# Spatiotemporal Modeling of the Smart City Residents' Activity with Multi-Agent Systems
## 3 Research Methodology
### Agents' Interactions
The conducted simulations aim to determine how the long-term change of people's trust (mutual and to institutions) over time affects the level of social participation and, indirectly, the development of open civil society and deliberative democracy. The model includes three groups of actants (agents) interacting with each other in the city:  
1. People (residents);
2. Institutions (governmental agencies, businesses, educational facilities, healthcare);
3. Spatial objects (districts characterized by parks, monuments, rivers, and so on). In the adopted model, the authors of the study take into account the various modifying functions (see Figure 1) of the trust parameter in the interactions between two agents:  
* The \"linear\" function, which is the basis for the formulation of the others. The assumption is that this function, with the interaction of the agent \(i\) with the agent \(j\), is as follows: \[trust_{\textit{People}}^{i}trust_{\textit{People}}^{i}+c\Delta_{trust_{\textit{People}}}\] (1) \[ck_{\textit{edit}}\left(1-edu^{i}\right)+k_{\textit{hap}}\left(1-\textit{ hap}^{i}\right)+k_{\textit{veare}}\left(1-\textit{veat}^{i}\right)+k_{\textit{ age}}\left(1-\textit{age}^{i}\right)+k\] (2) \[\Delta_{trust_{\textit{People}}}trust_{\textit{People}}^{i}-trust_{ \textit{People}}^{i}\] (3) where: \[k_{\textit{edit}}\left(\textit{education parameter change modifier;}\right.\] \[k_{\textit{hap}}\left(\textit{satisfaction parameter change modifier;}\right.\] \[k_{\textit{ivan}}\left(\textit{wealth parameter change modifier;}\right.\] \[k_{\textit{agre}}\left(\textit{age parameter change modifier;}\right.\] \[k\left(\textit{change modifier.}\right.\]
* The \"reinforcing\" function differs from the linear function in the manner of calculating parameter \(\Delta_{trust_{\textit{People}}}\) : \[\Delta_{trust_{\textit{People}}}tan\left(trust_{\textit{People}}^{i}-trust_{ \textit{People}}^{i}\right).\] (4)
* The \"diminishing\" function also differs from the linear function in the manner of calculating parameter \(\Delta_{trust_{\textit{People}}}\) : \[\Delta_{trust_{\textit{People}}}tgh\left(trust_{\textit{People}}^{j}-trust_{ \textit{People}}^{i}\right).\] (5)
* A function that uses the fan-idol relation; based on the situation that a person (fan) will imitate another person (idol) when s/he notices a significant similarity of specific features. Then, s/he changes the parameter (trust in people) towards theidol parameter. * A function that uses the fan-anti-idol relation; based on the situation that a person (fan) will want to distinguish themselves from the other (anti-idol) when s/he notices a significant difference of specific features. Then, s/he changes the parameter (trust in people) in the opposite direction to the anti-idol parameter. Moreover, it is assumed that the agent's trust that is included in the above dependencies is treated depending on the place where he resides. The trust of the agent staying at the place of residence is increased by 50%, while for the agent staying at the workplace, it is reduced by 20%. In addition, when the agent is in an entertainment location, his trust counts as 10% more. At the same time, the same trust for an agent staying at the governmental agency or health clinic is reduced by 50%. An agent residing in an industrial area (Old Factory or Mordor) also counts as 15% smaller, while when he is in the GreenLand or OldTown districts, it counts as 15% more. The introduced methodology is used and validated in the following section.