Game Theory: An Important Beginning for Further Understanding

Game theory is a set of tools that help you make informed, logical, and accurate decisions and help you understand data. The more information about the players and the situation we have, the more accurately we can analyze and make a prediction.

Today we will start with a simple introduction – we will define what game theory is, why it is needed, and what it covers. In what follows, we will consistently use this knowledge to practice.

Game theory: What is it?

Let’s think about this scenario: morning in the city, snow everywhere, you need to get to an IT school GoMother. There are two options: take a car or use public transport. You know that by public transport you will get to school in an hour: buses run according to the schedule, and you have already used this route more than once. By car you can cover the distance twice as fast, but it depends on the traffic – if there are traffic jams, you can lose and few hours.

Suppose you decide to leave by car. Do you remember where you usually traffic jams form in winter and you choose a route to avoid them and arrive on time.

But, when you drive up to the required street, you find that a traffic jam has already formed here. It so happened that many have chosen the same strategy as you, and are trying to circumvent possible traffic jams on this route.

In this case, you did not influence the choice of other drivers on their route. However, their actions directly affected you – you got stuck in a traffic jam. They also did not know that you had chosen this route and made their decisions based on their calculations. This is how a car navigator chooses the most efficient path.

It follows from this that someone can choose the old route that you abandoned and not run into traffic jams. Because traffic jams have already moved to other sections. Some may opt for public transport, reducing traffic on the roads. And this also helps to avoid traffic jams on the preliminary route. Others may not go anywhere at all, staying at home.

The main opinion is that different decisions of different people in different situations have different influences on us. This influence also has the opposite effect – our actions affect others. Sometimes it is possible to predict how the choice of actions affects the situation. This is the essence of game theory.

The concept of the game

The author of game theory is the physicist, mathematician, and engineer John von Neumann (in some sources -Neumann). He defined a game by referring to a situation where the following conditions are met:

1. It has at least two members.
2. Each participant has his interest.
3. Each participant has several options for action.
4. Each makes a decision based on information about the actions of others.
5. There are general rules known to all. They can change, shrink, or expand, but they become known to everyone quickly enough.

From this point of view, most of our everyday situations are influenced by game theory. Even normal negotiations over wages or where to spend holidays are subject to game theory.

At first, John von Neumann explored poker as a game and tried to find universal strategies that led to victory (hence the name of the theory). But then he extended the application of his theory to all such situations where the behavior of one participant affects his position and the behavior of others.

Game Theory: Strategy

Game theory is about finding the most profitable strategy for a particular player. A strategy is a sequence of actions: what he does and what messages he sends to other players. Some games are impossible to win, in which case the best strategy is to lose as little as possible or stay in the game for as long as possible. Online shooters have such a strategy, where the playing field is constantly shrinking.
We will mainly talk about winning strategies but at the same time. We will consider other results. The task of data analytics in this case is to collect information about all the players. And their strategies and understand which approach is best for us.

Types of different games

Depending on the behavior of the participants and the rules governing the game. Games can be divided into several different categories. These categories can interact and intertwine with each other.

Zero and non-zero-sum games

In zero-sum games, the victory of one participant means the defeat of the other, and vice versa. In non-zero-sum games, the victory of one participant does not necessarily lead to the defeat of the other. In such games, all participants may receive their winnings.

Cooperative and non-cooperative games

In cooperative games, participants can work together to achieve the best results and coordinate their actions. However, this cooperation is not permanent. And any player can leave such a coalition at any time and play independently.

Symmetric and asymmetric games

In symmetrical games, each participant has the same set of strategies. While in asymmetric games there can be different sets of strategies for different players.

Full games oh or incomplete information

In games with complete information, each player knows all the possible strategies of the other participants and can draw conclusions based on them. In games with incomplete information, no one knows what strategy the other player has chosen. Our traffic jam example is an incomplete information game.

Parallel and sequential games

In consecutive games, the participants act in turn (not necessarily in order, but only one player acts in one turn). In parallel games, all players act simultaneously and do not know about the actions of others until they have taken their actions. The example with the road to school is an example of a parallel game.

Application of games in mathematics

Game theory uses a complex mathematical apparatus. This means that for every game you can create a simulation or model and consider different possible outcomes for different players’ strategies. Some strategies have mathematical backing, while others based on the probabilities of success when choosing a particular strategy. In our case, this is useful because for simpler games we can create an algorithm and immediately test it in practice – simulate the behavior of different players and analyze, what result will it lead to. We will also look at this in more detail in the following articles. To do this, we need the Python programming language – a universal tool to build different models. If you are not yet familiar with the Python programming language, our school offers a course to learn this language from scratch.

Applications of Game Theory

Game theory finds application in almost all areas of life:

• in the economy – when choosing partners for trade and making deals;
• in negotiations – to determine the strategies of agreement and the terms of cooperation;
• in mathematics – there is a separate section devoted to combinatorial games;
• in politics – when making decisions based on the actions of other states;
• in everyday life – when you need to solve problems based on incomplete information;
• in video games – to find the most effective strategies.

What’s next?

Next time we will explore the problem of the prisoner – this example is often used to demonstrate the principles of game theory in real life This is not the only example, but the most famous. We will look at how this example functions in theory and try to simulate it in practice – we will write the program code and determine the optimal strategy. So follow our website and subscribe to our social networks!