Game theory is a branch of mathematics that deals with the study of decision-making in strategic situations, where the outcome of an individual’s choice depends on the choices made by others. It is widely used in various fields such as economics, political science, psychology, and biology. In this article, we will explore the different factors that make up game theory.
The first factor in game theory is the players involved. Players can be individuals or groups that make decisions based on their own interests. The number of players can range from two to many, and each player has a set of possible choices or strategies.
A strategy is a plan of action that a player can take in a given situation. A player’s strategy depends on what they believe other players will do. In game theory, there are two types of strategies – pure and mixed.
A pure strategy is when a player chooses one specific action regardless of what others do. For example, in a game of rock-paper-scissors, if a player always chooses rock as their move, it is considered a pure strategy.
On the other hand, a mixed strategy involves choosing multiple actions with certain probabilities. For example, if there are two possible moves – A and B – and a player chooses A 60% of the time and B 40% of the time based on what they think other players will do.
The payoff in game theory refers to what each player gains or loses depending on the outcome of the game. It can be represented as numerical values assigned to each possible outcome.
For example, consider a simple game where two players have two possible strategies each – cooperate (C) or defect (D). If both cooperate, they both receive 3 points each (CC).
If one cooperates while the other defects (CD), then the defector gets 5 points and the cooperator gets 1 point. If both defect, then they both receive 2 points each (DD). The numerical values assigned to these outcomes are the payoffs.
In game theory, information refers to what each player knows about the other players’ strategies and payoffs. There are two types of information – complete and incomplete.
Complete information means that all players know all the possible strategies and payoffs of the game. On the other hand, incomplete information means that some players do not know certain aspects of the game.
Equilibrium is a state where no player can improve their outcome by changing their strategy, given what they know about other players’ strategies. In game theory, there are different types of equilibria such as Nash equilibrium and dominant strategy equilibrium.
Nash equilibrium is a state where no player can improve their outcome by changing their strategy, assuming that all other players stick to their current strategies. Dominant strategy equilibrium is a state where one strategy dominates over all others for a player, regardless of what other players do.
Game theory has many practical applications in various fields such as economics, political science, psychology, and biology. Understanding its different factors such as players, strategies, payoffs, information, and equilibrium can help us make better decisions in strategic situations. By using these elements effectively in our analysis of games we can make better decisions based on logic rather than chance or impulse.