Game Theory and its Applications

Game Theory is a branch of mathematics that using scenario design and analysis attempts to predict the behaviors and decision outcomes of the parties, called players, who have the right to make decisions in interaction with each other.

Rock-paper-scissors hand game is a well-known example of this type of interactive game (multiple actors, multiple rules, choices and specific outcomes for each situation).

Suppose you went to the market with a friend to buy fruit. Your friend loses you in the crowded market. There are two ways you can either wait for your friend to return or go where your friend may have gone. But which option is better? It depends on your friend’s options! He also has two choices, and here the game theory has a solution for two-player (you and your friend and finding each other) and multiplayer games.

The game theory seeks to simplify the complex conditions in which animals, humans, organizations, businesses, economies, and countries interact, to identify the basic game of that interaction. By identifying the existing options, those which are scarce, it then tries to predict the goals and priorities of those involved, as well as the rules and achievements of the game, and the probability of the occurrence of each of them.

Game theory can be used to better understand and analyze existing situations wherever there are limited resources, different decision options, different outcomes from different choices, and the possibility of collaboration or competition between players.

Game setting

To define the game setting, it is necessary to specify the following elements:

The number of players: the involved parties of the game, each having at least two strategies.

Strategies per player: a chain of actions that the player can take at different stages of the game.

Sequential game: which player adopt moves in each stage of the game?

Perfect information: what information can every player know about his opponent’s moves and preferences at each moment of the game?

Outputs of the game: What are the results when the game is over?

Types of Games in Game Theory

In the game theory, different types of games help in the analysis of different types of problems and are formed on the basis of the number of players involved in a game, the symmetry of the game, and cooperation among players.

The different types of games are listed below:

• Cooperative and Non-Cooperative Games: In cooperative games, through negotiations and agreements, players are convinced to adopt a particular strategy. On the contrary, in non-cooperative games, players decide on their own strategy to maximize their profit.
• Normal Form and Extensive Form Games: In Normal Form games, a matrix of game description is made to help identify the dominated strategies and Nash equilibrium. However, in extensive form games, a decision tree is made to represent events that can occur by chance.
• Simultaneous Move Games and Sequential Move Games: In simultaneous games, two players make simultaneous moves (strategies), without any prior knowledge of the other party’s move. But in sequential games, players have knowledge about the other players’ moves.
• Constant Sum, Zero Sum, and Non-Zero Sum Games: Constant Sum is when the sum of each outcome is always zero. Poker, for example, is a constant sum game. On the contrary, in the Zero Sum game, the gain or loss of each player is exactly balanced by those of the other players. However, non-zero sum games demonstrate a situation where one player’s gain or loss is independent of the other players’ gain or loss.
• Symmetric and Asymmetric Games: In symmetric games, strategies and moves adopted by all players are the same. In this game, the players’ decisions are dependent upon the strategies used, not on who is playing them. However, in asymmetric games, the players’ adopted strategies are different.

Applications of Game Theory

What impact would it have on your achievements if you were able to foresee the reaction of your competitors before taking any action? What would be the result if you do this with the help of scientific methods instead of relying on your own guesses?

The following are just a few examples of game theory applications:

• Stock trades and the investors’ reactions and decisions against stock market developments and the behaviors and decisions of other investors
• OPEC member countries’ decision to change the amount of oil extraction and sale and their compliance or non-compliance with quota arrangements
• Corporate behavior regarding product pricing in monopoly or multilateral competition markets
• Animal interaction with one another in social life (hunting or sharing achievements or supporting each other)

Generic Games

Generic Games, or Archetypal Games named by Peter Senge, are highly repetitive forms of games, and there are numerous examples of them being independently studied in detail.

In the game theory, there are many generic games that you may have heard of:

• Prisoner puzzle
• Chicken Game
• Ultimatum game (which is very much discussed in the negotiation)
• Minority Game
• Trust Game
• Public Goods Game
• Dictator Game

Game Theory and Nobel Prize

Eleven of those who have so far been awarded the Nobel Prize have been active in the field of game theory.

This is a very large and quite interesting number and points to the role played by game theory in the various sciences.

Nowadays game theory has a valuable position in the analysis of social networks and it seems that with the development of social networks, its importance is further increased.