Game Theory: The Science of Intelligent Decision Making

Remember the movie 'A Beautiful Mind'? It tells the story of a brilliant mathematician battling schizophrenia and moving forward. After the release of the movie, this mathematician named John Forbes Nash became popular among the common people overnight. He later won the Nobel Prize for the theory he discovered based on a PhD thesis he submitted at the age of 21. The title of the thesis was 'Non Cooperative Game'. Many people may think, why did 'game' come in mathematics? In fact, there is a huge theory called game theory, which is no longer confined to mathematics or science. It is used in many areas including economics, social science, politics, trade, international relations.



Game theory provides a theoretical framework for what the intelligent behavior of multiple agents engaged in competitive relationships should look like. In many places it is called the 'Science of Strategy'. Competing agents are reviewed here as 'players'. This competition between players is called a 'game'. The whole game has an outcome depending on the actions of the players. Game theory can be used to predict the future of such relationships in the real world. However, game theory will work only when people make rational decisions.



The first mathematical formulation of game theory was given by John von Neumann and Oskar Morgenstern. Due to various limitations of their framework, the theory was initially used only under specific and limited conditions. However, this situation has changed over the past seven decades. John Nash was the first to make a significant contribution to this theory after Newman and Morgenstern. As a result, a generalized framework of game theory has been developed that can be used in economics, social sciences, business, international relations, computer science, biology and many other fields. Since the seventies, game theory has become the most important tool for any analyst, where he has to face the decisions of other intelligent opponents. In this paper, we will not discuss the theoretical part of game theory. Rather, I will try to understand the pattern of rational decision-making using various examples. One such area of discussion is trade.



Many examples can be given of businesses that are engaged in intense competition. One such example is the rivalry between Pepsi and Coca-Cola. Let's say, Coca-Cola decides to lower the price of their product. As a result, they will have higher sales than Pepsi. Thus, they can earn more profit.



On the other hand, Pepsi definitely doesn't want to lose customers. So they will also be forced to reduce the price. Thus they will arrive at an equilibrium position where the two goods have equal value. Since the price reduction is not actually attracting more customers, Coca Cola will not consider reducing the price. Thus, there is an unwritten agreement between the companies, that they will keep the price high and thus the profit will be high.



Another question can be answered using game theory. That is why most shops are clustered. Often there are no restaurants within a few miles. But it can be seen that many company restaurants are united in one place. Let's say you decide to sell ice cream on the beach. The beach is a mile long. So which place to choose for your store can make the most profit? Of course in the middle, right? Let's say you set up shop there.



The next day he went to the beach and saw that his friend had opened another ice cream shop. You decide to share the beach between yourselves. So, move your shop a quarter right from the middle of the beach. And your friend's shop took a quarter left of center. As a result, all those who wandered along the beach bought ice cream from you. And those who came to the left bought ice cream from your friend's shop. It is the best location for buyers. The next day he went to the beach and saw that your friend has moved his shop to the middle to get more customers. That is, he gets all the customers on the left, and a part of your customers also goes to his store. The next day you go to your friend's area and set up shop to win the ice cream war. Your friend, no less, set up shop a hundred meters to the right of yours. As a result, the buyer of the large area of the right came to his share. You sit a hundred meters to his right to get that share. He moved his shop again, you moved yours. Thus, throughout the day you and your friend engaged in a battle to move the store. In the end, both settled in the middle of the beach, where both were getting half the customers.



You arrive at a position called 'Nash Equilibrium'. No one can improve themselves from this position. If you move your shop your friend will get more customers and if your friend moves his shop you will get more customers. Your first strategy didn't last because it wasn't in an equilibrium as defined by the Nash Equilibrium. So, your friend was able to improve his position by moving shop. In the real world, this is why companies keep their stores side by side. Because if they cannot achieve Nash Equilibrium, they will suffer fierce competition from rivals. And buyers can come from anywhere. Although the mathematical and logical framework of game theory dates back to 1944, there are examples of such rational thinking from much earlier times. Socrates tells one such story of the Battle of Delium: A soldier waits with his comrades in the front camp to resist an enemy attack. If their resistance is successful, his personal contribution is not essential. If he stays in combat, there remains a risk of him being wounded or killed. Since his contribution is not essential, there is no justification for taking this risk. On the other hand, if the enemy wins the battle, his risk of death is higher. And in this case, this risk is completely meaningless. Because, even if he participates in the battle, their defense will collapse. As a result, the best decision for the soldier is to flee the battlefield regardless of the outcome of the battle.



All of the troops here are in a similar situation. So, if they all think the same, the situation will surely arise where they lose the battle. That is, none of them will want to participate in war. Individual decisions made by everyone here created a situation that was undesirable for everyone. The question is, in reality, do soldiers think like this on the battlefield? Rather the opposite is seen there. The greater the fear of losing the battle among the soldiers, the more motivated they appear. On the other hand, troops that believe they will win are more likely to be indifferent to individual contributions.



Long before the advent of game theory, military leaders have been seen taking various steps to avoid such situations. One such military leader was the Spanish hero Hernan Cortez. While he led a small force into Mexico, his troops had great reason to doubt their own abilities. Because the number of Aztec forces there was huge. Cortez worried that his soldiers might flee in terror. So he burned all his ships. There was no other way for his army to escape. When escape became impossible, the only way for the Spanish soldiers to survive was to fight desperately.



Cortez burned his ships for all to see. This act creates a discouragement among the enemies i.e. the Aztecs. They thought that if a commander dared to destroy his only means of escape, there must be a reason behind it. Which is why despite his small force, he instilled so much confidence. Aztec soldiers did not see fit to fight against a commander who had such reasons not to lose. As a result, Cortez secured an easy victory.



Another classic source for such an argument is Shakespeare's Henry Five. At the Battle of Agincourt, Henry decided to kill his French prisoners in front of the enemy. However, Henry argued, the prisoners would put Henry at risk by freeing themselves. But in the light of game theory the matter can be interpreted differently. Henry's soldiers saw that the prisoners had been killed. They also know that the enemy also witnessed these killings. Therefore, Henry's soldiers know that if they lose the battle and are imprisoned by the enemy, the enemy will avenge the killing. That is, their consequences will be dire. Similar to the soldiers of the cortege, but figuratively their ships are burned in this case. That is, there is no escape.

Thomas Hobbes's book Leviathan is considered a foundation of modern political philosophy. This book argues for the justification of state law enforcement over citizens. Here, too, the trick of game theory comes into play. Hobbes claimed that the best state for all men is where they can do whatever they want. However, many times one requires the cooperation of another to enforce one's will. In these cases, many have a strong tendency to take unethical positions. Let's take an example. Tahmid needs to build a house and Ayan agrees to help him. However, Ayan's condition was that once Tahmid's house was built, he would have to help build Ayan's house. After the house was completed, Tahmid thought that if he refused the contract, he would not have to do the extra work. That is, he has to pay an extra price to keep the contract. If the contract is broken, that liability no longer exists. So he rejected the deal.

Ayan has no home and Tahmid will not help him. In game theory all agents are thought of as intelligent. In this case, Ayan has a good chance of robbing Tahmid's house. Tahmid had this fear before. So he appointed guards. It is costing him money indefinitely. Tahmid may plan to kill Ayan first to avoid this cost. As Ayan is equally intelligent, he will want to do the killing first. In this way, a chain of knowing each other's plans in advance will continue. If many agents form such a dangerous relationship with each other, there will be an extreme chaos in the society. Hobbes named this situation, 'war of all against all'. In such a situation human life will become miserable.



Hobbes' proposed solution was a ruler. People will appoint an agent who will punish the violator first. As long as this punitive role operates, the cost of breaking the contract will be greater than that of keeping the contract. So any rational and sane person would then want to protect the agreement. This argument is akin to sentencing deserters to death. If everyone kept the contract like this, that would be the normal state of society. Game theory answers many more questions. Why are heads of state around the world still not working to remove carbon dioxide? It is in the interest of the whole world that climate change should be stopped. But every country has a vested interest in carbon dioxide for industrial production, which is why global awareness is still lacking. Those who work on carbon removal will be left behind in the competition compared to other countries.



The concept of Nash Equilibrium helps us understand why society must intervene in certain areas of our lives to achieve desired outcomes. Legal obligations can force people to make decisions based on self-interest. Climate change is one such issue where everyone needs to be forced to make decisions beyond self-interest. However, it is difficult to reach a position on the overall scale, where everyone is competing with each other. Because reducing carbon removal means reducing economic profits. But, even the best decision made by self-centered thinking can put us in an undesirable situation overall. We should all realize this.