# Evolution Game Analysis of Supply Chain Synergy Benefits of Prefabricated Building Projects
## 4 Simulation Analysis
### Impact of Incentive Benefit Allocation Coefficients on the Evolution of Synergistic Relationships  
The synergistic benefits of the supply chain are reflected in three aspects: market synergistic benefits, management synergistic benefits, and operational synergistic benefits. Figure 9 shows the simulation of the impact of the change in the supply chain incentive benefit allocation coefficient on the synergistic operation strategy when the construction unit and prefabricated component manufacturer participate in the synergy under the condition of other parameters being unchanged. Assuming that the synergy cost is fixed and the synergy cost sharing coefficient is 0.5, there are two thresholds for the benefit allocation coefficient a, which range from 0.42 to 0.43 and 0.67 to 0.68, respectively, and can be discussed in three cases:  
Figure 9: _Cont._  
(1) When the incentive benefit allocation coefficient a is less than the threshold value of 0.42 to 0.43, with the advancement of time, y, z will eventually converge to 0. However, because the precast manufacturer will receive the government's financial support as part of the total benefit, coupled with the fact that at this time, the allocation coefficient of the precast manufacturer is greater than that of the construction unit, the synergy probability of the precast manufacturer will first rise slightly, and then fall as the synergy probability of the construction unit falls. (2) When the incentive benefit distribution coefficient a is greater than the threshold value of 0.67 to 0.68, with the advancement of time, y, z will eventually converge to 0, and at this time, the larger a, the faster the rate of convergence, and ultimately both sides will choose not to participate in supply chain synergy. (3) When the incentive benefit distribution coefficient a within 0.43-0.67, x, y, and z are converged to 1 with the advancement of time, and there is a threshold value of 0.5, the coefficient a is closer to 0.5 from either side, y, z converge to 1 faster and the participants in the supply chain tend to choose the stable strategy (subsidy, synergy, synergy) in a shorter time. When 0.43 < a < 0.5, the total benefit of the construction unit is lower than the prefabricated component producer; at this time, the total benefit of the construction unit first decreases  
Figure 9: Evolutionary results of changes in the incentive benefit distribution coefficient. **(a)** Evolutionary results of changes in the distribution coefficient of low benefits. **(b)** Evolutionary results of changes in the distribution coefficient of medium benefits. **(c)** Evolutionary results of changes in the distribution coefficient of high benefits. and then increases. When 0.5 \(<\) a \(<\) 0.67, the total benefit of the construction unit is higher than the precast manufacturer; at this time, the two sides of the synergistic probability of the first decrease a small amount and then increase, and the speed of convergence of the construction unit is greater than the precast manufacturer. The above simulation results show that both the construction unit and the precast component manufacturer are more sensitive to the distribution coefficient of the synergistic incentive benefits in their strategy choices, and it can be found that the influence of a on the construction unit is more prominent in the stage of 0.5 \(<\) a \(<\) 0.67 because the construction unit can obtain higher benefits from the supply chain coordination at this time. Thus, the construction unit can choose to carry out supply chain coordination in a short reaction time. In the process of collaboration between the two parties, the closer the coefficient a is to 0.5, the more equitable distribution of synergy incentive benefits can be achieved, and the stronger the willingness of the two parties to carry out synergy; otherwise, it is easy to lead to one party's dissatisfaction with the distribution results and opt to not carry out supply chain synergy.