# Game Theory

This article describes the **Game Theory**, developed by **Oskar Morgenstern** and **John von Neumann** in a practical way. After reading you will understand the definition and basics of this powerful **strategy** and **decision making** tool.

## What is the Game Theory?

Game Theory is a probability calculation technique used to analyse situations with strategic interactions between different decision makers and predict the outcome of their decisions. Game Theory is especially useful for companies that, for example, want to enter a new market with a product or want to lower their prices in comparison with their competitors in order to increase their market share. It is about which choices a participant has and how those choices are influenced by the choices of other participants.

Game Theory is a branch of mathematics and it was described in the book *Theory of Games and Economic Behaviour* by economist Oskar Morgenstern and mathematician John von Neumann in 1944.

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From the start, Game Theory was born out of the analysis of decisions that are made when playing board games. This is also where it derives its name from. Ultimately, Game Theory, through application from other disciplines, has become a part of science.

Models are created in order to better understand the participants’ choices and to see how this impacts each other’s decisions.

## Game theory : Acting rationally

Game Theory assumes that people act rationally. Therefore, participants are at least as likely to make their chosen decision as the possible alternatives. This has to do with a part in the brain that is the called the **decision maker**. When approaching a busy intersection, this decision maker makes a fast-paced probability calculation before the decision is made to cross the intersection. This is how Game Theory also works: it is a mathematical rationalisation that occurs within us all when making a decision. Every human action is preceded by rational considerations made on the basis of a number of options. By doing so, the ‘games’ can be divided into different categories within Game Theory, which can assist in finding the most optimal outcome of a game. The outcome of a game can then provide important insight into taking (business) decisions.

## Main branches

Within Game Theory there are two main branches: cooperative and non-cooperative Game Theory. The difference between these two types of games is that binding arrangements can be made in cooperative games between the participants, while this is not possible in non-cooperative games. In addition, there are other branches that are closely linked to Game Theory, including Decision Theory. This is a part of cooperative Game Theory that focuses on a one-player game with one participant. It is often used in the form of a decision analysis, which shows what is the best choice, based on information obtained in advance. The focus is on preferences and beliefs.

## Payoff Matrix

With the help of a so-called simultaneous game, Game Theory can determine what the best decision is, if the participants determine their actions simultaneously and without knowing what the other does. A **Payoff Matrix** visually illustrates the payoff for each participant, with all possible combinations and decisions. Each participant can then look at what the best decision is, if the other party opts for decision x; this is also called the ‘best response-method’. The best decision (for now) is underlined in the Payoff Matrix. Then, the participant that is listed horizontally (the row player) makes a choice:

- If the participant in the vertical column chooses decision 1, the row player should choose decision 2.
- If the participant in the vertical column chooses decision 2, the row player should choose decision 2.

The participant who is listed vertically (the column player) also makes a choice:

- If the row player chooses decision 1, the column player should choose decision 2.
- If the row player chooses decision 2, the column player should choose decision 2.

We speak of a dominance strategy when a participant unilaterally chooses the same decision as the other, irrespective of the other’s choice.

## Game Theory example

Imagine that Dylan and Maria work at a project organisation. Every project involves large sums of money. That is why it is a good idea to first determine the profitability before starting a new project. There are many factors that are expressed in numbers in the matrix below.

Dylan is player 1 and the row player. The goal is to find out what the most dominant strategy will be for Dylan. Maria is player 2 and the column player. Her choices determine what Dylan will eventually do. Both have the choice to ‘start’ or ‘stop’ a project, and the value of choosing one of these options is expressed in numbers. The first number belongs to player 1 (Dylan) and the second number is that of player 2 (Maria).

Now you can determine what will happen to Dylan if Maria chooses to start the project -> Dylan scores a 1 if he also chooses to start, but a 2 if he wants to stop. Since 2 is a higher score than 1, Dylan chooses to stop in this case. What happens to Dylan if Maria opts to stop the project? -> Dylan scores -1 if he then starts the project, but a 2 if he stops. Because 2 is a higher score than -1, he will stop in this case as well. Regardless of whether Maria will start or stop the project, it is better for Dylan to stop. That is his most dominant strategy.

We can also look at Maria’s strategy. What will happen with Maria if Dylan chooses to start the project? -> Maria scores a 1 if she also starts, but -3 if she wants to stop. Because 1 is higher than -3, she will opt to start. What happens to Maria if Dylan chooses to stop the project? -> Maria scores -1 if she starts and a 3 if she also decides to stop. Because 3 is higher than 1, she will opt to stop in that case.

That means that stopping the project is the best strategy for both. Because Maria is player 2, her strategy is less dominant as it will be Dylan who will implement the most dominant strategy first. He will doubtlessly decide to stop the project.

## Sequential game

It is also possible that the two participants each make choices after one another. This is called sequential or simultaneous Game Theory. The one who first makes a decision may have the advantage, but should take into account all possible responses from the other participant. In sequential games, participants are aware of the actions of the other participants in their decision. In most cases, a sequential game uses a decision tree, which maps all possible combinations of actions. This makes it clear to a company whether or not to increase their prices and if they do so, how high the price increase should be to stay ahead of the competitor.

Game Theory provides many possibilities that can guide important strategic decisions. Nevertheless, it remains a probability calculation that is not entirely based on facts, but on possibilities that could occur. By collecting the proper information in advance, Game Theory can make a fairly good prediction. However, if things turns out to be different, then that is the reality and participants will have to act early on to adjust their decision.

## It’s Your Turn

What do you think? What is your experience with the Game Theory? Do you recognize the practical explanation or do you have more additions? What are your success factors for good strategic decision making?

Share your experience and knowledge in the comments box below.

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## More information

- Morgenstern, O. (1976).
*The collaboration between Oskar Morgenstern and John von Neumann on the theory of games*. Journal of Economic Literature, 14(3), 805-816. - Morgenstern, O. & Von Neumann, J. (2007, 1944).
*Theory of games and economic behavior*. Princeton University Press. - Weintraub, E. R. (Ed.). (1992). Toward a history of game theory (Vol. 24). Duke University Press.

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