Plastic Bags

A Game Theory Approach

Why plastic bags?

It isn’t pollution that’s harming the environment. It’s the impurities in our air and water that are doing it.

Dan Quayle- American politician and lawyer

There has been a tremendous increase in the amount of plastic in the oceans, which threatens to put in risk the life of humans and other marine animals. Reducing our consumption of plastics is essential to reducing this consumption.

Plastic bags have impacted the environment greatly, damaging it and allowing plastic (which takes over a century to degrade) to fall into the oceans. Giant islands of garbage are being formed by the currents in the oceans of the world and global pollution is reaching an all-time high. About 250, 000 tons of plastic are produced globally each year, and, of those, an estimated 100, 000 tons of plastic enter the ocean according to recent studies. It is time to reconsider if we want to damage the ecosystem and ourselves or to take action.

Below is an infographic that shows just how much damage we are doing to the environment, and where our garbage ends up.

What is the estimated amount of plastic floating above the water worldwide?
0 – 0.1 tons
1 – 10 tons
10,000 – 100, 000 tons
100, 000 – 100, 000, 000 tons

We must also remember that the pollution that we are causing in the ocean will have an impact not only in our generation but many more to come. According to the United Nations, “the global share of marine fish stocks that are within biologically sustainable levels declined from 90 percent in 1974 to 69 percent in 2013.” Refusing to take action may lead to further environmental and health problems worldwide. As the marine ecosystem is damaged by the plastic, so are we, as ingesting plastic may cause serious health concerns. Although few studies have been done, they all concluded that these “microplastics” were damaging to your well-being and healthiness, affecting your lungs and other vital organs.

Furthermore, this plastic is causing ocean acidity, putting in danger many endangered species. “Studies at open ocean and coastal sites around the world show that current levels of marine acidity have increased by about 26 percent on average since the start of the Industrial Revolution.” , according to the UN. “Moreover,” they warn, ” marine life is being exposed to conditions outside previously experienced natural variability.” This may lead to the endangerment and extinction of many species of fish and other marine creatures.

We are puruing change, but it hasn’t been enough so far…

“As of January 2018, 16 percent (or over 22 million square kilometres) of marine waters under national jurisdiction—that is, 0 to 200 nautical miles from shore—were covered by protected areas. This is more than double the 2010 coverage level. The mean coverage of marine key biodiversity areas (KBAs) that are protected has also increased—from 30 per cent in 2000 to 44 per cent in 2018. “

This great TED talk also gives us more insight into the pollution by plastic bags and these girls’ campaign to stop plastic pollution in Bali.

So, you might be thinking by now…

What is Game Theory?

Game theory is a branch in mathematics that can help us understand what dceisions are the most optimal for a certain “player”. Imagine it as analysing games to determine what move is the best for you so you can outsmart your opponent.

Game Theory can help us understand our issue, and, by analyzing the different factors that come into play in the creation of these plastic bags, we can better understand what might be causing this unprecedented pollution. To do so, we’ll create a matrix (a table in which to display our information) to better visualize the situation. But first, we’ll have to decide what we wish to model. In my case, I decided to model the production and consumption of plastic bags at a local level.

There are two players in this game, the shopkeeper (or buyer) and the factory manager (or seller). They each decide whether to buy/sell renewable bags or plastic ones.

This matrix represents the expected payoffs (how much a player gains by taking a certain action) of a seller of plastic bags and a buyer. If they both choose the same option, then they are able to do a transaction, otherwise, none of them obtain anything. The buyer wishes to buy renewable products as this will increase the number of customers in his shop whilst the seller wants to make a profit out of selling non-renewable bags.

The payoffs to each player are representative of how much they would be keen to one option or other and how much they are interested in pursuing it. The seller may also be encouraged to make non-renewable bags since this can help his image, even though he might not be making as much money.

This would be the corresponding matrix:

Buyer vs Seller
Sell Renewable Bags

Sell Non-renewable Bags
Buy Renewable
(10, 7)(0, 0)
Buy Non-Renewable
(0, 0)(3, 10)

After solving this matrix, we find that the Nash Optimalities (the equilibrium in which both players are maximizing their scores) are buying renewable bags and selling renewable bags, as well as selling and buying non-renewable bags. These are also the Pareto Optimalities (the solutions that give you the highest scores for any individual payoff). This means that both players will be inclined to buy or sell renewable and non-renewable bags.

There is, however, an advantage that the buyer possesses. This advantage is presented to us if we analyze the situation more carefully: knowing that my Nash equilibria solutions are also Pareto Optimal and that the optimal solutions to the problem are either all renewable or all non-renewable, I can now assume that both players would attempt to communicate in order to avoid neither of them obtaining a deal.

This, in turn, means that there is a high likelihood that the buyer and the seller will make a deal. They would then have to decide whether to opt for renewable sources or not. Most probably, the buyer would make a threat to the seller saying that he will only buy renewable bags, which would force the seller to make renewable bags. This is a major advantage that the buyer has against the seller, as it would drive him out of business to not be able to sell his bags. This would have a great impact in the context of our game since it shows that buying renewable bags would likely be an advantage to retailers and shops, and it also shows that they could force producers to switch to more renewable bags. Thanks to this, there will be more recycling and pollution would likely decrease, both in our oceans as well as in our cities, creating a bigger impact in the world.


Inform more shops of the advantages that using renewable bags might have! A collective call (or “threat”) for more renewable materials would likely change the seller’s minds about what types of bags they could produce, as they would start making more profit if they were to sell these renewable products. This would impact global production, as well as help the environment. It would also help the various ecosystems of the world, who are being affected by the dangerous levels of pollution in the world!

The only way that we can stop plastoic from taking our oceans and health is by working together. So, talk to your community and share this post to inform more people of what we can do to change the world!

Consider donating to plastic pollution NGO’s, such as Plastic Oceans!



“Goal 14 .:. Sustainable Development Knowledge Platform.” United Nations, United Nations,

“Fatal Effects of Plastic Pollution.” Earth Eclipse, 23 Dec. 2016,

Moore, Charles. “Plastic Pollution.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., 12 Mar. 2019,

Treat, Jason, and Ryan Williams. “We Depend On Plastic. Now, We’re Drowning in It.” National Geographic., 16 May 2018,

Share this project
  1. April 29, 2019 by Kirsten Mettler

    For a short time, I worked with a group in CT working to ban single-use plastic bags. They were surprised that though citizens seemed to largely be in favor, stores were not enforcing new regulations as they came in. I think that it will be very important as we make change about plastic bags to ensure that the rules are being followed. This ties back into the game theory of it: if the costs don’t change for the companies, they have no reason to change their policies.

  2. April 29, 2019 by Yasmina Haddad

    I live in a suburb of Miami called Coral Gables, and since May of 2017 plastic bags have been banned. I love your approach on the topic in terms of explaining the economic advantages renewable bags have as a way to convince retailers to utilize them. Great presentation!

  3. May 05, 2019 by Taichi Kakitani

    I have done research about ocean debris specifically, and I too agree that this issue is huge and problematic worldwide. As you said in your presentation, it could affect our future generations and the entire ecosystem. I liked how you used the game theory concept in explaining people’s preferences and how the buyers can start the change. Good job.

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