# A Blockchain-Based Trust Model for Uploading Illegal Data Identification
## 4 Key Technology
### Incentive Mechanism and Nash Equilibrium  
Game theory is a mathematical theory and method to study the phenomenon of competition; it is a new branch of modern mathematics. Many scholars have made great contributions to the advancement of science and technology by combining game theory with other applications, including economics, evolutionary biology, and computer science [24]. The goal of game theory is to mathematically predict the behavior of a target. The behavior of these participants depends not only on themselves but also on the behavior of others. One of the most common forms of game theory is the strategic form of multiplayer games. The definition consists of a set of actors (IN), a set of strategy profiles, and an incentive function. The INs constitute the basic type of dynamic game with complete information in game theory. The so-called complete information means that the incentive mechanism of each IN is known to others. The IN game is defined as follows:  
**Definition 1**. : _Identification game. This is a game of Number INs, \((\mathit{INC},\mathit{ST},\mathit{EX})\)._  
Where \(\mathit{INC}=\{\mathit{IN}_{1},\mathit{IN}_{2},\ldots,\mathit{IN}_{Number}\}\) is a set with \(Number\) INs. Each IN is selected through the reputation-based random selection algorithm, and these INs form an identification committee. \(\mathit{ST}=\mathit{ST}_{1}\times\mathit{ST}_{2}\times\ldots\times\mathit{ ST}_{Number}\) is the action strategy configuration of a group of INs, where \(\mathit{ST}_{h}\) is a set of action strategies for identification node \(\mathit{IN}_{h}\). \(\mathit{IN}_{h}\) can choose any action \(\mathit{AC}_{h}\in\mathit{ST}_{h}\). Each IN may take different actions in each identification process, namely, \(\mathit{AC}=\{\mathit{AC}_{1},\mathit{AC}_{2},\ldots,\mathit{AC}_{Number}\}\). \((h=1,2,\ldots,\mathit{Number})\). \(\mathit{EX}=\{\mathit{EX}_{1},\mathit{EX}_{2},\ldots,\mathit{EX}_{Number}\}\) is a set of incentive functions. \(\mathit{EX}_{h}\) is the incentive function of identification node \(\mathit{IN}_{h}\) for specific action strategy \(\mathit{AC}_{h}\). \(\mathit{EX}_{h}=\{R_{h},P_{h}\}\) where \(R_{h}\) and \(P_{h}\) represent reputation incentive and token incentive respectively. In the identification process, the identification game roughly has two actions, reporting illegal data information to IBC and keeping silent, namely, \(\mathit{AC}_{h}=\{\mathit{AC}^{\prime}_{h},\mathit{AC}^{\mathrm{s}}_{h}\}\). In the game process of \(Number\) INs, the INs that report illegal data information are put into the reporting set \(\mathit{IN}\), and the INs that do not report illegal data information are put into the silent set \(\mathit{INS}\), where if \(\mathit{AC}_{h}=\mathit{AC}^{\mathrm{c}}_{h}\) then \(\mathit{IN}_{h}\in\mathit{IN}\); If \(\mathit{AC}_{h}=\mathit{AC}^{\mathrm{s}}_{h}\) then \(\mathit{IN}_{h}\in\mathit{INS}\). These operations determine whether the data information is illegal. Only when the number of elements in the \(\mathit{IN}\) is greater than \(\mathit{Illegal}\) or equal to \(\mathit{Illegal}\), the data information will be identified as illegal data. For details, refer to Definition 2. Otherwise, the IBC identifies it as normal data information. The identification is complete now. **Definition 2**. : _Confirmation of illegal data information._  
When \(||INR||>=Illegal\), where \(1<\frac{1}{2}Number<Illegal<Number\). That is, if there are no less than \(Illegal\) INs reporting the data information, the IBC considers the data information illegal. Otherwise, IBC considers that the data information is normal. Here \(Number\) should be as large as possible, the larger the \(Number\), the higher the credibility of the identification result. In addition, \(Illegal<Number\) and \(Illegal>2\), in order to more fairly and credibly identify the data information. When INs identify, INs need to pay the corresponding deposit for each report to the IBC.