can you create a mult-agent modeling example in story from from this involving 7 agents turned into animistic objects and processes? Choice of parameter ranges A major challenge when developing a model is the question, how to find suitable parameter ranges or settings. The following parameter ranges were defined on the basis of theoretical considerations, the modelers’ experience (who had conducted multiple test runs) or on the basis of empirical findings. 1. Change rate (c) How much does an agent change his or her behavior on the basis of a simulation cycle (agents can have up to 19 interactions per simulation cycle)? This parameter controls the speed of learning of or adapting to the behavior of the other agents (e.g., on the basis of social learning). To find a suitable parameter range for c we have to answer the question: How long do adolescents need (on average) to become homogenous? For example: How long does a non-smoker need, who enters a group of smokers, to adapt his or her smoking behavior to the average group behavior? Or how fast does an adolescent change the average marihuana consume during a school year? Empirical findings to define a suitable range for our parameter c are rare. Therefore, a suitable parameter range was estimated on the basis of model experience. The change rate c is crucial for the behavioral change. A suitable range appears to be [0.005; 0.0005], as values > 0.005 lead to a much too fast change in behavior and values < 0.0005 result in much too small behavioral change. 2. Effect reduction (r) The effect reduction has an influence on how fast preferences grow respectively decrease. Having a high effect reduction value means that preferences change fast (i.e., they can increase fast or drop fast). To find a suitable parameter range, we need to consider some theoretical assumptions. In general the process of preference formation is quite fast (i.e., within a couple of weeks). To find a lower bound for the parameter range, let us assume that we have got two agents with an initially low preference for each other. But at the same time both agents are quite similar (which is possible in the model). In this case the agents should be able to form a friendship within a school year. Only few empirical findings give information about the exact duration of friendships or non-friendships. Nevertheless, Hallinan (1979) described a longitudinal study on friendship formation in 4 classes of 6th graders and 1 class of 4th graders. For the 6th graders the absence of dyads (friendships) lasted from 189 to 400 days. If we have a look at the logistic growth function of the preference formula (see formula 3 in the article) and set the term (St+1*ij – θS*) to a fixed value, we are able to estimate a suitable parameter range for r. With r set to 0.05, we need 716 simulation steps (or about 72 simulated school days) to receive a preference value of 0.8, given an initial preference value of 0.1 and (St – θS*) = 0,1 ∀ t. This is a lower bound for the formation of a friendship with initially low preference. With r set to 0.01 we need 3583 (or about 358 simulated school days) steps to reach a preference value of 0.8 (with same constraints as before). This defines our upper bound for a friendship formation with initially low preference values. Therefore a suitable parameter range for r is [0.01; 0.05]. 3. Theta similarity (θS) Theta similarity is used as a threshold to calculate the interaction value. If the (true) similarity is above this threshold, it is very likely that an agent A has a positive interaction with another agent B. If the similarity value is below, it is very probable to have a negative interaction with the other agent. On the basis of several model tests values we can define values between 0.7 and 0.8 as a suitable parameter range for theta similarity. 4., 5. Min mutuality and max mutuality (minM, maxM) Min mutuality and max mutuality influence the decision whether an interaction between two agents takes place or not (see also section "The interaction frequency" in the article). If the mutuality value is below min mutuality, it is set to min mutuality. In general this guarantees that an interaction is still possible, even if two agents have a very low mutuality value for each other. On the other hand, if the mutuality value is above max mutuality, the mutuality value is set to max mutuality. This guarantees that an agent A does not permanently interact with an agent B, which he/she likes very much. Suitable values range from 0.0 to 0.2 for min mutuality and 0.8 to 1.0 for max mutuality. 6. Sdinteraction value (σV) Sdinteraction value indicates the standard deviation for sampling the interaction value. The higher this value, the higher the deviation of the interaction value from the mean interaction value μ, that is defined on the basis of the normalized similarity value (mean equation031 (μ ∈ [-1,1], similarity threshold θS; see also section "The interaction value" in the article) A deviation value of 0.2 can be defined as a standard value, a range from 0.0 (nearly no deviation) to 0.4 (indicating a moderate deviation) is appropriate for sdinteraction value. 7., 8., 9. Weight factors (wPop, wV, wP) Parameter ranges for the weight factors wPop, wV, and wP can be defined depending on the modelers' objectives. Ranges can be varied to test different assumptions, i.e. to compare different scenarios (e.g., a scenario with a major impact of popularity on the evaluation vs. a scenario with a major impact of the interaction value). As a constraint the sum of all weight factors has to be one (wPop + wP + wV =1). For the parameter settings in the model analysis we developed a scenario, where the interaction value has a relatively strong impact on the evaluation compared to the impact of the popularity value. Still, the impact of popularity should be substantial in this scenario and the corresponding weight factor should have a moderate value. The influence of preference was not taken into account in this scenario (see also appendix C in the article). Thus, we defined wPop ∈ [0.2; 0.4] and wV ∈ [0.6; 0.8]. 10. Alpha (α) Alpha indicates the amount of time needed until an agent A can perceive the real behavioral profile of another agent B. At the beginning of a simulation an agent A has a biased perception of another agent B and his/her behavioral tendencies. The more time the agents spend together at school, the more visible the true behavioral profile becomes. The decrease is exponential (see also formula 1.2 in the article). Alpha can range from 0.0001 to 0.000001. If alpha is chosen within this range, a decrease of an average initial distortion of 0.4 to almost 0 needs (approximately) 300 to 4000 iteration steps. 11. Theta perceived similarity (θS*) Theta perceived similarity is used for calculating the preference value (see formula 3 in the article). It gives the threshold for an increase or a decrease in the preference. If the perceived similarity value is above theta perceived similarity, there is an increase in preference, else preference drops. Generally the similarity value has to be bigger than 0.5 for an increase in preferences. A similarity value of 0.5 indicates that two agents have (on average) a difference of 0.5 in their behavioral profiles (agent A is 50% "different" from agent B). A suitable parameter range for theta perceived similarity range is 0.7 to 0.8. So an agent A can tolerate (on average) a difference of 20%–30% and still start/increase liking another agent B. Initialization parameters (basic) i1-i4. Average initial behavioral distribution, sd initial behavioral distribution (μB1,0, μB2,0, σB1,0, σB2,0) The initial values of the behavioral profiles are randomly drawn from two different normal distributions (for the basic initialization) [13]. Therefore we receive two initial agent populations: A risky population and a conventional population (each generally consisting of 10 agents). Empirical findings indicate a moderate negative correlation between risk and conventional behavior in adolescents (i.e., Jessor 1992). Therefore we initialize our agents with conventional and risk behavior negatively correlated (so most of the agents are initially high in risk behavior and low in conventional vice versa). Thus, for the risky population the risk behavior for each agent is drawn as a random sample from a normal distribution with mean μB1,0 ∈ [0, 6; 0, 8] and the standard deviation σB1,0 ∈ [0, 1; 0,3]. Their conventional behavior is drawn from a normal distribution with mean μB2,0 ∈ [0, 2; 0, 4] and standard deviation σB2,0 ∈ [0, 1; 0,3]. For the conventional population risk behavior is drawn as a random sample from a normal distribution with mean μB2,0 and standard deviation σB2,0, conventional behavior is drawn with μB1,0 as mean and standard deviation σB1,0.

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