A Study on Strategies for Enhancing the Resilience of Manufacturing Industrial Chains Based on Three-Party Evolutionary Games

Imagine the global economy as a massive, bustling city where millions of tiny workers, factories, and trucks are constantly moving goods from one place to another. This city is the "industrial chain." Sometimes, a giant storm hits (like a pandemic or a war), or a bridge collapses (a technology bottleneck), and the whole city grinds to a halt. To keep the city running, we need "resilience"—which is just a fancy word for the ability to bounce back quickly, adapt to the mess, and keep things moving even when everything goes wrong.

But here's the tricky part: building a resilient city isn't a solo job. It requires three main groups to work together: the Government (the city mayor who makes the rules), the Chain-Leading Enterprise (the big boss factory that sets the pace), and the Other Enterprises (the hundreds of smaller suppliers and partners). The problem is that these three groups often play a game of "chicken." The big boss might think, "Why should I spend money to fix the city if everyone else will just ride my coattails?" The smaller suppliers might think, "I'll just wait and see if the mayor pays me to help." And the mayor might think, "I can't force them to help if it costs too much." This is a classic coordination failure, where everyone acts in their own self-interest, and the whole city ends up vulnerable.

This paper dives into that exact drama. Using a mathematical tool called an "evolutionary game model" (think of it as a super-advanced simulation of how people learn and change their minds over time), the authors explore how these three groups can stop playing games and start working together. They don't just guess; they run computer simulations to see what happens when the mayor changes the rules, when the big boss spends more money, or when the smaller suppliers get better at talking to each other. The goal is to figure out the perfect recipe to turn a chaotic, risky city into a super-resilient one.

The Big Game: Who Plays What?

The authors set up a three-way game involving the Government, the Chain-Leading Enterprise (the "Big Boss"), and the Other Enterprises (the "Supporting Crew"). Each player has two choices:

1. The Big Boss: Do they make a huge, expensive investment to make the supply chain tough and ready for anything (Active Investment), or do they just keep doing the bare minimum to save cash (Passive Investment)?
2. The Supporting Crew: Do they team up, share secrets, and help the Big Boss when things get tough (Cooperation), or do they just do their own thing and hope for the best (Non-Cooperation)?
3. The Government: Do they step in with strong rules, big rewards, and strict penalties (Strong Regulation), or do they just sit back and watch (Weak Regulation)?

The paper argues that right now, the system is stuck in a bad loop. The Big Boss is scared to spend money because it's expensive. The Supporting Crew is scared to help because they don't want to do the work for free. And the Government is struggling to force them to cooperate without breaking the bank.

The Simulation: Testing the Rules

To solve this, the authors built a digital playground using MATLAB R2024b. They didn't just look at real-world data; they created a virtual world where they could tweak the knobs and see what happened. They used a specific case study of the new energy vehicle industry in Changzhou, China, as their inspiration. In this real-world example, a company called Li Auto (the Big Boss) spent a massive 11.3 billion yuan on research and development in 2025. This huge investment helped other companies, like Sanhua Holding Group and Inovance Technology, become leaders in their own fields. The local government also chipped in with a 5-billion-yuan special fund and fast-track policies.

The authors took the logic from this real success story and plugged it into their math model to see if they could predict the outcome. They calibrated their model parameters using data from the Li Auto, Sanhua Holding Group, and Inovance Technology 2025 Annual Reports, as well as the Changzhou New Energy Vehicle Industry Special Policy. While the specific numerical values assigned in the simulation were set to reflect relative magnitudes and hypothetical scenarios (such as future investment levels), they were grounded in these real-world company reports and policy documents to ensure the simulation accurately depicted the evolutionary trends of the system.

They tested different scenarios by changing numbers like:

• Penalties ($F_g$): How much the Big Boss gets fined if they don't invest.
• Subsidies ($S$): How much money the Government gives the Big Boss for investing.
• Rewards ($R_m$): How much the Government pays the Supporting Crew for helping out.
• Costs ($C_e$ and $C_u$): How much it costs for the Big Boss to invest and for the Crew to cooperate.
• Information Coefficient ($k$): How well the Crew can share info with the Big Boss (like a digital walkie-talkie).

What the Numbers Say: The Recipe for Success

The simulations revealed a very clear path to a happy ending. The system naturally wants to settle into a state where the Government is Strong, the Big Boss is Active, and the Crew is Cooperative. But getting there requires the right mix of tools.

1. The Stick and the Carrot:
The paper found that penalties are a powerful "stick." When the government increases the fine for the Big Boss doing nothing, the Boss quickly switches to investing. It's like a parent saying, "If you don't clean your room, you lose your video game time." The threat of losing money forces the Big Boss to act.
However, penalties alone aren't enough. The subsidies (the "carrot") are crucial. When the government gives money to the Big Boss for investing, it makes the investment feel less risky. The simulations showed that as subsidies go up, the Big Boss's willingness to invest skyrockets.

2. The Cost of Doing Business:
Here's a big hurdle: Costs. The simulations showed that if it costs too much for the Big Boss to invest ($C_e$) or for the Crew to cooperate ($C_u$), the whole system stalls. Even with good rules, if the price tag is too high, everyone just gives up. The paper suggests that the government needs to help lower these costs, perhaps through tax breaks or better technology, to make it worth everyone's while.

3. The Magic of "Talking" (The Information Coefficient):
One of the most interesting findings involves the Information Transmission Coefficient ($k$). Think of this as the quality of the internet connection between the Big Boss and the Crew. If the connection is bad ($k$ is low), the Crew can't help effectively, and the Big Boss doesn't see the value in investing. But if the connection is super fast and clear ($k$ is high)—thanks to digital platforms and data sharing—the Crew can help the Big Boss solve problems instantly. The simulations showed that improving this "digital connection" makes the whole system converge to the happy ending much faster. It turns a messy, slow process into a smooth, high-speed collaboration.

4. The Long Game:
The paper also looked at what happens if the Government doesn't see the long-term benefits. If the Government thinks, "Fixing this chain won't help the economy much," they won't bother regulating. But if they see that a strong chain brings huge rewards like economic growth and job creation ($R_g$), they are much more likely to keep the pressure on. The simulations showed that when the Government values the long-term win, they stick with the strong rules, which keeps everyone else playing along.

The Verdict: A Win-Win-Win

The paper concludes that there is a "sweet spot" where everyone wins. If the Government sets the right penalties and rewards, lowers the costs for everyone, and builds better digital bridges for communication, the system naturally evolves into a state of Strong Regulation, Active Investment, and Cooperative Partnership.

However, the authors warn that if the costs are too high or the rewards are too low, the system can get stuck in a "bad equilibrium." In this bad state, the Government does nothing, the Big Boss saves money by doing nothing, and the Crew refuses to help. The result is a fragile chain that breaks easily.

The key takeaway is that policy matters. It's not just about telling companies to "be resilient." It's about designing a system where being resilient is the most profitable and logical choice for everyone involved. By using a mix of strict rules, financial help, and digital tools, the government can guide the Big Boss and the Crew out of their selfish games and into a team that can weather any storm.

In short, the paper suggests that with the right mix of carrots, sticks, and high-speed internet, we can turn a fragile industrial chain into a super-strong one, ensuring that our economy keeps running smoothly no matter what the world throws at it.