Game theory is a mathematical tool that helps us understand decision-making processes in situations where multiple players are involved. It is commonly used in economics, political science, and popular culture. In this article, we will discuss the basic elements of game theory that form the foundation of this field.
In game theory, the term “player” refers to any entity that can make decisions. This could be an individual person, a company, a government agency, or even a group of people.
Players are often referred to as “agents” in academic literature. Each player has their own set of actions they can take.
Actions are the decisions that players can make in the game. For example, if two companies are competing for market share, their actions might include advertising campaigns or price reductions. The set of possible actions available to each player is known as their “action set”.
Payoffs represent the outcomes that result from the players’ actions. In simple terms, payoffs can be thought of as rewards or punishments for each player depending on their choices. The payoff for each player is quantified by assigning a numerical value to each outcome.
A strategy is a plan of action that a player chooses to follow in order to achieve their desired outcome. A strategy can be thought of as a complete plan that specifies what action to take at every possible decision point in the game.
A dominant strategy is one that always leads to the best outcome for a player regardless of what other players do. In other words, it is always in the best interest of a player to choose their dominant strategy regardless of what other players do.
A Nash equilibrium occurs when no player has an incentive to change their strategy given the strategies chosen by all other players. In other words, it is a state where all players are playing their best response to what they think the others will do.
In some games, players have different levels of information about the game. This can affect their decision-making process and ultimately the outcome of the game.
In a game with complete information, all players know the rules of the game, the actions available to each player, and the payoffs associated with each outcome.
In a game with incomplete information, some players may not know certain aspects of the game. For example, in a poker game, players do not know what cards their opponents are holding. This can make decision-making more complex.
Game theory provides a framework for analyzing strategic interactions between multiple decision-makers. By understanding these basic elements of game theory – Players, Actions, Payoffs, Strategies and Information – we can better understand how individuals and organizations make decisions in various situations. Game theory has applications in various fields such as economics, political science and psychology.