Introduction to the Game Theory

One thing that makes us human is that we cannot exist without interacting with one another. Sometimes, it may seem like we have always found a way to survive, even with these interactions. Our economic structures and development call for these interactions because there would be no production or exchange if there is no understanding between individuals. In all situations, consumers consider what producers are making and their affordability before making the consumption decision. On the other hand, manufacturers look at how much consumers are buying their products before making production decisions.

However, these interactions are not always good; sometimes, they cause disastrous confrontations, which could turn out really bad. Across human history, there have been countless recordings of wars and fights, all of which lead to the fullness of the corporation. In many cases, social interaction is potential harmonious and corporative, and conflicting and disaster. Take, for instance, the relationship between couples, siblings, countries, management, neighbors, and many others. Today, you will hear two parties are existing in peaceful terms, and tomorrow they will be fighting. There is always some sort of force behind these relationships.

For instance, it could be understood to argue that technology and development have been key in the facilitation of these relations. There are all types of institution cropping up and scientific inventions that aim to make human life much easier. They have all existed as part of human society today to fuel and facilitate these interactions. A good example is the internet technology. Today, it is hard to imagine a world without social media and the World Wide Web that has made the world seem like a small village. When it comes to market, the technology has become a vital aspect of fueling the buyer-seller relationship. However, there is a huge negative impact drawn from this technology, whereby it encourages cheating and fraud.

Understanding relationships

In the labor market, employers and employees seem to have a conflicting idea about wages and working conditions. In these labor unions and labor laws, come up to draw the line between what is right and what is wrong. By doing so, they encourage proper coexistence by ensuring these challenges and conflicts have been addressed. Apart from these, we have been faced for many years, by cultural and religious norms, like altruism or reciprocity, which may potentially create negative interaction between people. However, culture is constantly changing due to human interaction. The evolve to align with the changes in the underlying interactions. For this reason, it is not easy to understand human behavior in its social and institutional context unless there is proper knowledge of human interaction.

And there are several subjects dedicated to the study of these interactions, including economics, psychology, and pollical science. Each of these subjects deals with specific aspects of human life. Many times, however, they take individuals in isolation in order to provide useful data. What this means is, an expert will have to assume that one's behavior does not have any effect on another individual. Under some situations, this assumption and be verified, especially when it comes to how significant the effect is or is not. For example, the price charged by a small wheat farmer in an African country will not impact the price of the product in the rest of the world. Also, the probability that a one-person vote will change the outcome of a country's presidential election is very insignificant. Hence, if we are interested in a larger area of study, it is safe to assume their action will not affect the entire system.

This assumption, however, as led to wrong conclusions on many occasions. If you consider what that same farmer charges in the same area, compared to others around the home, we can say their actions affect others directly linked to them. If they set the price very low, consumers will not go to their competitors, which leads to their products getting spoilt. And if they set too high, the chase away potential buyers. So, assuming that they don't consider this effect while making their decisions, then we will not understand their behavior properly. On the other hand, a small committee of voters may consider the vote of one of them to determine where they cast theirs.

The game theory is based on these exact interactions within groups of people, in which the action of one directly affects the others. But this, not enough reason to set the proper environment of the game theory; people have to act or behave strategically, understanding that their actions affect others around them. One must understand that their actions have an effect on the results, yet this does not necessitate strategic behavior if the individual does not understand this fact. In this case, it is safe to say the game theory looks at strategic interaction within a specific group of people.

Important terms in the game theory

The game theory is simply based on the games that people play. Let's take an example of a case where two or more players are involved in know payouts of quantifiable consequences. Were can use the game theory to know what will come out. But before looking at this, let's consider some terms used in the study of this idea.

- Game. A game is defined as any set of situations a result depends on the action two or more participants who must make decisions.

- Players. These are strategic decision-makers involved in the game context.

- Strategy. Every player gets into a game with the aim of winning. And to do this, they have to come up with a plan of action they will take, considering the set of circumstances that might come up with the game.

- Payoff. With every step a player takes, there is an outcome, some which are pre-determined, and others are not. This is called a payoff, and it can be in any quantifiable form, like cash or utility.

- Information set. At every given point a game, there is information that must be made available to help players in their question. This term is usually used where the game has a sequential component.

- Equilibrium. This is a point in the game where both players have made their decisions, and the outcome has been reached.

There must be assumptions of the rationale in every economic concept, and the game theory is not different. Also, there is the assumption of maximization, where it is assumed that the players make rational decisions and will do everything possible to maximize payoffs in the game. It is important to study these assumptions because they help us determine how consumers make a decision. The game theory is critical in explaining the relationship between consumers and producers within and economy.

For those who wish to examine games that are already underway, it is assumed on your behalf that there is an inclusion of all payoffs associate with an outcome within the listed payouts. If any "what if" scenario may arise, it must be included within the listing. Also, the number of the player in a certain game can be infinite – in theory – but most games only consider two players. The simplest example is a game involving two players, which is a sequential game.

Game theory is basically the study of rational behavior in the case that involves interdependence. It is the best and formal method of analyzing how a group of rational individuals interact when they have a strategy. Traditionally, it was used in determining zero-games in which the losses from the other party initiate one party's gains.

Since humans are naturally rational, they take actions that are carried in their goals. Interdependent is where any player is impacted by others' behaviors, whereby their actions depend on the prediction of how others will respond. In other words, before an individual takes a step, they must know how their actions will affect others. For this determination to work, the actor must have knowledge of other's aims as well as all the options at their exposure.

The Game Theory and Economics

The game theory is not just a game, but a thought that has been used over the years to make a decision regarding price, output, product development, product promotion, and other business situations. This theory has become a vital aspect of the modern business realm as it helps decision-makers in the economic sphere to achieve, or get as close as they can to their goals.

Here are some of the most common examples of the game theory applied in economics:

- Buyers and sellers are negotiating a price. We already know that price is one of the main determinants of consumers making decisions and producers making a profit. For this reason, each of them must get the best deal that makes them feel satisfied.

- A firm and its competitors. A company is always faced with marketing strategy decisions that best beats what the competition is offering. From time to time, they interact with this competition either positively or negatively. The firm can use the game theory to determine the strategies that work the best.

- Auctions. Actions are like a game of luck where the highest bidder wins the day.

- Prisoner's dilemma

There is a need to analyze the cooperation in the game theory, which is done through a non-zero-sum game known as the Prisoner's Dilemma. This idea was originally presented by Merrill Flood and Melvin Dresher while working at RAND in 1950. Later, Albert W. Tucker formalized the game with rewards that come from a prison sentence, terming it, "Prisoner's Dilemma." In this situation, there are two members of a criminal gang who are arrested and imprisoned. Each of them is placed in solitary isolation, and they have no way of communicating with each other.

On the other hand, the prosecutor does not have sufficient evidence to lock them based on the main charge; hence, they are expecting to spend a year in prison for a lesser charge. At the same time, the prosecutor comes up with a bargain or offer for each prisoner. They are given a rare opportunity to betray the other for committing the crime or remain in solidarity with the other prisoner. So, they are faced by three major dilemmas;

- If A and B tell on each other, they risk serving two years behind bars

- If A speaks but B remains silent, A will go free as B serves three years, or otherwise.

- If none of them speaks, they will only serve one year on a lesser charge.

There are two moves for each of these players – to either cooperate or defect. The main point of concern is that each player gains when they cooperate; however, if only one cooperates, he/she will at the expense of the other. And they both lose if both defects.

According to economists, the Prisoner's Dilemma games are zero-sum because there is no cooperation. The results are already pre-determined that either each gains 0 if they defect, or one defects and gains (+10), while the cooperator gets (-10), which brings the total to 0. There is a positive gain where each of them cooperates, where each gets 5, making a total of 10. One-sided defection makes bigger gain (10) than cooperation. And this is why there is always a temptation for defection, as shown in the table below.

 Action of A / Action of B

 Cooperate

 Defect

 Cooperate

 Fairly Good (+5)

 Bad (-10)

 Defect

 Good (+10)

 Mediocre (0)

The sequential move theory

The Prisoner's Dilemma game is a simple game in which both players need to move at the same time. Apart from this, there is another game that involves players making their moves in specific sequences. It is called Sequential Move Games. In this case, player A is a newer player on the market, and they can either enter the market or avoid it altogether. Player B is already established in the market, and he can either choose to accommodate player A as a competitor and avoid raising prices, or initiate a price war. Player A has a better chance of entering the market because B gains a payoff (1) if he/she accommodates them, or lose (-1) if they start a price war.

Author: James Hamilton