How can Game Theory be used to find the optimal location for a new semiconductor factory in the USA?

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The Issue

Technology is at the core of our society right now. People everywhere use it to do a wide variety of things, ranging from watching movies to making spreadsheets. As we become more reliant on technology in our lives, developments are being made to improve the current electronics that we have. This includes better cars with the ability to self-drive, better processors for computers, and better graphics for more realistic games. As more and more companies develop more advanced machines, this will drastically raise the need for semiconductors, something that the world is in short supply of, but is a vital component in all electronics. Without these semiconductors, many people are left without the means to do their work from home since they might not have the most up-to-date hardware. People also may not be able to purchase a new car since cars also rely heavily on semiconductors.

How can we solve this?

The world is currently in short supply of semiconductors. Even though all the factories producing semiconductors are operating at 100%, there is still not enough to accommodate the ongoing and growing demand in the future. The main player here is the semiconductor companies that are actually producing these chips. They have been running into a lot of problems while in the creation of these semiconductors. Taiwan Semiconductor Manufacturing Company (TSMC) currently has a host of issues on its hands. They are facing a drought in Taiwan which is slowing production since semiconductors require a lot of water to produce. Semiconductor companies are also dealing with the issue of bad yields since companies have designed semiconductors to be so small that the slightest mistake can ruin a whole batch of chips. The question is, how should the supply chain be improved to accommodate the growth in semiconductor demand? 

For my model, I will be taking a look at one of the proposed solutions to the issue which is to build more factories around the world. Currently, most of the factories for semiconductors are located in Asia. TSMC and other companies have considered investing overseas to build new factories in the USA but there have been no confirmed deals at this point. I will try to determine the best location for a new semiconductor location in the USA, taking into consideration factors like shipping to other parts of the US and how close other factories they are, etc.

The Solution

For this project, let’s assume that the factory that we are planning on building will be 150,000 square feet in size. I have decided on this number since a semiconductor factory is quite large and other factories seem to have similar dimensions. 

Here is a list of the possible candidate states that the factory could be built it. More explanation on how I came up with these below:

TexasSouth Carolina
AlabamaMichigan
KentuckyMissouri

The way that I have decided on the list of possible candidate states is by taking a look at the locations of major car factories in the USA. The businessmen would want to have the factory closest to these car manufacturing plants since it would be easy to transport the goods there. However, consumers would rather have the factory closer to them since these factories can also make chips for smartphones and other electronics. To ensure that the location is best for maximizing the profit of the car industry, we want to have it closest to as many car factories as possible. However, the consumers would rather have the factory closest to them as possible. As seen below, the majority of the car factories are located on the eastern side of the US. Here is a list of the number of car factories in each state:

State:Number of car factories
Texas3
Mississippi2
Missouri3
Alabama4
Georgia1
South Carolina3
Tennessee4
Kentucky4
Indiana4
Illinois2
Ohio5
Michigan11

To ensure that we have a better picture, we also want to make sure that we choose a state that has relatively cheap land costs since it would also not make sense if there was a factory that had huge upfront costs and high property taxes. Taking that into consideration, here is a table for the percent that each state charges for average land price and the property tax:

State:Average cost per square foot (upfront cost), property tax (price paid each year)
Texas$116 /sq. ft (17.4M)                    | 1.80% ($313,200)
Mississippi$94 /sq. ft (14.1M)                      | 0.81% ($114,210)
Missouri$112 /sq. ft (16.8M)                    | 0.97% ($162,960)
Alabama$91 /sq. ft (13.65M)                    | 0.41% ($55,965)
Georgia$102 /sq. ft (15.3M)                    | 0.92% ($140,760)
South Carolina$108 /sq. ft (16.2M)                    | 0.57% ($92,340)
Tennessee$112 /sq. ft (16.8M)                    | 0.71% ($119,280)
Kentucky$93 /sq. ft (13.95M)                    | 0.86% ($119,970)
Indianna$94 /sq. ft (14.1M)                      | 0.85% ($119,850)
Illinois$148 /sq. ft (22.2M)                    | 2.27% ($503,940)
Ohio$105 /sq. ft (15.75M)                  | 1.56% ($245,700)
Michigan$106 /sq. ft (15.9M)                    | 1.54% ($244,860)

Payoffs and justifications:

Since the decision here is to find the most optimal location for a factory, the players involved would be consumers and businessmen. For each payoff (x,y), “x” will be the payoff to the businessmen, and “y” will be how convenient the semiconductor factory is for the consumers. For the consumers, the best option is as close to the east coast as possible since a lot of people live in cities like New York or Washington DC. For the businessmen, they would want to have the factory in a state closest to the car factories but also with low land costs. 

States payoffs:

Texas: (1,0) The state of Texas has a pretty substantial upfront cost for the factory and the tax that the factory will receive each year is also really high. On top of that, Texas only has 3 car manufacturing plants in the state and its neighboring states do not have many either. Out of all the states, Texas is the most west and because of that, it will not be able to service a lot of people on the east coast. 

Missouri: (3,2) Missouri is not really close to any nearby car factories. It has 3 in its own state but that is still really poor as there are much better options out there. In terms of location, it is really far west and it would not be a great choice for the consumers as well.

Alabama: (10,6) Alabama is close to many other states with car factories and the cost of building there is also relatively low. While the location is not the best for serving consumers, it is better than some of the other states which is why I gave it a 6. 

South Carolina: (6,8) This state is not really close to any neighboring states with car plants however, it does have pretty good tax rates. This state is also on the east side but it is more south than east. 

Kentucky: (9,8) Kentucky borders many different states that have multiple car factories in them. On top of that, there are 4 car factories within the state. It is also fairly close to the east coast.

Michigan: (12,7) While Michigan does not have the best prices on land, it is great for getting products to the factories. In Michigan alone, there are 11 car factories and its neighboring states Indiana and Ohio make up 9 more combined. 

Nash Equilibrium Solution:

Each of the two players have 3 strategies that they can choose from. They could either place the factory in the west, in the central area (by Indianapolis) or they could place it on the east side. Here is the game represented as a matrix:

After filling out the matrix, here is the solution:

From the matrix, it can be seen that the most optimal solution would be to place the factory in Kentucky. The location is optimal since it is close to a number of car factories surrounding the state and also, it is relatively east so that consumers are happy since they do not have to wait as long for their eFrom the matrix, it can be seen that the most optimal solution would be to place the factory in Kentucky. The location is optimal since it is close to a number of car factories surrounding the state and also, it is relatively east so that consumers are happy since they do not have to wait as long for their electronics.

 

2 Comments

2 comments

  1. Interesting Nick!

  2. That is really cool how you narrowed it down based on multiple factors and then used the matrix to get your answer. Nice work!

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