Chapter 8 Agent-based Modeling and Simulations JACOPO A. BAGGIO Agent-based modeling and numerical simulations are means that facilitate exploring the structural and dynamic characteristics of systems that may prove intractable with analytical methods. This chapter examines the issues related to them, particularly their use in the study of socio-economic systems. As an application example, a simple model is built to analyze the movements of tourists and the relationship between these and the attractiveness of a tourism destination. Complex Adaptive Systems and Simulations Social and ecological systems might be inherently impossible to predict (Bernstein et al., 2000) and can be defined as complex adaptive systems (CAS). It is not easy to define CAS in an unambiguous way. However, following Levin (2002), a system can be called complex when a certain number of elements
its components
interact in interdependent ways. These interactions are typically non-linear and, although ‘simple’ at a local level, build up in a non-predictable way, generating behaviors and structures not derivable as a straightforward composition of the local characteristics. The properties of a CAS described above result in some characterizing features (Levin, 2002; Waldrop, 1992). More precisely, such systems are characterized by: . . . . Non-determinism. It is impossible to precisely determine the behavior of CAS; the only predictions that can be made are probabilistic. Presence of feedback. Whether positive or negative, loops are present in such systems and the relationships that form between the components become more important than the components themselves. Distributed nature. It becomes very difficult to precisely locate functions and properties. Qualitative difference between larger and slower functions (or cycles) and smaller and faster ones (Holling, 2001, 2004; Levin, 2002; Waldrop, 1992). 199 200 . . . Part 2: Numerical Methods Limited decomposability. The structure of such systems is studied as a whole. Again, the interactions between the components are fundamental variables, thus it is very difficult, if not impossible, to analyze CAS by decomposing them. Self-similarity. A system will have similar structures at different scales. Emergence and self-organization. Global structures might emerge in a CAS, although it is not possible to foresee these by looking at its components. Interactions between species in an ecosystem, the behavior of consumers and/or people and groups in a community, the stock market, immune systems, river networks and patterns of birds’ flight are all examples of CAS: they represent often emergent configurations that it is not possible to understand via a reductionist analysis, i.e. via an approach that reduces a complex system into sub-components, assuming that relations between these sub-components are stable and static. The study of CAS calls for a new strategy, where cross-disciplinary comparisons are carried out in order to identify features that are common to different systems in different domains (Lansing, 2003). CAS differ from systems studied in other disciplines such as classical physics, where success is achieved due to the high power of theoretical predictions, and to the accurate representation of that part of reality that the researcher wants to represent (Henrickson & McKelvey, 2002). If we are dealing with CAS, it is possible to argue that a theoretical model should help in understanding the fundamental processes, regularities and universalities that might or might not exist in such systems. Simulation may prove to be a very valuable tool in order to analyze and understand the complexities of social and ecological systems. Formal models are a representation of reality, not reality itself, and modeling is the activity of abstracting what we think are the fundamental features of a real system for a specific purpose. Models used to represent reality can be a result of different techniques: statistical, physical, mathematical (e.g. differential equations) or simulations. Statistical models are constructed from existing data, thus they might be inherently flawed if we are to model complex systems that display non-linearities, critical thresholds or sensitive dependence from initial conditions. Statistical models are able to forecast only if the system that we want to represent is fairly stable (Farmer & Foley, 2009). Moreover, in economics, general equilibrium models are used. Unfortunately, these models assume a predetermined ‘perfect’ world and hence are not able to display patterns such as those observed in the recent financial crisis (Farmer & Foley, 2009). These model categories might be appropriate to explain the desired outcomes only under a predetermined set of conditions, while Agent-based Modeling and Simulations 201 failing to explain the outcomes of CAS. Mathematical models can be more complex, but the complexities that exist in social and ecological systems often do not allow for differential equation-based models to have exact analytical results, unless we are to greatly simplify and make strong assumptions (e.g. the homogeneity assumption) on the system in order to obtain tractable representations (e.g. the impossibility of finding an analytical solution to the three-body problem, as pointed out by Poincaré, 1892
1899). We follow Galan et al. (2009) and define as mathematically intractable a formalized model that, given today’s state of mathematics, cannot provide solutions or understandable insights into the model’s behavior. For example, currently, the required assumptions and simplifications needed for tractable mathematical models do not permit a correct representation of the unique features of much human behavior (e.g. reflexivity, learning and heterogeneity of agents) (Henrickson & McKelvey, 2002). A CAS should not be modeled as an entity that passively responds to external forces as does a physical object. Simulations (or computational modeling) on the other hand, can be used to build formal representations of reality (thus a model) without the need for over-simplification or overly strong assumptions. They seem a natural candidate for representing CAS, while other techniques might be more appropriate for explaining the behavior of systems that are fairly stable and in which the outcomes are a result of linear combinations of the internal relationships, rely on equilibrium and focus on universality. In other words, the laws that govern human behavior are a result of a chain of path selections, thus inherently different from certain laws of physics, such as F ma. Simulations imitate processes (Hartmann, 1996) and can be thought of as representations of reality in which it is possible to explore different hypotheses, assumptions and parameters. They provide insights into the world represented through the use of analogy (Peck, 2008). They may be helpful for descriptions, building scenarios or devising new theoretical developments (Garson, 2009; Hartmann, 1996). Simulations enable us to explore the dynamics of a real process, where it is often not possible to proceed by empirical experiments because of scale, cost, ethical considerations or theoretical impossibility (e.g. what would have been the response to a policy that has not been implemented but that could have been a possible alternative solution?) and so on (Hartmann, 1996). Simulations are a powerful tool if used correctly, and most effort should be directed toward reflecting on the assumptions made in order to represent reality and to understand the behavior of the model to be implemented (Silvert, 2001). It is crucial to understand the role of assumptions in the model-building process. Every equation, parameter, rule, inclusion or exclusion of variables is based on certain hypotheses, and a model is only as good as its assumptions (Silvert, 2001). Thus, the primary role of a researcher should 202 Part 2: Numerical Methods be to identify and understand the implications of these assumptions. Every theoretical model, especially when seeking to represent a CAS, needs to be built through a process of continuous interaction between modelers and researchers or practitioners who deal with empirical issues. It is vital to understand what is happening in the field and how case studies, experiments and other techniques are used (Peck, 2008; Silvert, 2001). Agent-based Models Agent-based models (ABM) (or individual-based models (IBM) as they are often called in ecology) allow simulation of a system from the bottomup, that is, through an ensemble of individual entities called agents. These behave according to a predetermined set of rules and are subject to defined initial parameter configurations (Bonabeau, 2002; DeAngelis & Mooij, 2005; Macy & Willer, 2002). Agents in the model can represent any scale of social or ecological organization, from single individuals to institutions, from single organisms to species (Bonabeau, 2002; DeAngelis & Mooij, 2005; Macy & Willer, 2002; Peck, 2008; Srbljinovic & Skunca, 2003). The use of ABM has grown consistently in the last 15 years in ecology as well as in the social sciences (Breckling et al., 2006; DeAngelis & Mooij, 2005; Macy & Willer, 2002). Human beings, as well as the environment in which they live, are definitely complex, non-linear, path-dependent and self-organizing (Bonabeau, 2002; DeAngelis & Mooij, 2005; Macy & Willer, 2002). Understanding the dynamics that govern such social and ecological systems may provide a description of a system not at a global level (i.e. using standard analytical techniques), but as an emergent configuration of the interactions between individual agents (Macy & Willer, 2002). Even simple ABMs can display complex and surprising behavior patterns, such as Schelling’s (1969; 1971) segregation models, which provide interesting and novel information about the mechanisms of social groupings (Bonabeau, 2002). ABMs look to be a promising technique for the study of emergent phenomena and CAS. They do not assume that a system will move toward an equilibrium, although the system modeled might reach an equilibrium (e.g. segregation in the Shelling model). In ABMs, at every simulation time step, agents act according to the surrounding environment and take action following the rules defined, thereby allowing for the discovery of critical thresholds and emergent behaviors not easily observable or not inferable when considering single agents. This happens, for example, when interactions between agents are characterized by non-linearities, thresholds, agent memory, path dependence and time-based correlations, such as with learning and adaptation, when space is explicit and fundamental and agents’ positions are not fixed, or when populations are heterogeneous (Bonabeau, 2002; Breckling et al., Agent-based Modeling and Simulations 203 2006; DeAngelis & Mooij, 2005; Macy & Willer, 2002). This is because the description of a single agent’s characteristics with reference to the whole system can be very difficult to model in an analytical way (Srbljinovic & Skunca, 2003). As agent behavior becomes more complex, the complexity of equations increases easily beyond tractability. Moreover, in ABMs, stochasticity (i.e. probabilistic behavior) is not ‘noise’, but is applied with consciousness to agents (Bonabeau, 2002). Thus, in an ABM, agents are programmed to obey predetermined rules, reacting to certain environmental conditions, interacting between themselves and able to learn and adapt (Bonabeau, 2002; Gilbert & Terna, 2000). The modeler needs to define the agents by programming their cognitive abilities and the interactions between themselves and with the environment. More precisely, a researcher who uses computer-simulated ABM to represent a real system needs to complete a model-building process that can be delineated in three stages (Galán et al., 2009). First, the modeler needs to conceptualize the system that will be represented, thus defining the purpose, the ‘research question(s)’ and identifying the critical variables of the system and their inter-relationships. Subsequently, it is necessary to find a set of formal specifications that is able to fully characterize the conceptual model. Finally, the model needs to be coded and implemented. As noted by Gilbert and Terna (2000), the model is iterative, every agent receives input from the environment, processes it and acts, generating a new environmental input until a predetermined condition is met (e.g. time limit or all agents find themselves in a given condition). Figure 8.1 graphically represents this process. ABMs can generate a series (time series in most cases) of state variables at different scales. The results should be analyzed using Setup Agent interactions Ag 1 Ag 2 Environment Ag 3 Ag 4 Environment Stop? No Ag 5 Figure 8.1 Graphical representation of the simulation process Yes Output 204 Part 2: Numerical Methods advanced statistical techniques and tools (e.g. network theoretical tools or time-series analysis), since a single simulation run is just a particular case in the infinite parameter space. Example: ABM applications Numerous applications of ABMs exist, especially in the social sciences and ecology (Bernardes et al., 2002; Bodin & Norberg, 2005; Cuddington & Yodzis, 2000; Hovel & Regan, 2008; Nonaka & Holme, 2007; Schelling, 1971; Sznajd-Weron & Sznajd, 2000; Sznajd-Weron & Weron, 2002; Weins, 1997; Wilson, 1998). As an example, let us consider a model in which a number of agents are spread over a two-dimensional lattice. Each of them has an opinion that, for the sake of simplicity, can only assume two values. An agent can change his/ her opinion conforming to that of their four immediate neighbors if they have equal opinions. Let us also assume that these changes happen with a certain probability distribution influenced by an external factor. This is the simple scheme proposed by Sznajd-Weron and Sznajd (2000), based on the well-known model for the magnetization of a material proposed by Ising (1925), which has become probably the most famous model in the recent history of physics. This simple ABM has attracted much attention and many applications have demonstrated its validity. For example, it has been used to reproduce distributions of votes in political elections (Bernardes et al., 2002), to guess how strong an advertising campaign has to be in order to help one of two products to win a whole market, even if initially it had the minority market share (Schulze, 2003), or to simulate price formation in a financial market (Sznajd-Weron & Weron, 2002). The Schelling (1971) model of segregation re-implemented in the NetLogo environment, an agent-based modeling software, can be taken as an example (Iozzi, 2008; Wilensky, 1997). Schelling developed two different ABMs in order to explain self-segregation (Schelling, 1969, 1971). The simplest uses a one-dimensional space (a line) in which two type of agents (blue and red, circle and crosses) are randomly placed. Each agent knows his/her neighbors in a determined region (number of agents left and right from a determined agent). Each agent can be in two different states: happy or unhappy, depending on how many neighbors of the same type he/she has and an internal parameter that defines a ‘happiness threshold’ (i.e. the percentage of similar agents wanted in the neighborhood to be happy). If the agent is unhappy, he/she will move to another empty space (or patch). At every time step, happiness is computed and the simulation stops when no more unhappy agents exist. Even with this Agent-based Modeling and Simulations 205 simple rule, it is possible to discover an interesting emergent behavior as the population converges and self-segregates, producing regions populated by one type of agent and regions populated by the other. The other model of segregation proposed by Schelling uses a twodimensional space. Here, the neighborhood is defined as the von Neumann neighborhood (i.e. the four cells orthogonally surrounding the cell where the agent is placed). This second model resembles the first in terms of agents’ attributes (happiness thresholds and movement). Again, after a certain number of time steps the model converges to a state where no unhappy agents exist, and regions of different types of agents are created (thus, again, there exists selfsegregation and regions of only circles or only crosses appear). The ‘strength’ of self-segregation depends critically on the ‘happiness threshold’ of each agent, as shown in Figure 8.2. It is possible to develop a pseudo-code that permits a better understanding of the mechanisms involved in the model. In the NetLogo environment (Wilensky, 1999) it is necessary to first set global variables and variables that will determine the properties of each single agent. In the above example, global variables are average similarity and the percentage of unhappy agents. Average similarity is computed by looking at what percentage of agents are of the same type (the same color in our example). Four agent-specific variables exist: (1) happy? reports whether an agent is happy, thus if the threshold condition is met assumes values true or false; (2) similar-nearby reports how many neighboring patches are occupied by an agent with the same color; (3) other-nearby reports how many neighboring patches are occupied by an agent with a different color; (4) total-nearby is the sum of the previous two variables. Once the main variables that are used or computed by the model are defined, one has to initialize the model (thus performing a setup procedure). It is good practice to reset all variables to zero before the setup. In the setup of the Schelling model, it is necessary to input the number of agents that will populate our world. Once the agents are created, we need to assign them a specific color (in the example used, agents are equally split between red and green) and assign them to a location (agents in this case are randomly assigned). If an agent is assigned to a cell where another agent already exists, the agent will try to find another location and will move until he/she finds an empty cell. Once the agents have their own color and are placed on the twodimensional space, it is possible to set the ‘happiness threshold’ variable. In the example proposed, this threshold is equal for all the Part 2: Numerical Methods 206 (a) (b) (c) (d) Figure 8.2 Self-segregation in the NetLogo simulation for three different values of the ‘happiness threshold’ for two types of agent (green, red). Figures were generated using the same random seed (90) to ensure that the differences in the results reported graphically are only an effect of the happiness threshold parameter. A represents the initial state, B represents a world in which happiness threshold25%, C happiness threshold50% and D happiness threshold  75%. agents in the model, but it is also possible to assign different happiness thresholds to every agent (this may be an interesting extension in order to look for possible differences between the original model and the ‘personalized happiness threshold model’). Once the model is set, it is possible to start the simulation, thus looking for patterns to emerge during the time development of the model. In order to run the simulation, at every time step, agents need to perform predetermined tasks. In our example, the simulation stops Agent-based Modeling and Simulations 207 when all agents are happy. (Thus, happy?true Ö agent); if there are unhappy agents, these will move, looking randomly for a new empty cell (they keep moving randomly until they find an empty cell1). Once all the agents have checked if they are happy or not (and in the latter case they have moved), global variables and agent-specific variables are computed, and the simulation is ready to enter a new time step. As noted earlier, the simulation will run until all the agents are happy, thus until for every agent the variable happy? is set to true. Issues with Agent-based Models ABMs are often very complicated, both conceptually and mathematically, thus understanding them in detail can be quite an intricate exercise (Galán et al., 2009). Skepticism exists around computational models, because the results might be counterintuitive (although counterintuitive does not necessarily mean incorrect). Here, it is worth remembering that the main purpose of simulations and ABMs is to allow for new theoretical developments and advances. If the model is considered plausible (within reason) and coded correctly, even if its results might be counterintuitive, we can look toward a possible theoretical advance or the development of a new theoretical understanding of the system under study. One risk is that the results might be the consequence of an unknown process inside the ‘black box’ (the computer) used to perform the simulation (Macy & Willer, 2002). The latter can be and has to be tackled by publicizing the models and by exposing the models’ code to the scientific community so that it will be possible to validate and to replicate the results. Moreover, the value of ABMs for theoretical development could be dismissed as ‘muddying the water’, as the number of variables, parameters and their relationships may approach the complexity seen in the real world (Peck, 2008). It is important to take into account that ABMs are not a universal solution. Currently, there is no formal methodological procedure for ABM building, although certain similarities with all model-building methods exist. The first step that needs to be considered is that there are no discrepancies between what we think we are representing and what the coded model is actually doing (Galán et al., 2009). One needs to be careful when planning and structuring the model. In particular, it is always worth taking into account that a model has to serve a purpose, and hence, has to contain the right level of detail. As already noted, a model cannot retain all the real world’s details and it should be a simplified, although meaningful, part of reality (Axelrod, 1997; Bonabeau, 2002). When constructing a model, we need to abstract from the real world, thus in ABMs more than in other modeling techniques, it is 208 Part 2: Numerical Methods necessary to refer to practitioners or to draw on empirical research or carefully review the existing literature in order to gain insights into processes and fundamental behaviors that characterize single agents and their relationships with these or the environment. It is important to look for implications, and evaluate that very same model. Furthermore, without a clear research question to answer, a model will not be useful in understanding the part of reality under investigation. Thus, we need to thoroughly identify assumptions and ‘measure’ the impact of each one of them on the results produced by the model (Galán et al., 2009). Moreover, ABMs should be treated carefully when looking at the quantitative aspects of the results (Bonabeau, 2002), because the importance and the validity of ABMs relies on their ability to explain different configurations arising from the set of parameters used, and in allowing a (mainly) qualitative understanding of the system studied. ABMs and simulations need to be treated and approached differently from traditional analytical models (Peck, 2008). The most challenging aspect of ABMs resides in careful understanding and planning of how single agents will behave. The choice of rules that will allow them to interact with the environment and between themselves is a central issue. There is a need for a systematic procedure and it is necessary to avoid assumptions that are not confirmed by ‘general wisdom’ (existing literature, experts assessments, etc.). Therefore, as already stressed, continuous interaction and feedback between researchers and experts is necessary to shed light on the appropriate parameter space to explore and the interactions that exist between agents, and to assess the appropriateness of the model at its different stages (initiation, running, validation) (Farmer & Foley, 2009; Galán et al., 2009; Peck, 2008). Even when we engage continuously with experts and we carefully plan our simulation following all the good practices defined for the modelbuilding process, there is still room for error and artifacts of methodology to distort the results (Galán et al., 2009). More precisely, errors refer to a disparity between the coded model and the model that the modeler intended to code (e.g. the modeler wants the model to call for TaskA before TaskB, but the model runs TaskB before TaskA). It is important to highlight the fact that this type of error does not exist if there is no disparity between the actual model and what was meant by the researcher, thus it is not possible to assert that an error exists if we do not know the modeler’s objectives. Obviously, the modeler’s intentions should always be clearly stated. Artifacts, on the other hand, are disparities between the assumptions made by the researcher and thought to be the cause of specific results and what is actually causing them. This might happen because sometimes it is necessary to formulate hypotheses that are not critical for the representation of the system, but are required in order to run the simulation code (e.g. the size of a grid Agent-based Modeling and Simulations 209 might influence the results although the very same size is not a critical assumption of the system we are modeling). It is important to point out that an artifact ceases to be an artifact as soon as it is discovered, and the cause of the results becomes known. Both errors and artifacts can be avoided. In order to avoid errors, one needs to meticulously check the coding procedure and all its parts in order to make sure that the coded model is performing exactly as it was intended to. Artifacts can be avoided by implementing a model with the same critical hypotheses but with different assumptions, in order to check how results are affected. This is a common procedure to assess the validity of the outcomes. Evaluation of an Agent-based Model Validating, verifying and evaluating ABMs can be a tough task. Simulation behaviors are usually not understandable at first glance (Srbljinovic & Skunca, 2003). Nonetheless, it is possible to evaluate an ABM or a simulation. The first criterion is reliability, which can be assessed by producing different separate implementations and comparing the results. This is not, however, sufficient by itself to evaluate an ABM. Taber and Timpone (1996) propose three more methods for validating a simulation model. They ask: (1) Do the results of a simulation correspond to those of the real world (if data are available)? (2) Does the process by which agents and the environment interact correspond to the one that occurs in the real world (if the processes in the real world are known)? (3) Is the model coded correctly so that it is possible to state that the outcomes are a result solely of the model’s assumptions? Answering the first two questions allows us to assess the validity of the representation (model), thereby gauging how well the real system we want to describe is captured and explained by its representation. Answering the third question guarantees that the model’s behavior is what the modeler really intended it to be (Galán et al., 2009). Evaluating an ABM requires data from the real world and the involvement of knowledgeable experts who might be able to give insights into the ‘real’ processes and dynamics to evaluate its plausibility as a representation of reality. Moreover, it is worth stressing the importance of the conceptual accuracy that is needed in order to build ABMs that are able to advance our theoretical understanding of a system. Every part of the code in a model should be grounded in the literature or informed by experts (i.e. empirical researcher and practitioners), and the final test of any ABM is its importance in advancing understanding and the development of new formal theories. 210 Part 2: Numerical Methods Example: Simulating the arrivals of tourists Tourism is a complex system as is the object named tourism destination, considered today to be a crucial unit of analysis for the understanding of the whole sector. Its behavior can be considered that of a CAS (Baggio, 2008; Farrell & Twining-Ward, 2004; Faulkner & Russell, 1997; McKercher, 1999). A growing strand of literature has maintained that a linear deterministic description is not sufficient to explain the behavior of a system whose components may have many different relationships among them. This problem is even more evident when considering the dynamic behavior of a destination. As discussed in the previous sections, the most important result of an agent-based approach to modeling complexity is the realization that it is not possible to fully predict the dynamic evolution of a complex system (Doran, 1999). It is well known that tourism forecasting is a complicated and difficult activity. It is, though, an important venture that has attracted a myriad of studies. Usually, the quantity measured is the number of tourist arrivals, predicted by analyzing an historical time series and using mathematical and statistical procedures (Song & Li, 2008; Song & Witt, 2000). However, even the most sophisticated methods seem unable to provide reliable results (Tideswell et al., 2001). It is also difficult to choose the most appropriate one, as similar techniques give different results in different conditions or environments (Papatheodorou & Song, 2005), or can even be influenced by country-specific characteristics (Wackera & Sprague, 1998). What would be valuable is some method to predict, for a reasonable time span, the quantities of interest (tourist arrivals) or, given certain variations in some of the destination parameters, how these quantities may change with an accuracy sufficient to draw scenarios that can help in the decision making or planning process. The attractiveness of the destination is a major determinant of the arrivals of visitors to a place. Several attempts have been made to define this concept and to find measurable elements to assess it (Mazanec et al., 2007; Pike, 2002). Moreover, a large number of studies have been devoted to investigating the elements that contribute to the attractiveness of a destination and how to exploit them in order to improve the destination’s ranking in the international arena. The level of achieved attractiveness is known to be related to destination outcomes, such as tourist arrivals, stays or expenditures. Also, as expected, increases in destination attractiveness are reputed to be good determinants of the increase in both arrivals and stays in a location. One interesting problem, rarely discussed, is the relationship that could exist between the effort made to improve attractiveness and the returns this improvement might provide. Moreover, while most Agent-based Modeling and Simulations 211 papers describe single destination cases, the influence of other systems pursuing the same objectives and implementing similar plans is an important factor that could result in outcomes different from those expected. This is the typical problem that is almost impossible to study with analytic methods, but is a good candidate for ABM. The model A simple model was designed to investigate the relationship between attractiveness and tourist arrivals and was implemented in the NetLogo environment (Wilensky, 1999). The model is illustrated in Figure 8.3. There is a certain number of destinations (25), all inter-connected. An attractiveness attribute is assigned to each link (the route between two destinations); attractiveness assumes values (0
1) with 0 being the most attractive destination. Agents, representing travelers, are assigned to each destination at the beginning of the simulation (100 agents per destination). Each agent has a personal threshold (change) indicating a willingness to travel, and a memory, so that agents remember the last visited destination. Willingness to travel is randomly assigned to agents and assumes values in the interval (0
1). As a global parameter for the model, a probability to return to the previously visited destination is defined. The model runs for a defined number of time steps (100). At the first time step, the agents randomly choose, with a probability Figure 8.3 The NetLogo model of tourist arrivals 212 Part 2: Numerical Methods dependent on the difference between their personal threshold and the attractiveness of the destinations, a place to go. All travels are single trips, agents return to their original location after visiting a new place. At each subsequent time step, agents choose the next destination following the same rule. If the probability to return is greater than zero, agents return to the last visited destination with that probability (otherwise, choice is random as for the first trip). Results Different simulation runs were performed. First of all, the attractiveness values were assigned according to two different distributions: random (uniform) and exponential. The latter is obviously more realistic and it mimics the real distribution of tourist arrivals to destinations (Baggio, 2008; Ulubaşoğlu & Hazari, 2004; UNWTO, 2009). The figures shown in the next pages report the results of the model. In all the figures, mean arrivals is the number of tourist arrivals per destination averaged over 100 runs and frequency is the number of destinations receiving that number of tourists. When memory effects are disregarded (agents choose randomly at each time step), the distribution of arrivals resembles the attractiveness distributions (Figure 8.4 and 8.5). A second series of runs was performed with different probabilities to return to the last visited destination (run 1 0; run 2 0.25; run 3 0.5; run 4 0.75; run 5 1). Memory effects seem not to be significant in affecting the distribution of destination arrivals. That is, attractiveness of a destination and the willingness to travel of a single agent seem to be more important than memory effects, at least in our simplified model (Figure 8.6 and 8.7). Increasing the attractiveness of a tourism destination Let us now assume that a number of destinations put in place some actions to improve their attractiveness. How will this improvement be related to the number of visitors arriving? Will the increase radically change the final distribution of arrivals? Three destinations with the lowest value of attractiveness were randomly selected and the simulation was run (in the same cases as above) with a 200% and a 400% increase in the attractiveness parameter (a threefold and a fivefold increase). The total number of travelers is constant (it is a fixed model parameter), but the distribution changes slightly. The three destinations experience an obvious increase in arrivals to the detriment of the others. The distributions are thus differently skewed, but, in essence, the way in which the whole Agent-based Modeling and Simulations 213 Figure 8.4 Distribution of mean arrivals when attractiveness is uniformly distributed Figure 8.5 Distribution of mean arrivals when attractiveness is exponentially distributed ‘world’ is behaving does not seem to change significantly (Figure 8.8 and 8.9). When we analyze the relationship between improvement in attractiveness and arrivals for the destinations considered, however, we find some important differences. Table 8.1 summarizes the results. A rise in the attractiveness of a destination results in an increase in 214 Part 2: Numerical Methods Figure 8.6 Mean arrivals for randomly distributed attractiveness and different probabilities to return Figure 8.7 Mean arrivals for exponentially distributed attractiveness and different probabilities to return Agent-based Modeling and Simulations 215 Figure 8.8 Mean arrivals for randomly distributed attractiveness and different probabilities to return, with different attractiveness for three destinations Figure 8.9 Mean arrivals for exponentially distributed attractiveness and different probabilities to return, with different attractiveness for three destinations Part 2: Numerical Methods 216 Table 8.1 Relationship between increase in attractiveness and arrivals Arrivals increase Random distribution (%) Exponential distribution (%) 200 75 53 400 124 87 Attractiveness increase (%) arrivals, as expected. However, the outcomes are significantly lower than the effort spent in improving the destination’s image. This effect is more pronounced when the attractiveness values are exponentially distributed. With a very simple ABM, it has been possible to replicate, at least at a very general level, the behavior of travelers, and to perform a series of experiments by changing the model parameters. Different scenarios have been built and these, combined with other investigations on the subject, could be the basis for more considered decisions by a destination manager. The model presented here is a very basic view of the phenomenon. Many assumptions made are strongly simplified, and some can also be considered not very close to a real situation. Our objective here was only to exemplify the process of ABM building. In our case, for example, it can be determined that, even with all the simplifications introduced, the model is able to render results that are reasonable and reproduce, at least at a general level, what happens in the real world. To expand the model, it is possible to increase the level of sophistication by specifying better and more realistic parameters and rules. The knowledge of a specific situation derived from other studies can give guidance in implementing more complete agent behaviors (e.g. dynamic thresholds, imitation effects and cost effects), and better and more complete characterizations of the destination attractiveness qualities can be devised. Concluding Remarks ABMs and numerical simulations have recently confirmed their importance as tools to study a wide class of natural and artificial systems. In all cases in which a direct modification of the system, or of the parameters that govern its behavior, are impossible for practical or theoretical reasons, ABMs have proved to be able to provide useful Agent-based Modeling and Simulations 217 insights into the objects of study. Obviously, many limitations exist and a strand of the literature has highlighted them well and provided methods to assess their validity and reliability, as well as their usability from both a theoretical and a practical point of view. If these basic rules are respected, a well-designed ABM can be a useful instrument for the researcher. This chapter has discussed the main issues related to ABMs and has provided a simple example of their use in an analysis of the relationships between the attractiveness of a tourism destination and the movement of tourists. It has been shown how even a very simplified model is able to provide interesting results. It is also noted that, with further refinement and by combining these outcomes with more traditional methods of inquiry, ABMs can be an important generator of future scenarios to be analyzed and discussed to gain better knowledge of the mechanisms governing a system’s evolution. Note 1. For more detailed discussion of the problems of random movement and differences between the NetLogo implementation and the original movement described by Schelling, see Iozzi (2008). References Axelrod, R. (1997) Advancing the art of simulation in the social sciences. Complexity 3 (2), 16
22. Baggio, R. (2008) Symptoms of complexity in a tourism system. Tourism Analysis 13 (1), 1
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