Solving The Problem of Clean Water and Sanitation Using Game Theory


The video above talks about the importance of clean water, and why we need it. Make sure to watch the video before proceeding to the rest of the post or after reading this post, as this video contains important information and statistics.


Problem: Clean water and sanitation.

Clean water and sanitation I believe is a right to everyone. Everyone should have access to clean water. This is I believe the most important issue in the world right now. Many developed countries have large amounts of access to clean water and sanitation, but on the other hand, developing countries suffer from the lack of clean water and sanitation.

I believe that If we increase the access of clean water to countries all over the world, the world will develop. According to the Tropical Medicine and International Health, 2014, “If everyone, everywhere had clean water, the number diarrhoeal deaths would be cut by a third.” Deaths caused by unclean water are a big issue, and are situations which should be avoided by providing developing countries with water. If problems like these are avoided, life expectancy of people living should go up.

According to the Human Development Report, 2006, “Around the world up to 443 million school days are lost every year because of water-related illnesses.”  If people all around the world have access to clean water, more students will attend school without worrying about water and sanitization. More students will understand what their learning, and their concentration will be on learning rather than on water and where they are going to get it from. For more facts and statistics on this topic, make sure to visit the link below:

Importance of This Topic to Me

Importance: I live in Nigeria, and I see people at times suffer from dirty water and poor sanitation. I believe that these people need the basic necessity to make a future for themselves and for their relatives. The fact that some people get clean and fresh water, and other people don’t, makes me realize how important water is, and how clean water isn’t provided to everyone. It also makes me realize how important water is and how not having clean water can heavily impact your life.

Matrix Model


Developed Countries (DDC)
Strategy A: Provide money, service, and equipment for clean water on a deal for DGC to payback 150% percent after clean water is a success

Strategy B: Give money, service, and equipment for clean water and sanitation for free.

Developing Countries (DGC)

Strategy A: Agree

Strategy B: Disagree, and try to negotiate.


Utilities for DDC

+5 – For getting paid 150%

-2 – For providing money, equipment, and service

-1 – If DGC negotiate

+2 – If DDC play strategy B and DGC disagree

Utilities for DGC

-5 – For paying back full amount plus extra 50% (150%)

+ 10- For getting money for access to clean water

-5 – If DGC disagree and try to negotiate.

Utilities are all additive

Getting To The Solution

Solved using Saddle points

Pareto Optimality

Solution Explained

For non-game theory audience, the first matrix above is a model of possible options for both developed and developing countries. These options/strategies for DGC is to give developing countries access to clean water. The developed countries are also trying to maximize their profit and what they get in return for helping the developing countries. The best strategy for both developing and developed countries would be to play strategy A (AA). This gives a payoff of (5,3) respectively. This seems to be the solution of this “game”. The strategies are explained above, and so are the utilities to the game. Using two methods called Pareto optimality, and Nash Equilibrium (used saddle points), I have solved this game.

Nash Equilibrium is a method to find the best optimal solution for both players. Nash equilibria are defined as the combination of strategies in a game in such a way, that there is no incentive for players to deviate from their choice. This is the best option a player can make, taking into account the other players’ decision and where a change in a player’s decision will only lead to a worse result if the other players stick to their strategy. Using this method, I have used a process called “checking for Saddle Points” to find the Nash Equilibrium. Using that, the Nash Equilibrium is (5,3) The next graph I have made, was made for checking Pareto Optimality. Named after Vilfredo Pareto, Pareto optimality is a measure of efficiency. … That is, a Pareto Optimal outcome cannot be improved upon without hurting at least one player. Using the graph, any point between the line AB and AA is Pareto Optimal. DGC A, DGC A is Pareto Optimal. DDC B, DDC A is Pareto Optimal. DGC mixed strategy of A&A, DDC mixed strategy of B&A is Pareto Optimal

In this game, the DGC get their clean water and equipment, but they will have to pay 150% back to DDC, so I do believe that this is win-win situation for both sides.

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  1. April 28, 2019 by Erica

    Hi Abhinav! I was so excited to read about this topic because it was so different from all the other posts I had seen. The way you described and applied game theory to clean water and sanitation was fascinating and I had never thought of it. I really hope you share this idea with more people and maybe one day your thoughts can come into existence!

  2. April 30, 2019 by Omar

    Hey Abhinav, I was really interested in this topic when I saw it as I didn’t get how game theory could solve our clean water problem. But after going through your post and reading what you had to say I totally understand how game theory can solve the clean water problem. Good job on making a great and organized post and being able to think outside the box like that.

  3. April 30, 2019 by Naman.Bharwani

    Hi Abhinav, I really like the work you have done. Your topic is very interesting, especially because I did not realize that game theory could be used to solve the issue of clean water.

  4. May 01, 2019 by Sahil Dansingani

    Hi abhinav I really liked your work and the idea of using game theory seriously wowed me.

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