Game theory is a fascinating and complex subject that has a wide range of applications in various fields like economics, political science, psychology, and sociology. It is a mathematical framework that helps us understand how individuals or groups make decisions and interact with each other in various scenarios.
Game theory involves three essential components – players, strategies, and payoffs. In this article, we will explore these three parts of game theory in detail.
In game theory, players are the individuals or groups who participate in the game. These players may have different characteristics like preferences, beliefs, information sets, etc.
For example, in an economic game like the Prisoner’s Dilemma, there are two players – the criminal suspects who have been arrested by the police. Each player has to decide whether to cooperate with the other player or betray them to get a reduced sentence.
Strategies refer to the actions that players can take in a game. These actions are based on the player’s preferences and beliefs about what other players might do.
A player’s strategy can be either pure or mixed. A pure strategy is a specific action that a player takes with certainty whereas a mixed strategy is when a player chooses an action randomly based on probabilities.
For example, in rock-paper-scissors game, there are only three pure strategies available – rock, paper or scissors. However, if both players play randomly at 1/3 chance for each strategy then it becomes a mixed strategy.
Payoffs refer to the rewards or losses that each player receives after playing their respective strategies. The payoff matrix displays all possible outcomes of the game based on each player’s strategy choice and specifies how much each player gains or loses from each outcome.
For example: consider two companies competing for market share; if both companies lower their prices then both lose profits but if one lowers the price and the other doesn’t then the former gains market share and higher profits while the latter loses out.
In summary, game theory is comprised of three essential components – players, strategies, and payoffs. These components help us understand how individuals or groups make decisions in various settings. By studying game theory, we can gain insights into how people behave in strategic interactions and make more informed decisions in real-world scenarios.