# A Blockchain-Based Trust Model for Uploading Illegal Data Identification
## 4 Key Technology
### Incentive Mechanism and Nash Equilibrium
If the data information is not identified as illegal data information, IN will not be able to recover the deposit and deduct the credit value. According to the above analysis, the detailed incentive mechanism design is shown in Definition 3. **Definition 3**. : _Incentive mechanism. Design the incentive mechanism according to the final identification result._  
When the identification result is that the data information is illegal as follows:  
\[\forall IN_{h}\in INR,\ R_{h}(AC^{\prime})=R_{h}+\mu\times(R_{MAX}-R_{h}) \times\frac{Correct}{Count},\ P_{h}(AC^{\prime})=\frac{R_{h}}{R_{MAX}}\times SAL \tag{3}\]  
\[\forall IN_{h}\in INS,\ R_{h}(AC^{s})=R_{h}-\mu\times(R_{h}-R_{MIN})\times \frac{Count-Correct}{Count},\ P_{h}(AC^{s})=0 \tag{4}\]  
When the identification result is that the data information is normal as follows:  
\[\forall IN_{h}\in INR,\ R_{h}(AC^{\prime})=R_{h}-\mu\times(R_{h}-R_{MIN}) \times\frac{Count-Correct}{Count},\ P_{h}(AC^{s})=-\frac{R_{h}}{R_{MAX}}\times SAL \tag{5}\]  
\[\forall IN_{h}\in INS,\ R_{h}(AC^{s})=R_{h}-\mu\times(R_{MAX}-R_{h})\times \frac{Correct}{Count},\ P_{h}(AC^{s})=\frac{R_{h}}{R_{MAX}}\times SAL \tag{6}\]  
Equations (3) and (6) are the reputation and token reward formulas when the identification nodes successfully identify data. Equations (4) and (5) are the reputation and token penalty formulas when the identification nodes identify data incorrectly. Among them, \(\mu\) is a reputation factor, which is responsible for controlling the increase and decrease speed of the reputation in different situations. \(\mu\) is suggested [0.1, 0.3]. \(Count\) is the times of participation and \(Correct\) is the times of correct identification. It should be noted that the advantage of doing this is that INs with a high reputation can be prevented from doing evil. Because every time IN does evil, IN will reduce a large amount of reputation value, thereby reducing income. At the same time, incentive mechanisms can encourage nodes with low reputation value to identify data correctly. Because IN identifies data correctly each time, IN will gain more reputation value, thereby increasing income. According to game theory, if an IN knows what other INs will do in the future, IN will choose an action strategy that maximizes payoff based on the actions taken by other INs, which is called the optimal reaction. Therefore, the optimal reaction to IN defines is as follows. **Definition 4**. : _The optimal reaction of identification node \(IN_{h}\)._  
Let \(AC_{-h}=\{AC_{1},\ AC_{2},\ldots,\ AC_{h-1},\ AC_{h+1},\ldots,AC_{Number}\}\) is the set of other INs actions without \(IN_{h}\). Then the optimal reaction action strategy for \(IN_{h}\) to other nodes is \(\forall AC_{h}\in ST_{h}\), so that \(EX_{h}(AC_{h},AC_{-h})\geq EX_{h}(AC_{h},AC_{-h})\), so that \(IN_{h}\) obtains the maximum benefit. The Nash equilibrium point can be regarded as a stable state between \(Number\) identification nodes. In this state, no other action strategy will be chosen by any IN. At this point, each IN will take the best action strategy to obtain the maximum benefit. **Definition 5**. : _Nash equilibrium: This is a special IN action point \(AC=(AC_{h},\;\;AC_{-h})\). If every INs action \(AC_{h}\) is the action policy of optimal reaction to the action \(AC_{-h}\) of the other identification nodes. That is, \(\forall IN_{h}\in INC\) and \(\forall AC_{h}\in ST_{h}\), you can obtain \(EX_{h}(AC_{h},AC_{-h})\geq EX_{h}(AC_{h},AC_{-h})\)._  
Based on the above definitions, the following theorems can be deduced:  
**Theorem 1**. : _In the node identification game, there are only two Nash equilibrium: \(AC=(AC_{1},AC_{2},\ldots,AC_{Number})\), where \(\forall IN_{h}\in INC,\;AC_{h}=AC_{h}^{c}\) \(AC=(AC_{1},AC_{2},\ldots,AC_{Number})\), where \(\forall IN_{h}\in INC,\;AC_{h}=AC_{h}^{s}\)_  
Proof of Theorem 1.: According to definitions 1 and 2, in a game with _Number_ INs, \(Number\geq 3\), \(\frac{Number}{2}<Illegal<Number\). where _Number_ and \(Illegal\) are both integers.