasks, and evaluate how this   effectiveness changes with the imposition of market barriers.  Categories and Subject Descriptors  I.2.11 [Artificial Intelligence]: Distributed Artificial   Intelligence    1. INTRODUCTION  Defection behaviour, that is, why people might stop   using a particular product or service, largely depends on the  psychological affinity or satisfaction that they feel toward  the currently-used product [14] and the availability of more  attractive alternatives [17]. However, in many cases the   decision about whether to defect or not is also dependent on  various external constraints that are placed on switching   behaviour, either by the structure of the market, by the   suppliers themselves (in the guise of formal or informal contracts),  or other so-called ‘switching costs" or market barriers [12, 5].  The key feature of all these cases is that the extent to which  psychological affinity plays a role in actual decision-making  is constrained by market barriers, so that agents are   prevented from pursuing those courses of action which would  be most satisfying in an unconstrained market.  While the level of satisfaction with a currently-used   product will largely be a function of one"s own experiences of  the product over the period of use, knowledge of any   potentially more satisfying alternatives is likely to be gained  by augmenting the information gained from personal   experiences with information about the experiences of others   gathered from casual word-of-mouth communication. Moreover,  there is an important relationship between market barriers  and word-of-mouth communication. In the presence of   market barriers, constrained economic agents trapped in   dissatisfying product relationships will tend to disseminate this  information to other agents. In the absence of such   barriers, agents are free to defect from unsatisfying products  and word-of-mouth communication would thus tend to be  of the positive variety. Since the imposition of at least some  forms of market barriers is often a strategic decision taken  by product suppliers, these relationships may be key to the  success of a particular supplier.  In addition, the relationship between market barriers and  word-of-mouth communication may be a reciprocal one. The  structure and function of the network across which   word-ofmouth communication is conducted, and particularly the  way in which the network changes in response to the   imposition of market barriers, also plays a role in determining  which market barriers are most effective. These are complex  questions, and our main interest in this paper is to address  the simpler problems of investigating (a) the extent to which  network structure influences the ways in which information  is disseminated across a network of decision makers, (b) the  extent to which market barriers affect this dissemination,  and (c) the consequent implications for overall system   performance, in terms of the proportion of agents who are   satisfied, and the speed with which the system moves towards  equilibrium, which we term stability.  An agent-based model framework allows for an   investigation at the level of the individual decision maker, at the  387  978-81-904262-7-5 (RPS) c 2007 IFAAMAS  product-level, or at the level of the entire system; we are   particularly interested in the implications of market barriers for  the latter two. The model presented here allows for an   investigation into the effects of market barriers to be carried  out in a complex environment where at every time period  each agent in a population must decide which one of a set of  products to purchase. These decisions are based on   multiattribute information gathered by personal product trials as  well as from the referrals of agents. Agents use this gathered  information to search for a product that exceeds their   satisfaction thresholds on all attributes - so that the agents may  be said to be satisficing rather than optimising (e.g. [15]).  Market barriers may act to influence an agent to continue  to use a product that is no longer offering satisfactory   performance. We allow agents to hold different opinions about  the performance of a product, so that as a result a referral  from another agent may not lead to a satisfying experience.  Agents therefore adjust their evaluations of the validity of  other agents" referrals according to the success of past   referrals, and use these evaluations to judge whether or not  to make use of any further referrals. The level of   satisfaction provided to an agent by a product is itself inherently  dynamic, being subject to random fluctuations in product  performance as well as a tendency for an agent to discount  the performance of a product they have used for a long time  - a process akin to habituation.  2. BACKGROUND  2.1 Word-of-mouth communication  Much of the work done on word-of-mouth communication  in the context of social psychology and marketing research  has focused on its forms and determinants, suggesting that  word-of-mouth arises in three possible ways: it may be   induced by a particular transaction or product experience [11],  particularly when that transaction has been an especially  good or bad one [1]; it may be solicited from others [10],  usually when the task involved is difficult, ambiguous, or  new [7]; and it may come about when talk of products and  brands arise in the course of informal conversation,   particularly when a ‘passion for the subject" is present [4].   Wordof-mouth becomes more influential when the source of the  communication is credible, with credibility decisions based  largely on one or a combination of evaluations of professional  qualification, informal training, social distance [7], and   similarity of views and experiences [3].  The role of word-of-mouth communication on the behaviour  of complex systems has been studied in both analytical and  simulation models. The analytical work in [8] investigates  the conditions under which word-of-mouth leads to   conformity in behaviour and the adoption of socially efficient   outcomes (e.g. choosing an alternative that is on average better  than another), finding that conformity of behaviour arises  when agents are exposed to word-of-mouth communication  from only a small number of other agents, but that this   conformity may result in socially inefficient outcomes where the  tendency toward conformity is so strong that it overwhelms  the influence of the superior payoffs provided by the socially  efficient outcome. Simulation-based investigations of   wordof-mouth [6, 13] have focused on developing strategies for  ensuring that a system reaches an equilibrium level where  all agents are satisfied, largely by learning about the   effectiveness of others" referrals or by varying the degree of   inertia in individual behaviour. These studies have found that,  given a sufficient number of service providers, honest   referrals lead to faster convergence to satisfactory distributions  than deceitful ones, and that both forms of word-of-mouth  provide better performance than none at all. The   simulation framework allows for a more complex modelling of the  environment than the analytical models, in which referrals  are at random and only two choices are available, and the  work in [6] in particular is a close antecedent of the work   presented in this paper, our main contribution being to include  network structure and the constraints imposed by market  barriers as additional effects.  2.2 Market barriers  The extent to which market barriers are influential in  affecting systems behaviour draws attention mostly from  economists interested in how barriers distort competition  and marketers interested in how barriers distort consumer  choices. While the formalisation of the idea that   satisfaction drives purchase behaviour can be traced back to the  work of Fishbein and Ajzen [9] on reasoned choice, nearly  all writers, including Fishbein and Ajzen, recognise that this  relationship can be thwarted by circumstances (e.g. [17]).  A useful typology of market barriers distinguishes   ‘transactional" barriers associated with the monetary cost of   changing (e.g. in financial services), ‘learning" barriers associated  with deciding to replace well-known existing products, and  ‘contractual" barriers imposing legal constraints for the term  of the contract [12]. A different typology [5] introduces the  additional aspect of ‘relational" barriers arising from   personal relationships that may be interwoven with the use of  a particular product.  There is generally little empirical evidence on the   relationship between the creation of barriers to switching and the   retention of a customer base, and to the best of our knowledge  no previous work using agent-based modelling to generate  empirical findings. Burnham et al. [5] find that perceived  market barriers account for nearly twice the variance in   intention to stay with a product than that explained by   satisfaction with the product (30% and 16% respectively), and  that so-called relational barriers are considerably more   influential than either transactional or learning barriers. Further,  they find that switching costs are perceived by consumers  to exist even in markets which are fluid and where barriers  would seem to be weak. Simply put, market barriers appear  to play a greater role in what people do than satisfaction;  and their presence may be more pervasive than is generally  thought.  3. MODEL FRAMEWORK  3.1 Product performance evaluations  We use a problem representation in which, at each time  period, every agent must decide which one of a set of   products to choose. Let A = {ak}k=1...p be the set of agents,  B = {bi}i=1...n be the set of products, and C = {cj }j=1...m  be the set of attributes on which the choice decision is to be  based i.e. the decision to be made is a multiattribute choice  one. Let fj : B → [0, 1] be an increasing function   providing the intrinsic performance of a product on attribute j (so  that 0 and 1 are the worst- and best-possible performances  respectively), and Sij : A × [0, 1] → [0, 1] be a subjective  opinion function of agents. The intrinsic performance of  388 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)  product i on attribute j is given by fj (bi). However, the  subjective opinion of the level of performance (of product i  on attribute j) given by agent k is given by sij(ak, fj (bi)).  All subsequent modelling is based on these subjective   performance ratings. For the purposes of this paper, each agent  belongs to one of three equally-sized groups, with each group  possessing its own subjective performance ratings.  We assume that the subjective performance ratings are  not known a priori by the agents, and it is their task to   discover these ratings by a combination of personal exploration  and referral gathering. In order to model this process we   introduce the notion of perceived performance ratings at time  t, denoted by pij(ak, fj (bi), t). Initially, all perceived   performance ratings are set to zero, so that the initial selection of a  product is done randomly. Subsequent variation in product  performance over time is modelled using two quantities: a  random perturbation jkt applied at each purchase occasion  ensures that the experience of a particular product can vary  over purchase occasions for the same agent, and a   habituation discounting factor Hikt tends to decrease the perceived  performance of a product over time as boredom creeps in  with repeated usage. Our habituation mechanism supposes  that habituation builds up with repeated use of a product,  and is used to discount the performance of the product.  In most cases i.e. unless the habituation factor is one or  extremely close to one, this habituation-based discounting  eventually leads to defection, after which the level of   habituation dissipates as time passes without the product being  used. More formally, once a product i∗  has been chosen by  agent k, the subjective level of performance is perceived and  pi∗j(ak, fj (b∗  i ), t) is set equal to si∗j(ak, fj (b∗  i ))Hi∗kt + jkt,  where jkt is distributed as N(0, σ) and Hi∗kt is an   decreasing function of the number of time periods that agent k has  been exposed to i∗  .  In evaluating the performance of a product, agents make  use of a satisficing framework by comparing the perceived  performance of the chosen product with their satisfaction  thresholds Γk = {g1k, . . . , gmk}, with 0 ≤ gik ≤ 1. Agent  k will be satisfied with a product i∗  selected in time t if  pi∗j(ak, fj (b∗  i ), t) ≥ gjk, ∀j.  3.2 Decision processes  In designing the mechanism by which agents make their  choice decisions, we allow for the possibility that satisfied  agents defect from the products that are currently satisfying  them. Satisfied agents stay with their current product with  probability Pr(stay), with a strategy prohibiting satisfied  agents from moving (e.g. [6]) obtained as a special case when  Pr(stay) = 1.  A defecting satisfied agent decides on which product to  choose by considering all other products for which it has  information, either by previous personal exploration or by  referrals from other agents. The selection of a new   product begins by the agent identifying those products from  which he or she expects to gain a satisfactory performance  on all attributes i.e. those products for which δik < 0, where  δik = maxj [gjk − pij(ak, fj(bi), t)], and selecting a   product from this set with selection probabilities proportional to  −δik. If no satisfactory product exists (or at least the agent  is unaware of any such product) the agent identifies those  products that offer at least a minimum level of ‘acceptable"  performance γ−  k . The minimum level of acceptability is   defined as the maximum deviation from his or her aspirations  across all attributes that the agent is willing to accept i.e.  a product is minimally acceptable if and only if δik < γ−  k .  Agents then select a product at random from the set of   minimally acceptable products. If the set of minimally   acceptable products is empty, agents select a product from the full  set of products B at random.  The decision process followed by unsatisfied agents is largely  similar to that of defecting satisfied agents, with the   exception that at the outset of the decision process agents will  chose to explore a new product, chosen at random from the  set of remaining products, with probability α. With   probability 1 − α, they will use a decision process like the one  outlined above for satisfied agents.  3.3 Constraints on decision processes  In some circumstances market barriers may exist that  make switching between products more difficult,   particularly where some switching costs are incurred as a result of  changing one"s choice of product. When barriers are present,  agents do not switch when they become unsatisfied, but  rather only when the performance evaluation drops below  some critical level i.e. when δik > β, where β > 0 measures  the strength of the market barriers. Although in this   paper market barriers do not vary over products or time, it is  straightforward to allow this to occur by allowing barriers  take the general form β = max(β∗ +Δtuse, β∗  ), where β∗ is a  barrier to defection that is applied when the product is   purchased for the first time (e.g. a contractual agreement), Δ is  the increase in barriers that are incurred for every additional  time period the product is used for, and β∗  is the maximum  possible barrier, and all three quantities are allowed to vary  over products i.e. be a function of i.  3.4 Referral processes  Each agent is assumed to be connected to qk < p agents  i.e. to give and receive information from qk other agents.  The network over which word-of-mouth communication   travels is governed by the small-world effect [18], by which   networks simultaneously exhibit a high degree of clustering of  agents into ‘communities" and a short average path length  between any two agents in the network, and preferential  attachment [2], by which agents with greater numbers of  existing connections are more likely to receive new ones.  This is easily achieved by building a one-dimensional lattice  with connections between all agent pairs separated by κ or  fewer lattice spacings, and creating a small-world network  by choosing at random a small fraction r of the connections  in the network and moving one end of each to a new agent,  with that new agent chosen with probability proportional to  its number of existing connections. This results in a   distribution of the number of connections possessed by each agent  i.e. a distribution of qk, that is strongly skewed to the right.  In fact, if the construction of the network is slightly modified  so that new connections are added with preferential   attachment (but no connections are removed), the distribution of  qk follows a power-law distribution, but a distribution with a  non-zero probability of an agent having less than the modal  number of connections seems more realistic in the context  of word-of-mouth communication in marketing systems.  When an agent purchases a product, they inform each  of the other agents in their circle with probability equal to  Pr(spr)k∗ + |δik∗ |, where Pr(spr)k∗ is the basic propensity  of agent k∗  to spread word of mouth and δik∗ captures the  The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 389  extent to which the agent"s most recent experience was   satisfying or dissatisfying. Agents are thus more likely to spread  word-of-mouth about products that they have just   experienced as either very good or very bad. If an agent receives  information on the same product from more than one agent,  he or she selects the referral of only one of these agents, with  selection probabilities proportional to Tt(k∗  , k), the degree  to which previous referrals from k∗  to k were successful i.e.  resulted in satisfying experiences for agent k. Thus agents  have the capacity to learn about the quality of other agents"  referrals and use this information to accept or block future  referrals. In this paper, we employ a learning condition in  which Tt(k∗  , k) is multiplied by a factor of 0.1 following an  unsatisfying referral and a factor of 3 following a satisfying  referral. The asymmetry in the weighting is similar to that  employed in [16], and is motivated by the fact that an   unsatisfying referral is likely to be more reliable evidence that a  referring agent k∗  does not possess the same subjective   preferences as agent k than a positive referral is of indicating the  converse.  Other referral process are certainly possible, for   example one integrating multiple sources of word-of-mouth rather  than choosing only the most-trusted source: our main   reason for employing the process described above is   simplicity. Integrating different sources considerably complicates  the process of learning about the trustworthiness of others,  and raises further questions about the precise nature of the  integration.  After determining who contacts whom, the actual   referral is modelled as a transmittance of information about the  perceived level of performance of an experience of product  i∗  from the referring agent k∗  to the accepting agent k i.e.  pi∗j(ak, fj (bi), t) takes on the value pi∗j(ak∗ , fj(bi), t−1), ∀j,  provided that agent k is not currently using i∗  . Information  about other products is not transmitted, and an agent will  ignore any word-of-mouth about the product he or she is  currently using. In effect, the referral creates an expected  level of performance in the mind of an accepting agent for  the product referred to, which that agent may then use when  making choice decision in subsequent time periods using the  decision processes outlined in the previous section. Once an  agent has personally experienced a product, any expected  performance levels suggested by previous referrals are   replaced by the experienced (subjective) performance levels  sij(ak, fj(bi)) + jkt and Tt(k∗  , k) is adjusted depending on  whether the experience was a satisfying one or not.  4. EXPERIMENTAL RESULTS  We examine the behaviour of a system of 200 agents   consisting of three groups of 67, 67, and 66 agents respectively.  Agents in each of the three groups have homogeneous   subjective opinion functions Sij. Simulations were run for 500  time periods, and twenty repetitions of each condition were  used in order to generate aggregate results.  4.1 Choice task difficulty  We begin by examining the effect of task difficulty on  the ability of various network configurations to converge to  a state in which an acceptable proportion of the   population are satisfied. In the ‘easy" choice condition, there are  50 products to choose from in the market, evaluated over  4 attributes with all satisfaction thresholds set to 0.5 for  all groups. There are therefore on average approximately  3 products that can be expected to satisfy any particular  agent. In the ‘hard" choice condition, there are 500   products to choose from in the market, still evaluated over 4  attributes but with all satisfaction thresholds now set to  0.7 for all groups, so there are on average approximately  4 products that can be expected to satisfy any particular  agent. Locating a satisfactory product is therefore far more  difficult under the ‘hard" condition. The effect of task   difficulty is evaluated on three network structures   corresponding to r = 1 (random network), r = 0.05 (small-world   network), and r = 0 (tight ‘communities" of agents), with   results shown in Figure 1 for the case of κ = 3.  0 100 200 300 400 500  0.00.10.20.30.40.50.60.7  Time  Proportionsatisfied  Easy task  r = 1  r = 0.05  r = 0  (a) Proportion of agents satisfied  0 100 200 300 400 500  0.00.10.20.30.40.50.6  Time  Shareofmarket  Easy task  r = 1  r = 0.05  r = 0  (b) Market share for leading product  Figure 1: Moderating effect of task difficulty on   relationship between network structure (r) and system  behaviour  Given a relatively easy task, the system very quickly i.e. in  little over 50 time periods, converges to a state in which  just less than 60% of agents are satisfied at any one time.  Furthermore, different network structures have very little  influence on results, so that only a single (smoothed) series  is given for comparison with the ‘hard" condition. Clearly,  there are enough agents independently solving the task i.e.  390 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)  finding a satisfying brand, to make the dissemination of   information relatively independent of the ways in which   connections are made. However, when it is more difficult to  locate a satisfying product, the structure of the network   becomes integral to the speed at which the system converges  to a stable state. Importantly, the overall satisfaction level  to which the system converges remains just below 60%   regardless of which network structure is used, but convergence  is considerably speeded by the random rewiring of even a  small proportion of connections. Thus while the random  network (r = 1) converges quickest, the small-world   network (r = 0.05) also shows a substantial improvement over  the tight communities represented by the one-dimensional  ring lattice. This effect of the rewiring parameter r is much  less pronounced for more highly-connected networks (e.g.  κ = 9), which suggests that the degree distribution of a   network is a more important determinant of system behaviour  than the way in which agents are connected to one another.  Similar results are observed when looking at the market  share achieved by the market leading product under each  level of choice difficulty: market share is essentially   independent of network structure for the easy task, with   average share converging quickly to around 35%. Set a more  difficult task, the convergence of market share to an   approximate long-run equilibrium is in fact fastest for the   smallworld network, with the random and tight community   networks taking different paths but similar times to reach their  equilibrium levels. Also interesting is the finding that   equilibrium market shares for the market leader appear to be  slightly (of the order of 5-10%) higher when network   connections are non-random - the random network seems to  suffer more from the effects of habituatation than the other  networks as a result of the rapid early adoption of the   market leading product.  4.2 Market barriers  In the remainder of this paper we focus on the effect of  various forms of market barriers on the ability of a system of  agents to reach a state of acceptable satisfaction. For   simplicity, we concentrate on the smaller set of 50 products i.e.  the ‘easy" choice task discussed above, but vary the   number of connections that each agent begins with in order to  simultaneously investigate the effect of degree distribution  on system behaviour. Tables 1 and 2 show the effect of   different degree distributions on the equilibrium proportion of  agents that are satisfied at any one time, and the   equilibrium proportion of agents switching products (moving) in  any one time period, under various levels of market barriers  constraining their behaviour. In these two tables,   equilibrium results have been calculated by averaging over time  periods 450 to 500, when the system is in equilibrium or  extremely close to equilibrium (Table 3 and 4 make use of  all time periods).  No WoM κ = 1 κ = 3 κ = 9  β = 0 0.27 0.44 0.56 0.58  β = 0.05 0.26 0.39 0.50 0.52  β = 0.2 0.14 0.27 0.32 0.34  β = 0.4 0.07 0.17 0.22 0.25  Table 1: Effect of degree distribution and market  barriers on proportion of market satisfied  No WoM κ = 1 κ = 3 κ = 9  β = 0 0.74 0.51 0.45 0.45  β = 0.05 0.66 0.43 0.38 0.37  β = 0.2 0.41 0.21 0.21 0.21  β = 0.4 0.17 0.09 0.09 0.09  Table 2: Effect of degree distribution and market  barriers on proportion of market moving  Three aspects are worth noting. Firstly, there is a strong  diminishing marginal return of additional connections   beyond a small number. The first few connections one makes  increases the probability of finding a satisfying product 60%  from 0.27 to 0.44 (for the first two contacts), followed by a  further increase of roughly 25% to 0.56 for the next four.  In contrast, adding a further 12 contacts improves relative  satisfaction levels by less than 4%. Secondly, word-of-mouth  communication continues to play an important role in   improving the performance of the system even when market  barriers are high. In fact, the role may even be more   important in constrained conditions, since the relative gains  obtained from word-of-mouth are greater the higher market  barriers are - just having two contacts more than doubles  the aggregate satisfaction level under the most extreme   barriers (β = 0.4). Finally, it is clear that the mechanism by  which barriers reduce satisfaction is by restricting movement  (reflected in the lower proportion of agents moving in any  particular column of Tables 1 and 2), but that increases in  degree distribution act to increase satisfaction by precisely  the same mechanism of reducing movement - this time by  reducing the average amount of time required to find a   satisfying brand.  Positive referrals Negative referrals  κ = 1 κ = 3 κ = 9 κ = 1 κ = 3 κ = 9  β = 0 0.21 0.93 3.27 0.00 0.00 0.00  β = 0.05 0.19 0.85 2.96 0.06 0.19 0.60  β = 0.2 0.13 0.57 2.04 0.30 0.92 2.83  β = 0.4 0.08 0.40 1.49 0.60 1.81 5.44  Table 3: Median number of positive and negative  referrals made per agent per time period  Perhaps the most interesting effects exerted by market   barriers are those exerted over the market shares of leading  products. Figure 2 shows the cumulative market share   captured by the top three products in the market over time, for  all types of market barriers using different degree   distributions. Again, two comments can be made. Firstly, in the  absence of market barriers, a greater proportion of the   market is captured by the market leading products when   markets are highly-connected relative to when they are   poorlyconnected. This difference can amount to as much as 15%,  and is explained by positive feedback within the more   highlyconnected networks that serves to increase the probability  that, once a set of satisfying products have emerged, one  is kept informed about these leading products because at  least one of one"s contacts is using it. Secondly, the   relatively higher market share enjoyed by market leaders in  highly-connected networks is eroded by market barriers. In  moving from β = 0 to β = 0.2 to β = 0.4, market leaders  collectively lose an absolute share of 15% and 10% under  the larger degree distributions κ = 9 and κ = 3 respectively.  The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 391  0 100 200 300 400 500  0.10.20.30.40.50.60.70.8  Time  Shareofmarket  κ = 9  κ = 3  κ = 1  No WoM  (a) β = 0  0 100 200 300 400 500  0.10.20.30.40.50.60.70.8  Time  Shareofmarket  κ = 9  κ = 3  κ = 1  No WoM  (b) β = 0.05  0 100 200 300 400 500  0.10.20.30.40.50.60.70.8  Time  Shareofmarket  κ = 9  κ = 3  κ = 1  No WoM  (c) β = 0.2  0 100 200 300 400 500  0.10.20.30.40.50.60.70.8  Time  Shareofmarket  κ = 9  κ = 3  κ = 1  No WoM  (d) β = 0.4  Figure 2: Effect of market barriers on the share of the market captured by the leading 3 products  In contrast, no change in collective market share is observed  when κ = 1, although convergence to equilibrium conditions  is slower. It seems reasonable to suggest that increases in  negative word-of-mouth, which occurs when an unsatisfied  agent is prevented from switching to another product, are  particularly damaging to leading products when agents are  well-connected, and that under moderate to strong market  barriers these effects more than offset any gains achieved by  the spread of positive word-of-mouth through the network.  Table 3 displays the number of attempted referrals, both  positive and negative, as a function of degree distribution  and extent of market barriers, and shows that stronger   market barriers act to simultaneously depress positive   word-ofmouth communication and increase negative   communication from those trapped in unsatisfying product   relationships, and that this effect is particularly pronounced for  more highly-connected networks. The reduction in the   number of positive referrals as market barriers impose   increasingly severe constraints is also reflected in Table 4, which  shows the median number of product trials each agent makes  per time period based on a referral from another agent.  Whereas under few or no barriers agents in a highly-connected  network make substantially more reference-based product  trials than agents in poorly-connected networks, when   barriers are severe both types of network carry only very little  positive referral information. This clearly has a relatively  greater impact on the highly-connected network, which   relies on the spread of positive referral information to achieve  higher satisfaction levels. Moreover, this result might be  even stronger in reality if agents in poorly-connected   networks attempt to compensate for the relative sparcity of  connections by making more forceful or persuasive referrals  where they do occur.  κ = 1 κ = 3 κ = 9  β = 0 0.13 0.27 0.35  β = 0.05 0.11 0.22 0.28  β = 0.2 0.05 0.10 0.14  β = 0.4 0.02 0.05 0.06  Table 4: Median number of referrals leading to a  product trial received per agent per time period  392 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)  5. CONCLUSIONS AND RELATED WORK  Purchasing behaviour in many markets takes place on  a substrate of networks of word-of-mouth communication  across which agents exchange information about products  and their likes and dislikes. Understanding the ways in  which flows of word-of-mouth communication influence   aggregate market behaviour requires one to study both the  underlying structural properties of the network and the   local rules governing the behaviour of agents on the network  when making purchase decisions and when interacting with  other agents. These local rules are often constrained by the  nature of a particular market, or else imposed by   strategic suppliers or social customs. The proper modelling of a  mechanism for word-of-mouth transmittal and resulting   behavioural effects thus requires a consideration of a number of  complex and interacting components: networks of   communication, source credibility, learning processes, habituation  and memory, external constraints on behaviour, theories of  information transfer, and adaptive behaviour. In this   paper we have attempted to address some of these issues in  a manner which reflects how agents might act in the real  world.  Using the key notions of a limited communication   network, a simple learning process, and a satisficing heuristic  that may be subject to external constraints, we showed (1)  the importance of word-of-mouth communication to both  system effectiveness and stability, (2) that the degree   distribution of a network is more influential than the way in  which agents are connected, but that both are important in  more complex environments, (3) that rewiring even a small  number of connections to create a small-world network can  have dramatic results for the speed of convergence to   satisficing distributions and market share allocations, (4) that  word-of-mouth continues to be effective when movements  between products are constrained by market barriers, and  (5) that increases in negative word-of-mouth incurred as a  result of market barriers can reduce the market share   collectively captured by leading brands, but that this is dependent  on the existence of a suitably well-connected network   structure.  It is the final finding that is likely to be most   surprising and practically relevant for the marketing research field,  and suggests that it may not always be in the best   interests of a market leader to impose barriers that prevent   customers from leaving. In poorly-connected networks, the   effect of barriers on market shares is slight. In contrast, in  well-connected networks, negative word-of-mouth can   prevent agents from trying a product that they might   otherwise have found satisfying, and this can inflict significant  harm on market share. Products with small market share  (which, in the context of our simulations, is generally due to  the product offering poor performance) are relatively   unaffected by negative word-of-mouth, since most product trials  are likely to be unsatisfying in any case.  Agent-based modelling provides a natural way for   beginning to investigate the types of dynamics that occur in   marketing systems. Naturally the usefulness of results is for the  most part dependent on the quality of the modelling of the  two ‘modules" comprising network structure and local   behaviour. On the network side, future work might investigate  the relationship between degree distributions, the way   connections are created and destroyed over time, whether   preferential attachment is influential, and the extent to which  social identity informs network strucutre, all in larger   networks of more heterogenous agents. On the behavioural side,  one might look at the adaptation of satisfaction thresholds  during the course of communication, responses to systematic  changes in product performances over time, the integration  of various information sources, and different market barrier  structures. 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