Strategy (game theory)

In game theory, a move, action, or ply is any one of the options which a player can 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]

The term strategy is typically used to mean a complete algorithm for playing a game, telling a player what to do for every possible situation. A player's strategy determines the action the player will take at any stage of the game. However, the idea of a strategy is often confused or conflated with that of a move or action, because of the correspondence between moves and pure strategies in most games: for any move X, "always play move X" is an example of a valid strategy, and as a result every move can also be considered to be a strategy. Other authors treat strategies as being a different type of thing from actions, and therefore distinct.

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.

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.