In game theory, dominance occurs when one strategy is better or worse than another regardless of the strategies of a player's opponents. Many simple games can be solved using dominance. Game theory is a branch of applied mathematics that uses models to study interactions with formalised incentive structures (games). It has applications in a variety of fields, including economics, international relations, evolutionary biology, political science, and military strategy. ... A strategy in game theory is a sequence of activities and reactions, that fully determine an agents bahaviour in a game or a business situation. ...

For two strategies A and B, A strictly dominates B if it results in a better outcome regardless of the actions of a player's opponents. A weakly dominates B if there are one or more opponent's actions for which A and B are equivalent in payoff, and at least one in which A is superior.

Dominant strategies

A dominant strategy is optimal regardless of what opponents do. Such a strategy is strictly dominant if it strictly dominates every other strategy. It is weakly dominant if it dominates all other strategies, but some are only weakly dominated.

If a strictly dominant strategy exists in a game, that strategy must be played in each of the game's Nash equilibria. Even if both player's have a dominant strategy, the resulting Nash equilibrium is not necessarilly Pareto optimal, meaning that there may non-equilibrium outcomes of the game that would be better for both players. The classic game used to illustrate this is the Prisoner's Dilemma. In game theory, the Nash equilibrium (named after John Nash) is a kind of optimal strategy for games involving two or more players, where no player has anything to gain by changing only ones own strategy. ... Pareto efficiency, or Pareto optimality, is a central concept in economics with broad applications in game theory, engineering and the social sciences. ... Will the two prisoners cooperate to minimise total loss of liberty or will one of them, trusting the other to cooperate, betray him so as to go free? The prisoners dilemma is a type of non-zero-sum game (game in the sense of Game Theory). ...

Dominated strategies

A strategy is called strictly dominated if a strategy exists that strictly dominates it, and weakly dominated if a strategy exists that weakly dominates it. Strictly dominated strategies cannot be a part of a Nash equilibrium, and as such it is irrational for any player to play them. On the other hand weakly dominated strategies my be part of Nash equilibria. For instance consider the following game:

Strategy C weakly dominates strategy D, but nonetheless, (D, D) is a Nash equilibrium.

One common technique for solving games involves iteratively removing dominated strategies. In the first step, all dominated strategies of the game are removed, since rational players will not play them. This results in a new, smaller game. Some strategies that were not dominated before may have become dominated in the smaller game. These are removed, creating a new even smaller game, and so on. Iteration is the repetition of a process, typically within a computer program. ...

There are two versions of this process. The first involves only eliminating strictly dominated strategies. If, after completing this process, there is only one strategy for each player remaining, that strategy set is the unique Nash equilibrium. The second process involves eliminating both strictly and weakly dominated strategies. If, at the end of the process, there is a single strategy for each player, this is also a Nash equilibrium. However, unlike the first process, Nash equilibria may have been eliminated. As a result we cannot conclude that it is the unique Nash equilibrium.