Game Theory: Mathematics of life.

Every single day, in every single way, we all make decisions. Sometimes, even if we are not actively making one, our body does it for us. Decisions are imperative to our existence and inevitable until we stop breathing. Humans will never escape them. To be indecisive is human; to decide is eternal. Every piece of information can open a new option, and every option can create an outcome of existence. On average, a person makes 35,000 decisions in a day. Decisions can be trivial, complex, rational, or irrational, but they will always have consequences that one must endure. Decisions surround us everywhere we go. We can be enslaved by them or rise with them. What if there was a way to always choose the best decision?

For almost every aspect of life, game theory can help us understand how to make the best decisions. It is a science of decision-making. Before we dive into game theory, let's first understand what a game is. A game is a formal description of a strategic situation. Any situation that demands a decision is a game. The London School of Economics defines game theory as a formal study of decision-making in which several players must make choices that potentially affect the interests of other players. As a decision-making tool, game theory can explain and predict an outcome under a set of decision-making rules. In this global pandemic, which continues to offer us nothing but struggles and confusion on every economic front, game theory can help us make the best decisions in just about every aspect of our lives, be it financial, existential, or even spiritual. The power and utility of game theory are immeasurable.

John Von Neumann developed game theory to solve critical problems in economics. Von Neumann was generally regarded as the foremost mathematician of his time and was said to be the last representative of the great mathematicians. He integrated pure and applied sciences. Von Neumann and Oskar Morgenstern wrote a book entitled "The Theory of Games in Economic Behaviour". He asserts that any situation is an outcome of a game played between two or more players. According to game theory, there are three components in any game: players, strategies, and pay-offs. The decision-maker in the game is called a player. Any possible plan of action a player chooses in the game is called a strategy. It can also be a complete plan of choices, one for each decision point of a player playing in an extensive game. Life more or less imitates large-scale games. A pay-off is a number that reflects the desirability of an outcome to a player. For any objective when an after-effect is random, the pay-offs are weighed based on their probabilities. The expected pay-off incorporates one's attitude towards risk. It applies to two or more players. In a game, the players share common knowledge of the rules, use available strategies, and gain possible pay-offs. However, often the players do not have perfect information about the events happening in the game. In game theory, the term absolute information is when at any point in time, a single player makes a move and also knows all actions made until then. Strategies are the heart of game theory. The concept of strategic interdependence is the mathematical modelling of strategic interaction between rational adversaries, where each action on one side would depend on what the other side would do. Life follows strategic interdependence as well.

Game theorists have found a limitation to Von Neumann's version of game theory. It focuses on optimal strategies for only one type of game known as a zero-sum game. In game theory, a zero-sum game is when any outcome of the sum of pay-offs to all players is zero. In a two-player zero-sum game, one's gain is another's loss. Their interests are diametrically opposed. The players neither increase nor decrease their available resources in a zero-sum game. A zero-sum game is where it stops coordinating with our real lives. In real life, a player can rapidly increase or decrease its resources. Life is not as simple as a zero-sum game. More complicated scenarios are possible in real life. For example, forming a coalition can exponentially increase awareness and access to increased pay-offs for several players all at once. Hence, game theory needed to evolve to fit a range of games.

John Forbes Nash Jr. was an American mathematician who made contributions to game theory. His work has provided insight into the factors that govern chance and decision-making inside complex systems found in everyday life. John Nash created the fundamentals of strategic equilibrium. A strategic equipoise is also called Nash equilibrium. It is a list of strategies, one for each player, which has the property that no player can unilaterally change their plan of action to get a better pay-off. Nash found a way to find optimal strategies for any finite game. A New Yorker article describes Nash equilibrium as a particular solution to games marked by the fact that one chooses the best outcome, given the strategies deployed by all other players.

A strategic equilibrium is reached in a game when none of the players want to change to another tactic because doing so will lead to an outcome that is worse than the current strategy. Nash shared the 1994 Nobel Memorial Prize in Economic Sciences with game theorists Reinhard Selten and John Harsanyi. However, in 1959, Nash began showing clear signs of schizophrenia. He improved his condition but eventually perished with his wife in a car crash while riding in a taxi on the New Jersey Turnpike in the United States of America on May 23, 2015. According to Forbes, Jon Von Neumann called Nash Equilibrium trivial, suggesting that it is mathematically simple.

A classic example in game theory is known as the Prisoner's dilemma, which is crucial in understanding the applications of game theory. In this scenario, there are two prisoners, George and Charlie, who have partnered in a bank robbery. Although the authorities lack evidence to convict them, they are aware that the duo has committed the crime. George and Charlie are in separate investigation rooms, and the officers are communicating the outcomes to them. The two strategies available to both criminals are either to confess or to keep quiet, with the pay-offs ranging from serving five, ten, or twenty years in prison.

If both George and Charlie confess, they will each get ten years in prison. If one confesses and the other remains silent, the one who confessed will go free while the other will spend twenty years in prison. If both of them choose not to divulge, they receive a five-year sentence. They both will not be allowed to leave their respective rooms until they choose an option provided to them.

The answer lies in fundamental finance reached by a single matrix. The devil is in the details of a term known as the dominant strategy, which weakly dominates another and is a strategy with the best pay-off no matter what the other player chooses. If George confesses and Charlie does not, George goes free. If he does not divulge and Charlie does, George receives a twenty-year prison sentence. If they both choose to confess, they get a ten-year prison sentence each. The best option for George is to confess, and hence, the best choice for both is to reveal their crimes. They both will turn on each other. That is their best option, their only dominant strategy. Why is the choice of them both not confessing the best choice? While this option will give both less time in prison than if they chose the option of confession, it would only work if each of them is sure that the other one would not turn on him. Would you bet 20 years on your partner? It is unknown whether George and Charlie would coordinate with each other at that level of cooperation. As a result, both will always be unlikely to choose not to confess because it has a harsher penalty than the option of confession. Confessing also gives them an outcome of going free. This dilemma illustrates how the application of rationality in some situations can be problematic, as most theories assume that agents or players always seek to maximise their utilities or payoffs. However, research shows that players do not always behave rationally. Thus, it is crucial to consider different perspectives and go easy on replicating sheer logic, as rational analysis can fail to conform to reality.

As seen in this example, the most rational strategy that would give both players less prison time was not the best choice. Instead, the best option involved both players doing more prison time. This dilemma highlights how other game theorists can address some issues with Von Neumann's version of game theory but struggle to solve the same problems in non-zero-sum games. Therefore, it is important to recognise that rationality may not always be the best approach, and one should consider other factors, such as emotions and social dynamics, when making decisions. In some cases, irrational actions may even lead to better outcomes than rational ones. By understanding the limitations of rationality, we can develop more nuanced and effective decision-making strategies.