# Volunteers in the Smart City: Comparison of Contribution Strategies on Human-Centered Measures
## 2 Model
### Implementation of the Model in Real-Life Scenarios
#### 2.1.1 Smart Grid: EV Charging  
In the smart grid scenario, we assume a neighborhood composed of households connected to each other via the infrastructure of the smart grid. Households consume a variable quantity of energy, depending on the appliances in use, and produce a variable quantity of renewable energy, depending on weather conditions. Electric vehicles (EVs), associated with households connected to the smart grid, are required to be periodically recharged. Demand-side management mechanism [13] is required to schedule and postpone appropriately EV charging, based on current demand and renewable energy production, i.e., energy availability.  
The _public good_ consists of the total energy surplus \(\sigma=\pi-\beta\), which is available to all households for charging the EVs. Its _value_ is computed from the current production of renewable energy \(\pi=\sum_{i}\pi_{i}\), and the current network load \(\beta=\sum_{i}\beta_{i}\)[14]. We assume that the energy surplus is lower than the total demand, i.e., at any given time \(\pi<\beta\); hence, a black-out is inevitable if all households decide to use the surplus simultaneously. _Contribution_ to the public good is then defined as opting out from consumption, i.e., renouncing to charge the EV of a charge \(v_{i}\) that might depend on contextual variables such as the current charge level, the availability of a charging station, and the current energy surplus. It is assumed that the values are privacy-sensitive as they might be used to infer habits, e.g., the work schedule, of the owners. Contribution entails a comfort cost that is assumed to be proportional to the corresponding value, as the utility of an EV depends on it being charged. _Values_\(v_{i}\)  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \(q_{-i}\) & \(q_{-i}+v_{i}<\tau\) & \(\tau-v_{i}\leq q_{-i}<\tau\) & \(\tau\leq q_{-i}\) \\ \hline
**Outcome** & **Failure** & **Depends on \(a_{i}\)** & **Success** \\ \hline \(U_{i}(a_{i}=C)\) & \(-B(\tau^{\ddagger},q^{\ddagger})-c_{i}^{\ddagger}\) & \(G(\tau^{\ddagger},q^{\ddagger})-c_{i}^{\ddagger}\) & \(G(\tau^{\ddagger},q^{\ddagger})-c_{i}^{\ddagger}\) \\ \(U_{i}(a_{i}=D)\) & \(-B(\tau^{\ddagger},q^{\ddagger})\) & \(-B(\tau^{\ddagger},q^{\ddagger})\) & \(G(\tau^{\ddagger},q^{\ddagger})\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Definition of utilities for agent \(i\). Let \(q_{-i}=\sum_{j\in A_{+}\setminus\{i\}}v_{j}=q-v_{i}\) be the total contributions, excluding agent \(i\), and \(\tau\) be the global requirement. This game qualifies as a threshold public goods game if \(G(\tau,q)+B(\tau,q)>c_{i}\), which is always verified for large enough values of \(G\) or \(B\).  
which corresponds to the charge that the EV can accumulate during a time period, are generated uniformly at random between 1 and \(n2\), while the corresponding _costs_\(c_{i}\) are determined by sampling a normal distribution centered around the value \(v_{i}\). The threshold \(\tau\) is dynamically computed at every timestep from the dataset to be inversely proportional to the difference between production and consumption: \(\tau=1-(\pi_{i}-\beta_{i})\).  
The baseload level \(\beta\)--non reschedulable load for each household--determines the aggregated consumption of the network and is obtained from Irish Smart Meter trial data [15]. On a single household level, on average, it ranges from 0.8 kW, during the night, to 3 kW, at evening peak time. The energy production level \(\pi\) is based on Irish wind production data, obtained from Irish electricity grid operator EirGrid [16], which represents an estimate of the total electrical output of all wind farms on the system. Individual contribution values and costs are randomly sampled from a uniform distribution that ranges from 1 to a maximum value that is determined by the simulations' parameters.