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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.21 No.2 pp.206-219

Synthesis of Linked Population Involving Kinship and Influential Ties Using Mate-Search Heuristics

Jeongsik Kim, Namhun Kim*
Electronics and Telecommunications Research Institute, Daejeon, Republic of Korea
Department of Mechanical Engineering, Ulsan National Institute of Science and Technology, Ulsan, Republic of Korea
*Corresponding Author, E-mail:
May 4, 2021 ; August 27, 2021 ; September 28, 2021


Agent-based simulation has been successful in generative approaches on the emergence of various social phenomena. However, many case-specific studies used to put aside the potential of generating linked individuals. This paper proposes a convergent format of agent-based simulation and demographic microsimulation to grow up a linked population with two known properties of our society: Small-world networks and mate-search heuristics. Given that population is the core entity of a society, a demographic base is developed and individual-level rules from multidisciplinary findings are added to assign the capability of social networks. The results demonstrate how the social structure affects the speed and maximum degree of the targeted diffusion and indicates the correlation between individual-level attributes and aggregate indices in modern society. A comparative study is then conducted to reproduce an extreme case of an empirical reality. The study is expected to offer an illustration for population incorporating influential networks and multidisciplinary hypotheses.



    Agent-based modelling and simulation (ABMS) has many motivating cases but limitedly reproduce their contributions on social systems (Macal, 2016;Lorscheid et al., 2019;Grimm et al., 2020). In particular, its vast applicability from natural science to engineering is not beneficial for its theoretical unification (Macal, 2019). ABMS methodologies are required to be more coherent so that researchers and policy makers efficiently test their hypotheses and knowledge across various disciplines. This research aims to explore a generative approach using a convergent modelling framework, which combines ABMS and demographic microsimulation (MSM). In this paper, the population is proposed as a medium for multiple sectors of our society. As a step, a population synthesis is proposed to incorporate findings on Small-world property (Watts and Strogatz, 1998) in network theory and human imitation heuristics (Todd et al., 2005) in demography.

    Demography has a relatively long history of adopting simulation methodologies by virtue of the relative abundance of accumulated statistics (Courgeau et al., 2017). The classic role of demographic simulations has been statistical estimation based on empirical data, which deal with population from a macroscopic viewpoint. In modern demography, two microscopic approaches of MSM and ABMS became popular thanks to their different strengths. The MSM has been earlier utilized based on the benefit of data-driven format to model a society of micro-level entities (i.e., individuals) by using statistical data from multiple sources, such as individual characteristics and national indices (Morand et al., 2010). For example, more than sixty microsimulation models of a national scale have been developed until 2013 to provide political implications with a series of social sectors (Li and O’Donoghue, 2013). On the other hand, the popularity of ABMS is thanks to its ability to capture nonlinear features (e.g., social interaction and prescriptive information) while reducing the excessive dependency on empirical data in existing methods (Silverman et al., 2011).

    Recently, many social scientists have adopted interdisciplinary approaches to compensate the shortcomings of each discipline (Schlüter et al., 2017). The modular extension of ABMS on the data-driven format has been suggested to study social phenomena of multiple sectors with the controlled dependency on data (Reinhardt et al., 2018). Basically, both methods belong to a class of discrete-event simulation and treat population as a set of micro-level actors with the multi-level analysis of individual, population, and interim-level phenomena (Richiardi, 2014). With the structural similarity, the combination has been conducted on the converged form (i.e., the modular extension on the data-driven base), while complementing one another for top-down and bottom-up perspectives of multidisciplinary studies.

    The scope of this study is to build a linked population on the convergent framework of ABMS and MSM. On the framework, we illustrate the add-on of special ties which are influential networks from Small-world property (Watts and Strogatz, 1998) and partnership networks from human imitation heuristics (Todd et al., 2005). The remainder of this paper is structured as follows. Section II provides a background for the reconfiguration of population models. In Section III, the reconfigured model is specified in the form of a base model and agent-based extensions. In Section IV, the proposed model is verified to reproduce the demographic reality of a rapidly changing society (the Republic of Korea in 2000, 2005, and 2010). The targeted dynamics is compared to a classic mate-search model (Billari et al., 2008), a successor of the imitation heuristics, to check the variability of each scenario in terms of two viewpoints (i.e., rewiring probability and generational interaction). Finally, Section V discusses the contribution and limitations of this research.


    2.1 Population with Mate-search Heuristics

    Mate matching has been selected for social scientists to incorporate social networks among individuals, in that marriage is a social contract for a special relationship between individuals and the quantitative aspect of the event has been recorded for a long time (Eversley, 2017). Wedding Ring model (WR model), developed by Billari et al. (2008), is one of the representative models to generate linked lives considering three types of social links (i.e., kinship, friendship, and partnership). The original goal of the model is to imitate the marriage behaviour based on micro-level rules. It describes how the micro-level behaviour rule of an unmarried agent can be applied to capture the macro-level curves of empirical age-at-first-marriage. The central idea of the work is that the share of married people within the social network of an individual affects its willingness to marry and the availability of potential partners as illustrated in Figure 1. Conceptually, the spread of marriage could represent a diffusion process in a complex system with supplementary functions based on several assumptions in the macro-level diffusion model of first marriage by Hernes (1972).

    The WR model has been combined with demographic and economic findings to incorporate various sociodemographic factors of the real society with the data-driven methodologies (Billari, 2015). A few extensions of the benchmarked model have been already reported to reproduce empirical demographic reality with the acceptable predictability. For example, Bijak et al. (2013) have shown its predictive capability with empirical fertility and mortality by conducting parametric modifications, which arithmetically relates to how agents feel social pressure from the share of married neighbours among relevant others. Noble et al. (2012) and Silverman et al. (2013) applied the concept of the WR model to develop a demographic laboratory and provide the political implications of practical problems.

    However, the extensions stick to the original form of composing the social structure, although the benchmarked model illustrates the marriage heuristics with a parsimonious structure (i.e., range-based algorithm for all interactions) as a theoretical abstraction for one possible mechanism that might generate the typical bell-shaped pattern of age-specific nuptialities (Prskawetz, 2017). In addition, the social structures of real societies must be differentiated by culture, generation, and region while the original work controlled social interactions based on a part of an old survey in US (Marsden, 1987). More specifically, the WR model restricts the maximum ranges for its social interaction by using an ‘age influence’ function based on a report which surveyed networks of Americans for core discussions. Even the survey reported that the personal networks for important discussions are ‘small, kin-cantered, relatively dense, and homogeneous’ while the ‘age influence’ function embedded in the benchmarked model reflects only the quantitative aspect by the age difference. Thus, the structure of social networks in the benchmarked model is capable of enhancing for the social structures in different space-times.

    2.2 Mate-search Models in Terms of Social Networks

    Mate-search models belong to a diffusion model of a social characteristic. In fact, a diffusion is a basic phenomenon of a society in which social networks play a fundamental role as a medium for the spreading of information. A lot of studies have investigated the effect of social networks on various diffusion processes such as infectious disease, innovation, and consensus (Rahmandad and Sterman, 2008;Kim et al., 2021). The implication of social networks has become important on social behaviours (Will et al., 2020) as well as demographic behaviour (David-Barrett, 2019). In agent-based computational demography, a few researchers reported the importance of social networks to replicate empirical patterns in the real world. For example, the famous model of segregation by Schelling (1971) shows a simple behaviour rule of finding a new position when the agent has an unsatisfactory neighbourhood and explains the segregation pattern in the real world.

    In the study of family formation, Fent et al. (2013) and Diaz et al. (2011) concludes that the social structures in population studies can account for patterns of first childbirth and effectiveness of family policies by taking social characteristics of age and education in single-sex population. In particular, Diaz (2010) has analysed different structures of the network on the predecessor of the WR model which has the same assumption of marriage heuristics for the diffusion process by the share of married agents. The author compared four different types of networks and successfully reproduced the bell-shaped curve of typical nuptiality in a one-dimensional setting of relevant others. However, the simulation model provides neither the typical curve of real nuptiality in a twodimensional environment nor the different context such as cultures or regions.

    In this paper, the interdisciplinary approach of the marriage heuristics in demography and the Small-world property in network theory is illustrated on an agentbased framework to investigate the dynamics of linked lives with Asian contexts. The Small-world property is a feature widely observed in real-world social networks which are not captured by the random graph. In the structure of this property, an agent tends to create a tie with another who has been linked to its acquaintance. Simply, the real networks have tight-knit community compared to randomly linked networks, not the level as the regular lattice structure. Thus, the rewiring probability of a wellknown model for the Small-world property is incorporated as a key input of the proposed simulation to accord more realistic social networks of the Asian context.

    This research contributes to providing agent-based linked population for model-based social studies. Given that population is the core entity for a society, this paper presents a generative approach to explore the linked population with the findings of the Small-world theory and mate-search heuristics. In the illustration, the propagation of the targeted diffusion is examined to assess the performance of each scenario in terms of two viewpoints (i.e., rewiring probability and generational interaction). Then, the developed model has been verified to successfully reproduce an extreme demographic reality in the Republic of Korea. Notwithstanding the limited outputs, it is noteworthy that the hypothetical behaviours at the micro level can reproduce the macro-level patterns of empirical statistics to overcome the shortage of the historical data (e.g. social networks).

    3. METHODS

    3.1 Base Model Grounded on Microsimulation

    The designed structure of the base model derives from the modular system of data-driven microsimulations (Spielauer, 2011). The fixed sequence of the unified structure can decrease ill-considered variances by minor structural changes, from the nature of ABMS, like the order or sequence of the intended events and the time of observations. Likewise, the behaviour for a default agent in the base model is limited to the essentials of life (i.e., birth, death, and ageing) which are ubiquitous on time and place. Of course, there must be countless basics by each discipline, and the question of which behaviours should be incorporated to represent human beings is controversial. For example, economic activity could be an essential behaviour to study various phenomena. In this paper, the scope is selected to reconfigure a demographic model on the convergent form. Thus, the four basic demographic behaviours (i.e., birth, death, marriage, and getting old) are incorporated.

    The only agent of the designed model is a human actor which has multiple state variables. The agent conducts a sequence of assigned actions of which part repeats in each step. These actions can be considered as aggregatelevel states in either discrete-event systems or discretetime systems except for the fixed order of the events in a step. The specific state of a simulation can thus be defined as the action states of the agents and the set of individual states. Actions can be divided into population- and individual- level actions. At each population-level action, agents have a series of chances to conduct assigned individual- level behaviours or state transitions. After all agents conduct the assigned behaviours of the populationlevel action, the agents move on to the next state. Thus, the individuals will experience the assigned action at the same phase. All action states of the base model are set to be passed once per step whereas the frequency needs to be properly tuned in that the excessive level of the frequency might be directly related to computational load and temporal resolution issue.

    The working mechanism of the designed model is illustrated in Figure 2. Both types of rectangles represent the stages of the model for the actions. It is noteworthy that the population-level stages of a model represent the global flow of the simulation. First, the model initializes all parameters and generates the starting population with given characteristics. After that, the simulation gets in the step 0 and agents start to conduct the assigned algorithm for each state. For example, the system records the result of the individual behavior at the step in the ‘record’ stage. After the record, the system will repeat all processes from the ‘remove’ stage until reaching the prearranged step and then finish the simulation at the ‘finish’ stage.

    An individual action in the stage of ‘remove’ is defined by using a microsimulation approach. In this format, the state transition of an individual occurs according to its transition probability. From the benefit of the microsimulation system, users can easily input table-type data for the transition rates between individual states from empirical statistics. An example of the data-driven transition is illustrated in Figure 3 where the solid line represents the state transition and the dotted line stands for the data flow. Initially, the conditional probability from a specific state (e.g., age ‘x’ and ‘alive’) to another (e.g., age ‘x’ and ‘dead’) is acquired based on empirical data (e.g., life tables). Then, the assigned transition will occur according to the input probability (e.g., mortality). Depending on availability of empirical data, the transition rates for a targeted state could be calculated under multiple characteristic conditions, such as age, sex, and date. With the structural advantage, researchers are expected to replace tables of transition rates based on statistical analysis or forecasting models for the transition (e.g., Lee-carter model for mortality (Lee, 2000)) or to add on another module for both population- and individual-level actions. As we have already had occasion to note, the base model is designed to consider two representative methods of data-driven microsimulation and agent-based modelling of which modular extension will be exemplified in the following subsections.

    The proposed model allows the propagation of information to flow in the specific direction of the sequence, possibly allowing the domino effect of a certain event through social interactions while guaranteeing simplicity of the base structure. The decreased complexity can be compensated by increasing the temporal resolution of simulation when necessary. In other words, the unit of simulation time is represented as a step which can easily be extended to pseudo-continuous system according to the frequency of actions. For example, an individual action of adding 0.5 or 1 year to age can occur in each step and then the time scale of a step must be a half or one year of the virtual world. The rigid structure connotes important issues for the modeler to add on new module. A certain event will never affect the preceding incidents at the same step because the transition of the system-level state is irreversible in the same step. Modelers thus need to place a certain module in the proper position or take account of changing the time scale of a step. In addition, the timeline of ages and record times should be clarified to prevent from the interpretation errors of result. For example, the ith observation is actually recorded during the (i-1)th step because the count of step might start from zero. This is further complicated in cases where agents get old during the step. Then, a zero-year-old agent in the record is a new baby while a one-year-old agent in the record is a zeroyear- old agent at the starting of the step.

    3.2 The Individual-driven Behaviours

    In the ‘individual behavior’ stage, each agent conducts the assigned algorithm as shown in Figure 2. The first thing is ageing because the time unit of one step is one year and the age of agent affects its decision for the other actions. Next, the agents aged over 15 choose up other agents within the characteristic interval of age and space (‘air’ and ‘sir’) for its relevant others to get the share of married agents (som) among the selected agents. Then, unmarried agents try to compute the social pressure (sp) according to equation (1 ), with default value of 0.05 at som=0.00, and find potential partners of opposite sex within another interval for a partner updated from equations (2) and (3). The unmarried agents get matched if the distance between them is smaller than the inherent intervals (i.e. ‘aip’ and ‘sp’) of both.

    sp=exp[β ( som-α ) / ( 1+exp [ β ( som-α ) ] ) ]

    aip=sp age

    sip=180π sp N -1

    where ‘som’ in the first equation is the share of married agents among the set of relevant others and α and β are the constants by which ‘sp’ converts the individual ‘som’ to the willingness and accessibility for marriage. In equation (2) and (3), ‘aip’ is the age interval for a partner and ‘sip’ represents the maximum spatial interval for a partner. The term ‘age’ is the current age and ‘sp’ is social pressure of the agent. In (3), ‘N’ is the population size of the simulation at the time.

    The key extension of the proposed model is who will be linked with the other in the phase of choose relevant others. A new behaviour of rewiring has been incorporated based on the WS model of the Small-world property (Watts and Strogatz, 1998). More specifically, all agents do:

    • i) get a nearest-neighbour network with the assigned spatial and age interval (identical to the original WR model)

    • ii) replace the neighbouring relevant others with randomly chosen agents at the pre-set rewiring probability (i.e., an input parameter of the simulation).

    Simply, this model proposes an add-on of the Smallworld property. The probability for the property is examined to find the appropriate social structure for a specific population in the result section.

    3.3 Experimental Setup

    The basic setting for the simulation is taken from the WR model to be compared to the developed model. All detailed parameters of the developed model are listed in Table 1 in which the empirical distribution has been replaced with the statistics of the targeted society (South Korea at the year 2000, 2005, and 2010 (Korean Statistics, 2011)). The only actor in the model is a human agent that exists on a ring with a randomly generated angular parameter from zero to 2π (i.e., spatial location) and does not move until the removal. An individual agent has characteristics to represent ID, spatial location, age, marital status, the spatial and age intervals for its relevant others with the link to the partner agent as well as the individual sets for relevant others and kinship. First, the range of age variable will be non-negative integers under 100. This study adopts two levels of ‘Never married’ and ‘Ever married’ to represent the marital status identical to WR model (Billari et al., 2008). Both maximum intervals for relevant others are randomly defined at the birth of the agent while the age interval has two additional characteristics for its mean and width.

    These agents will be generated and controlled following to the flow diagram in Figure 2. At the initial state, the model generates the given number (N) of agents with multiple characteristics following to the given distributions which are specified in Table 1. Each age has eight agents while its marital status is defined according to the age-specific distribution of the input statistics. After that, the simulation gets in the step 0 and agents start to conduct the assigned algorithm for each state. In the ‘death’ state, the agent will die according to the transition probability which has 0.0 for age levels from 0 to 99 and 1.0 for age 100+. Then, the alive agents will get chance to behave the assigned actions which have been described in subsection 3.2. Married women will be pregnant according to the age-specific fertility rates of South Korea in the year 2000, 2005, and 2010. At the ‘ageing’ state, it will add the time scale of a step (i.e., one year) to the ages of all agents. At the next state, zero-age agents will be generated while the number of births will be identical to that of the deaths at the starting of the step to fix the total population size. Here, the parent agents will be linked with the baby agent. At the ‘record’ state, the system records the result of the individual behaviours at the step. After the record, the system will repeat all processes from the ‘death’ state until reaching the prearranged step and then finish the simulation at the ‘finish’ state.

    To evaluate the performance of a diffusion process based on social networks, the analysis has been conducted on the original WR model and the proposed model. The input parameters of rewiring probability (p) are spaced 0.01 apart from 0.00 to 1.00. Here, the rewiring parameter of ‘0.00’ means no change of nearest neighbours while the input of ‘1.00’ stands for changing all neighbours to random agents (i.e., random graph). Note that WR model does not rewire social networks. Thus, the scenario of no rewiring (p=0.00) at the original age influence gives the same result as the benchmarked model. Another input option, so-called ‘Substitute Range’ option, is standing for which type of individuals replace one of the relevant others at each rewiring. A social network in the original model is composed of nearest neighbours in both ‘age’ and ‘space’. We set two age-based options of {Whole Age, Same Age} to check the effect of generational disconnec- tion. The agent in the option of ‘Whole Age’ picks a completely random agent for replacing, whereas the agent in the option of ‘Same Age’ picks a random agent who have the same age with the dropped agent in the original set. Thus, in the latter option, the rewiring probability does not affect the social networks of the system with respect to age level.


    This section describes the illustration of the developed model. The role of different influential networks is examined to assess its effect on the speed and maximum degree of the targeted diffusion on the original and proposed modelling alternatives. At the end, the extended capability of adopting the rewiring function will be checked to reproduce an Asian case of the empirical demographic reality.

    The modelling and simulation in this research have been conducted using a java-based simulation tool (Anylogic 8.2.3 university edition, available at on the same computing system. The simulation has not proven to be heavy in terms of computation time, with about two minutes per run on a standard desktop. System specification including processor, system type and memory information is listed below: Its processor is i7-7770 3.60GHz. The system type is 64-bit OS Windows 10. It also has 500GB SSD. The maximum available memory for simulation is set as 8GB.

    All the following outputs represent the averages of 30 runs to provide trustworthy results. The averaged outputs during 150 steps from the 151st step are recorded to give steady-state outputs and the unweighted moving average for the nearest five levels is applied to smooth out the erratic pattern of raw outputs. To analyse each scenario, the study observes the key information of nuptiality as well as two independent variables (i.e., ‘Clustering Coefficients’ and ‘Mean Age of ROs’). In the result tables (i.e., Table 2 and 3), we have five additional observations; ‘Clustering Coefficients’ is a typical measure for the tightness of social networks in small-world networks and it is calculated as the weights of the common agents between a set of relevant others for an actor and the other sets which the relevant others of the actor have had (Alam and Geller, 2012), ‘Mean Age of ROs’ is the mean age for individual sets of relevant others that whole population have chosen up, ‘Peak Hazard Rate’ means the peak of hazard rates over all age levels, ‘Mean Age for Marriage’ represents the mean age of married population during the step, and ‘Sum of Crude Rate’ represents the accumulated proportion of marriage for all age level.

    The input set of {0.00, 0.05, 0.10, 1.00} and {Whole Age, Same Age} is selected to highlight the basic dynamics in each modelling alternative. The colour maps of full rewiring probabilities are depicted in Figure 4, while Figure 5 and 6 show hazard rates of marriage from age 16 to age 60. Generally, the steady-state nuptialities by specificage levels draw the bell-shaped curves of the empirical observations and the increase of p shows unidirectional tendency in all observations of the diffusion. Both functions of age influence provide similar responses to the optional inputs of ‘Substitute Range’ and ‘Rewiring Probability’ while the rule-based alternative generates relatively higher peak values with small p. The rewiring probability seems to accelerate the speed of the diffusion whereas the effect is much smaller in the option of ‘Same Age’. The comparative analysis is conducted, in the viewpoints of the binary options and the fitting capability, to explore the performance of each scenario by increasing p.

    4.1 Substitute Range: Whole Age vs. Same Age

    The selected outputs in each age-based option reported the clear differences in most observations excepting the sum of crude rate. First, clustering coefficients become smaller by increasing p and almost zero in the case of ‘Whole Age’ at p=1.00. The decreasing levels of clustering coefficients are a quite different between the substitute ranges of rewiring because the ‘Same age’ restriction gives significant influence for the tightness in that eight agents exist on each age. Second, we can verify the expected effects on age level by the substitute-range options. The mean age of ROs significantly changes in the option of ‘Whole Age’ whereas it does not in the other.

    The higher rewiring probability gives bigger value for the peak of nuptiality as well as smaller value for the mean age of nuptiality. This tendency could be understood by the effect of the rewiring which promotes lower clustering and wider dynamics for sets of relevant others. Then, the wider range of interactions speeded up the diffusion process. The effect is more evident in the ‘Whole Age’ scenarios. Young agents, who are major candidates for marriage, may take higher share of married agents caused by the higher age level of rewired relevant others. In this sense, the ‘Substitute Range’ option is found to control the tightness of influential networks, which affects the sensitivity on the propagation of the targeted diffusion. Notwithstanding the extremely limited scenarios, the results indicate that the intergenerational communication can be a key factor to understand the marital changes of the advanced countries in which the young generation experiences a higher proportion of nuclear families and a lower proportion of the aged relevant others.

    4.2 Age Influence: Original vs. Rule-based

    In general, the outputs in both age influence options provide similar responses to the other inputs of rewiring probability and substitute range. In both modelling alternatives, as shown in Figure 5 and Figure 6, the steadystate patterns of nuptiality by specific-age levels draw the right-skewed and bell-shaped curves while higher rewiring probability accelerates the diffusion process. The relative sensitivity to rewiring probability, between the substitute ranges, has been observed as well. The control variables of clustering coefficients and mean age of ROs shows the similar tendencies in the both alternatives.

    On the other hand, the both modelling alternatives differ in the observations for the nuptiality. First, the nuptiality curves of the both look similar at the young age levels but different thicknesses of the tales in small p. As designed, rule-based age influence causes the decreased willingness to marry at very young age and the wider availability of potential partners for the aged population. Likewise, the observations in the Table 2 and 3 show the distinctions. The mean ages of marriage in the rule-based option are significantly bigger, excepting one scenario of p=1.00 and ‘Whole Age,’ with the similar peaks of the curves. The sum of crude rates, in the scenario of the original age influence and no rewiring (i.e. p=0), are much smaller than the other scenarios. Thus, the ‘age influence’ setting can give different results to the model and its adequacy need to be checked in the targeted context.

    4.3 Model Validation

    The fitting capability of the developed model is verified to reproduce an extreme case of the empirical demographic reality, the Republic of Korea, based on the marriage diffusion. The integration of rewiring probability is proposed to reproduce more similar distribution of the targeted diffusion to the given statistics. The warm-up period with rewiring can provide not only appropriate social networks in the starting population but stable outputs for short-term applications. The targeted pattern is selected to the statistics of the time points (i.e., year 2000, 2005 and 2010), at which Korean Statistics provides the marital life tables for the age-specific patterns of first marriages, to verify the minimum universality between the model and the empirical data.

    Figure 7 shows the fittest hazard patterns of marriage for both age-based options to the input empirical statistics of the year 2000 for the target pattern. The mean absolute error (MAE) is selected as a criterion to find the fittest pattern for the hazard rates over age 15. The MAEs of the fittest patterns from each scenario and the improvement rates compared to the benchmarked model (i.e., the scenario of ‘Original’ and ‘No Rewiring’ has been listed in Table 4. The minimum MAEs of the original age influence are 0.01713 (Whole Age) and 0.01609 (Same Age) with the input statistics while those of the rule-based age influence are much smaller as 0.00617 (Whole Age) and 0.00596 (Same Age). In both ‘Substitute Range’ options, the error decreases under 50% in the designed model. However, the original WR model was developed in a different context (i.e., Western countries) and the parametric modification of the social pressure function (i.e., α and β) has been reported to be adjusted for the specific time in the same country (Bijak et al., 2013). Thus, this result show that the fitting capability with the rewiring can be different by modelling alternatives which composes the influential networks of an individual. Of course, the parametric modification of the internal functions may provide different error levels in that all simulations in this paper used the original setting of the social functions.

    The rule-based scenarios successfully reproduced the empirical statistics with lower dependency on data, notwithstanding the limited context. The data-free approach gives the possibility to interpret the targeted diffusion in terms of the social networks. In the fittest pattern of each scenario, the similar levels of clustering coefficients have been observed near to 80% of the clustering coefficient in the nearest networks (i.e. p=0). These intermediate level of clustering coefficients are in line with the classical finding in the complex networks in that social networks in many societies have a small-world property (Watts and Strogatz, 1998). Still, an extensive survey is required to prove the universality of the property in the demographic diffusion. It implies the connection between the complex networks and the demographic study. With the accumulated verification, the model-based approach will be able to deduce the social networks of the society from the empirical statistics. Then, the replicated kinship and influential networks will be applied to find an efficient solution in practical problems.


    5.1 Discussion

    The simulation results of this study are accordance with those of the network studies in that the network structure significantly affects the speed of diffusion and the maximum share of the changed agents (Song et al., 2015). In the results, the lower clustered structure of social networks activates a much higher level of the diffusion. The rewiring promotes the level and timing of the diffusion although the influence on the process differs slightly by the age influence setting. With the fixed social pressure function, the structural change of both modelling alternatives is proved to give much better capability of fitting the marriage pattern for stable society. Interestingly, all scenarios of minimum MAEs to the empirical data exhibit the intermediate level of clustering coefficients identical to the Small-world property of our society (Gelfand et al., 2011). On the other hand, no intergenerational interaction is found to guarantee minimum tightness in the community and give relative insensitivity to the rewiring of social networks. It indicates the role of social networks on the decrease of marriages in modern society, where the young generation has relatively smaller links to the aged by a high proportion of nuclear families as reported in Hionidou (1995).

    A key novelty of this work is the comparative study using an encapsulated demographic base and multidisciplinary hypotheses, whereas other hybrid approaches focuses on the functional implementations (Wu and Birkin, 2012;Bae et al., 2016;Sajjad et al., 2016;Kim et al., 2017;Richiardi and Richardson, 2017;Singh et al., 2018). In particular, the effect of local interactions on complex adaptive system has been increasingly spotlighted in social sciences (Lusher et al., 2013). A lot more studies have explored social interactions as agent-based processes across disciplines (e.g., economy (Kim et al., 2016), existential security (Gore et al., 2018), and evacuation (Kim et al., 2021)). Still, there is no dominant guide to efficiently build an agent-based approach on multi-disciplinary systems (Balke and Gilbert, 2014;Ransikarbum et al., 2017).

    There is much scope for further applications. First of all, it is important to verify the developed simulation in various circumstances (e.g., in culture, time, and places) for its universal applications. The developed structural base can be applied to reduce the burden for further verifications (Sargent, 2013). Another limitation is that the verification scope is limited to take a parsimonious format such as a stepwise structure, where all events occur simultaneously at the designated states and limitedly allows the chronological heterogeneity. This limitation needs to be checked by increasing the resolution of simulation steps (e.g., pseudo-continuous model) which must demand a heavier computational load. In addition, the diverse social structures are required to validate the complex effect of social networks. There are multiple findings in the network study, excepting the selected structure of Smallworld property, to generatively build up the social network structure for a diffusion process such as scale-free networks (Barabási, 2009).

    5.2 Managerial Insight

    Many findings and theories in social science are closer to hypotheses rather than scientific laws. Moreover, limited records make it hard to check the repeatability of the hypotheses. With the concept of model-based social science, the coherent format enables for researchers and policy makers to modify and experiment modular form of hypotheses at least for social simulations. For instance, expected welfare services for the elders without a family (Noble et al., 2012) can be easily explored with multiple hypotheses in network science because it is still an open door as to which structure is appropriate to capture the underlying dynamics in a certain society. And the built social structure might be reused for other social phenomena. As an illustrative case, this study is expected to help policy makers for model-based social science.


    This work was supported by Institute for Information & communications Technology Promotion under the Korea government (MSIT, R7117-16-0219) and the Nuclear Safety Research Program through the Korea Foundation Of Nuclear Safety (KoFONS), granted financial resource from the Nuclear Safety and Security Commission (NSSC), Republic of Korea (No. 2003020-0120-CG100).



    The central idea of the wedding ring model.


    The Flow diagram of (left) population- and (right) individual-level actions in each step.


    The example of the data-driven microsimulation using transition rates.


    Four colour maps of stabilized marriage-at-age patterns by heterogeneous rewiring probability.


    The steady-state pattern with ‘Original Age Influence’ in the scenario of (a) ‘Whole Age’ and (b) ‘Same Age’.


    The steady-state pattern with ‘Rule-based Age Influence’ in the scenario of (a) ‘Whole Age’ and (b) ‘Same Age’.


    The fittest steady-state patterns to the empirical data of the year 2000 in the scenario of (a) ‘Original Age Influence’ and (b) ‘Rule-based Age Influence


    Detailed parameters of the developed system.

    Selected outputs in ‘Original Age Influence’

    Selected outputs in ‘Rule-based Age Influence’

    Mean absolute error (MAE) of the fittest hazard patterns

    Nomenclature of the key terminologies


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