What should everyone know about game theory

Game theory

This article deals with game theory in economics and uses some examples to explain the most important basics. In addition, a distinction between cooperative and non-cooperative game theory is shown.

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Game theory definition and overview

Game theory in economics is a mathematical theory that deals with the interactive decision-making patterns of a large number of players in a game. The aim is to provide predictions about the outcome of games (in the game theory sense) and to issue recommendations for action based on this. Games differ in terms of 6 criteria:

• Number of players (2-person / n-person)
• Payout structure (zero-sum game / non-zero-sum game)
• Cooperative / not cooperative
• Strategy options (mixed strategy or pure strategies)
• Information content of the players (perfect / imperfect information)
• Number of executions (finite / infinitely repeated game)

Based on this and with the help of the order of preferences of the individual players, the game can be graphically represented.

For this purpose, a bimatrix is ​​used in the normal form and a game tree in the extensive form. Depending on the initial situation, equilibria can then be determined in the games, such as the Nash equilibrium.

Cooperative game theory / non-cooperative game theory

Cooperative game theory assumes that binding contracts exist. This is the case if they can be enforced by an independent sovereignty. In games in non-cooperative game theory, it is assumed that equilibria can only be achieved through the players' own interests. So contracts are not binding, meaning players can change their strategy after announcing their intentions. Especially in microeconomics, non-cooperative game theory plays a bigger role.

Game theory in economics

If you look at game theory in economics, it is about the economic behavior of the respective players and their reactions to other actors. In particular, the Cournot competition be considered as a dynamic game. Other classic examples of game theory situations are the coward game, the ultimatum game or the Prisoner's Dilemma . For a better understanding, we go through the Chicken Game (also called the coward game) and explain the most important terms from game theory to you.

Chicken Game

The starting point is simple. Imagine you borrowed your parents' car and you are setting up a race with your buddy. The racetrack leads across fields and country roads for quite a while and you are equally fast. But then you have to cross a bridge and if you drive side by side on the bridge at the same time, you both fall down. The bridge is only built for one car at a time. Now you are faced with the question: will you brake and swerve, and thus lose the race, or will you continue driving and risk totaling the car?

Payout matrix from the coward game in normal form

First, we'll provide one for this game Bimatrix or payout matrix on, this could look like this:

Chicken gamePlayer 1 (you)
Continue driving4 , 0-3 , -3

Each player wins the most for himself if the other is a coward and evades (0.4); (4,0) - if both dodge neither wins (1,1,), and they get away with harmless. But if it comes to the case that both continue, both fall from the bridge and the cars are destroyed (-3, -3).

The extensive form of the game does not exist in our example, because there is no sequence, but the players make a decision at the same time. If you want to know how to do that Play tree , so the game in extensive form, take a look at our video!

Example of economic behavior

Game theory is also very important in a business context. So that the behavior or the reaction of the opponent is to be predicted, it is useful for determining the location or setting prices. For example, if company A lowers prices in order to increase sales, this may only make sense if the competitor also keeps prices constant. If company B also decides to adjust prices, this can result in reduced profits for both companies. With the help of game theory analyzes, attempts are made to address such problems.

Game theory solution concepts

After a game has been defined, the result can be analyzed with the help of game theory instruments. In this way, optimal strategies and equilibria can be determined. One distinguishes between dominant and dominated strategies , as well as between pure strategies and mixed strategies. Also by the Min-Max theorem and the repeated Eliminate strictly dominated strategies there are different solutions depending on the game.

Game theory Nash - equilibrium

John Nash established the so-called Nash equilibrium in 1950. It predicts the outcome for games in which all players behave optimally individually. A player here always chooses the strategy in which he can no longer do better by deviating.

In our example for the Chicken Game there are three Nash equilibria:

1) Nash equilibrium in pure strategies : Player 1 decides to play "Continue" and Player 2 plays "Dodge"
2) Nash equilibrium in pure strategies: Player 2 decides to play "Continue" and Player 1 plays "Dodge"
3) Nash equilibrium in mixed strategies: Player 1 and Player 2 choose 50% "Evade".

Information content of the players and number of repetitions

Finally, a game must be examined in game theory with regard to the information available and the number of repetitions. In our case, the Chicken Game, it is a non-cooperative game with incomplete or limited information. This is because player 1 is not able to find out about player 2's game strategy with any certainty. Furthermore, our example of the coward game is a game without repetitions. If a game is repeated (indefinitely) often, information on the outcome of the game can be obtained from previous games.