Strategy (game theory)

In game theory, a player's strategy is any of the options which they choose in a setting where the optimal outcome depends not only on their own actions but on the actions of others.^[1] The discipline mainly concerns the action of a player in a game affecting the behavior or actions of other players. Some examples of "games" include chess, bridge, poker, monopoly, diplomacy or battleship.^[2] A player's strategy will determine the action which the player will take at any stage of the game. In studying game theory, economists enlist a more rational lens in analyzing decisions rather than the psychological or sociological perspectives taken when analyzing relationships between decisions of two or more parties in different disciplines.

The strategy concept is sometimes (wrongly) confused with that of a move. A move is an action taken by a player at some point during the play of a game (e.g., in chess, moving white's Bishop a2 to b3). A strategy on the other hand is a complete algorithm for playing the game, telling a player what to do for every possible situation throughout the game. It is helpful to think about a "strategy" as a list of directions, and a "move" as a single turn on the list of directions itself. This strategy is based on the payoff or outcome of each action. The goal of each agent is to consider their payoff based on a competitors action. For example, competitor A can assume competitor B enters the market. From there, Competitor A compares the payoffs they receive by entering and not entering. The next step is to assume Competitor B does not enter and then consider which payoff is better based on if Competitor A chooses to enter or not enter. This technique can identify dominant strategies where a player can identify an action that they can take no matter what the competitor does to try to maximize the payoff. This also helps players to identify Nash equilibrium which are discussed in more detail below.

A strategy profile (sometimes called a strategy combination) is a set of strategies for all players which fully specifies all actions in a game. A strategy profile must include one and only one strategy for every player.