Prisoner’s Dilemma
Jack and James are two criminals who are caught by police and brought to a prison inside a jail. The Jailer is determined to make them confess to the crime. He approaches both of them and starts investigating them. But both Jack and James are very adamant and don’t admit to the commitment of the crime to the Jailer. So the Jailor decides to interrogate them individually. He gives them an offer. The offer is that the prisoner who confesses about the crime can go free and the other will get severe punishment. The game is set up so that if both prisoners remain silent, they will each receive a relatively minor punishment. However, to keep things interesting and make both of them confess to the crime, the Jailer further offers that if both prisoners confess, they both receive a moderate punishment.
In this situation, Jack and James are faced with a dilemma. They both know that if they both remain silent, then the jailor’s propaganda will fail and both of them can later walk free. However if the prisoner remains silent, but if the other one confesses, then we will get a severe punishment. In this situation what will Jack and James do?
Well, this situation has been widely studied by human psychologists and they refer this to as Prisoner’s Dilemma. The prisoner’s dilemma illustrates how rational actors can sometimes make decisions that are not in their own best interest because they are trying to anticipate and outmanoeuvre the other player. The prisoner’s dilemma has had a major impact on our understanding of how people make decisions in strategic situations. This dilemma was originally developed by Merrill Flood and Melvin Dresher while working at the RAND Corporation in the 1950s. This is nothing but one of the earliest and most famous applications of game theory.
What is Game Theory after all?
Game theory is a branch of mathematics that studies strategic interactions among rational agents. It was developed in the mid-20th century by mathematicians John von Neumann and Oskar Morgenstern, who sought to understand how rational actors make decisions in situations where the outcomes depend on the choices of multiple agents.
One of the key insights of game theory is that the optimal decision for a player depends not only on their own preferences but also on the actions and preferences of other players. This means that the behaviour of rational agents in strategic situations can often be counterintuitive, and can lead to outcomes that are not Pareto optimal (meaning that there is no way to rearrange the outcome to make some agents better off without making others worse off).
Game theory has had a major impact on a wide range of fields, including economics, political science, psychology, biology, and computer science. It has also been applied to various real-world problems, including auctions, negotiations, and conflicts.
“In game theory, we study strategic situations where players must choose between different actions, knowing that other players are doing the same.”
John von Neumann
The Tragedy of the Commons
Imagine that you and your friends are at a potluck dinner and there is only one slice of pie left. If you take the slice of pie, you will get to enjoy it, but your friends will be disappointed. If you leave the slice of pie for your friends, you will miss out on the enjoyment, but they will be happy. This is a classic example of the “Tragedy of the Commons,” in which individual selfishness leads to a worse outcome for everyone.
A few years ago, Indian telecom market was flooded with many telecom operators such as Idea, Airtel, Aircel, Docomo, Vodafone, BSNL and a few more. Because of so many players, the market was very competitive and operators would every month slash their rates and update their schemes to compete with others.
Another real-life example is with Indian Telecom Players. Let us say, Airtel launches a new offer. So now Idea would try to reduce its price so as to beat the Airtel offer. But Airtel knew that Idea would launch an offer to counter its offer. So again Airtel was now in a fix because if it reduces further, it will deplete its profit margins and if does not reduce further it will see its customers moving to Idea’s new offer. This is a classic example of Game Theory.
In a limited resource environment such as a phone consumer market where the total number of customers in a market is fixed, someone’s loss is someone else’s gain. For example, customers lost by Airtel would be a gain for Idea and so on. That is precisely the reason, why businesses try to stand out from the competition and don’t prefer to fall into the trap of cheap competition.
“The beauty of game theory is that it allows us to analyze complex situations in a simple and logical way.”
Kenneth Arrow
“The Stag Hunt”:
Imagine that you and a group of friends are out hunting in the forest. You come across two different animals: a stag and a rabbit. The stag is a much larger and more valuable prey, but it can only be caught if everyone in the group works together. The rabbit, on the other hand, can be caught by a single person. If everyone in the group chooses to go after the rabbit, you will all get a small reward, but if anyone chooses to go after the stag, the group will be more successful. This is an example of the “Stag Hunt,” in which the optimal outcome depends on whether or not the group is able to cooperate.
The tragedy of the commons is a concept in game theory that illustrates how individual self-interest can lead to negative outcomes for the group as a whole. The term was first coined by economist Garrett Hardin in a 1968 article, and it has since become a widely studied and influential idea.
At its core, the tragedy of the commons refers to situations in which a resource is shared by a group of individuals and each person has the incentive to use as much of the resource as possible, even if it is to the detriment of the group. This can lead to overuse of the resource and ultimately its depletion, resulting in a tragedy for everyone.
One classic example of the tragedy of the commons is the case of overfishing in the ocean. Imagine that a group of fishermen are all competing to catch as many fish as possible in a shared body of water. Each fisherman has the incentive to catch as many fish as they can since this will maximize their own profits. However, if all of the fishermen are pursuing their own self-interest, they may end up overfishing the area and depleting the fish population. This will lead to lower catches for everyone in the long run, even though each fisherman was acting in their own self-interest in the short term.
Another example of the tragedy of the commons is the case of air pollution. Imagine that a group of factories are all located in the same area and are emitting pollution into the air. Each factory has the incentive to produce as much as possible since this will maximize profits. However, if all of the factories are emitting large amounts of pollution, the air quality in the area will deteriorate, leading to negative consequences for everyone, including the factories themselves.
So, what can be done to prevent the tragedy of the commons? One solution is to introduce property rights so that individuals or organizations have ownership over the shared resource and have the incentive to preserve it. For example, if each fisherman had the right to a certain number of fish per year, they would have an incentive to conserve the fish population, since this would ensure a steady supply of fish in the long run.
Another solution is to introduce regulations or incentives that encourage sustainable use of the resource. For example, the government could implement a cap-and-trade system for air pollution, in which factories are given a limited number of pollution allowances and can buy and sell allowances as needed. This would create an economic incentive for factories to reduce their pollution and preserve the air quality in the area.
Ultimately, the tragedy of the commons is a reminder of the importance of considering the long-term consequences of our actions and the need for cooperation and regulation to prevent negative outcomes. By understanding and addressing the forces that can lead to the tragedy of the commons, we can work towards more sustainable and equitable outcomes for everyone.
Game Theory among us
Game theory is not just a mathematical concept, it can also be a powerful tool for motivation and personal growth. At its core, game theory is about making strategic decisions and finding the best course of action to achieve your goals. This same principle can be applied to our personal lives to help us stay motivated and focused on achieving our own objectives.
One way to use game theory for motivation is to think about your goals as the “prize” in a game. Just like in a game, you need to have a clear strategy and make smart, calculated moves to reach the prize. This means setting specific, achievable goals and developing a plan to achieve them. It also means being willing to adjust your strategy as needed and adapting to new challenges and setbacks.
“Game theory is a way of thinking about the world that helps us understand how to make smart decisions in situations of conflict or cooperation.”
Robert Aumann
Another way to use game theory for motivation is to consider the “opponents” or obstacles that may be standing in your way. In a game, you need to anticipate and outmanoeuvre your opponents to win. In life, you can use this same approach to overcome challenges and setbacks. By anticipating potential obstacles and developing contingency plans, you can stay motivated and on track to achieve your goals.
So, the next time you find yourself in a strategic situation, whether it be in business, politics, or even just a friendly game of chess, remember the lessons of game theory. By considering the interests and actions of others, and striving for equilibrium, you can make smarter decisions and increase your chances of achieving your goals.
Game Theory Applications
Game theory is more than just a branch of mathematics – it is a way of thinking about the world and the strategic decisions we make on a daily basis. It helps us understand how to navigate complex situations and achieve our goals, whether we are competing against others or working together towards a common objective.
One of the key insights of game theory is that our actions and decisions are often interconnected with those of others. In order to achieve success, we must consider not only our own interests but also the potential responses of those around us. This can be challenging, but it also presents us with endless opportunities to outmanoeuvre our opponents and find creative solutions to problems.
Another important concept in game theory is the idea of equilibrium or the optimal balance of power between players. By understanding the equilibrium of a situation, we can make informed decisions that maximize our chances of success. This requires not only understanding our own objectives and constraints, but also those of others.
Examples of Game Theory
Imagine that you own a small business that competes with several other firms in your industry. Your goal is to maximize your profits, but you also want to maintain a good reputation and avoid damaging relationships with your competitors.
One day, you receive an anonymous tip that one of your competitors is planning to release a new product that will be significantly cheaper and of higher quality than anything you currently offer. You know that if this product hits the market, it will be very difficult for your business to compete.
You have two options:
You can try to release a similar product before your competitor does, hoping to get a head start in the market. However, this will require significant investment in research and development, and there is a chance that your competitor will be able to release their product before you.
You can try to negotiate with your competitor, offering to buy the rights to their product or to collaborate on a joint venture. This option carries less risk, but it also has the potential to be less profitable if your competitor is able to secure a better deal elsewhere.
This situation can be analyzed using game theory. The two players in this game are you and your competitor, and the strategies available to each of you are releasing a similar product or negotiating a deal. The outcomes of the game will depend on the actions of both players and the resulting market conditions.
To determine the optimal strategy, you need to consider the costs and benefits of each option, as well as the likelihood of your competitor choosing each strategy. For example, if you believe that your competitor is highly likely to release their product no matter what you do, then it may be more profitable for you to negotiate a deal rather than try to compete directly. On the other hand, if you think that your competitor is open to negotiation and that you have a good chance of releasing a similar product before them, then that may be the better option.
By thinking about the strategic interactions between you and your competitor, you can make a more informed decision about how to respond to the threat of the new product and maximize your chances of success. This is just one example of how game theory can be used to analyze real-world situations and make strategic decisions.
“Game theory is about predicting how people will behave, not about predicting how they should behave.”
Herbert Simon
Let us consider another interesting example. Imagine you are a farmer trying to decide whether to plant corn or wheat on your land this year. You know that the demand for corn is higher, but it is also a riskier crop to grow – there is a chance that you will have a poor yield due to drought or pests. Wheat, on the other hand, is a more reliable crop, but the demand is lower, so you will make less money if you choose to plant it.
This situation can be analyzed using game theory. In this case, there are two players – you, the farmer, and the market, represented by the demand for the two crops. Your goal is to maximize your profits, while the market’s goal is to determine the price of the crops.
One approach you could take is to consider the equilibrium of the situation. If you believe that the demand for corn is high enough, and the risk of a poor yield is low enough, then planting corn might be the optimal strategy. On the other hand, if the demand for corn is not as high, or the risk of a poor yield is too great, then planting wheat might be a better choice.
Of course, this is just one example of how game theory can be applied in the real world. By understanding the strategic interactions between different players and considering the equilibrium of a situation, we can make more informed and rational decisions in a wide range of contexts.
“Game theory teaches us that even in the most selfish of situations, cooperation can be the best option for all parties involved.”
Robert Axelrod
Finally here is one more example to see the benefits of Game Theory. Imagine that you and a friend are trying to decide where to go for dinner. You both have your own preferences for types of food and restaurants, and you want to choose a place that you will both enjoy. This decision can be modelled as a game, with each of you trying to maximize your own satisfaction.
One option is to use a simple strategy called “tit-for-tat,” in which each player copies the action of the other player on the previous move. In this case, you and your friend could take turns suggesting restaurants until one of you agrees to the other’s suggestion. This strategy is simple and effective, as it allows you to find a compromise without getting stuck in an endless loop of suggestions.
Another option is to use a more complex strategy called “minimax,” in which each player tries to minimize the maximum potential loss. In this case, you and your friend could list out all of the possible restaurants and then evaluate them based on how much you would each enjoy them. You could then choose the restaurant that minimizes the maximum potential disappointment for either of you. This strategy is more time-consuming, but it ensures that you both get a restaurant that you are at least somewhat happy with.
There are many other strategies that you could use to make this decision, and the best one will depend on your specific preferences and the specific situation. The important thing is to think about the game theoretically and to consider the actions and objectives of the other player. By doing so, you can make a decision that is mutually beneficial and satisfying.
“Game theory is the study of human conflict and cooperation within a strategic framework.”
John Nash
Conclusion
In conclusion, game theory can be a useful tool for motivation by helping us to think strategically about our goals and the steps we need to take to achieve them. By staying focused, adaptable, and proactive, we can stay motivated and on track to reach our objectives.