# In Game Theory, What Is a Dominant Strategy?

CM Bowen
CM Bowen

In game theory, a dominant strategy is a series of maneuvers or decisions that gives a player the most benefit, or “gain,” no matter what the other players do. Sometimes it’s used intentionally by a calculating player, but it’s often used more or less accidentally, with the dominance only appearing at the end of the transaction. Game theory is a mathematical and economic way of understanding transactions that involve thought and intentionality. It can be applied to traditional games and that’s where it gets its name, but most often it’s used to describe major economic, political, or financial decisions. Here, the individual actors are likened to players, and the transactions analogized to a game. There are a number of different ways to categorize strategies, and domination isn’t always the same in ever situation. Certain moves can be seen as weakly dominant or strongly dominant, for instance. A situation known as a Nash equilibrium can also be influential: in these scenarios, each player’s strategy is optimal, and as such, even if domination is available none of these strategies may be chosen or used. Identifying dominant tactics that are either available or used in a given scenario can be somewhat complex, and usually requires a firm grasp of both higher math and economics.

#### Game Theory Generally

Game theory is the branch of mathematics that analyzes strategies used in competitive situations in which the outcome of a player's actions depends on the actions of other players. In these contexts, many scenarios can be thought of as “games.” Financial transactions are some of the most common, but business decisions and even interpersonal relationships can be included. The theory usually has both mathematical and psychological components. Economists focus on things like probabilities and likely ramifications of particular moves and decisions, whereas the psychological aspect brings in things like a person’s potential response to situations of pressure, and how people typically react to perceptions and feared or wished-for outcomes. The idea of a dominant or winning strategy is mostly mathematical, but does have broader implications across many disciplines.

Regardless the setting or the game at issue, some things remain fixed. There must be at least two players in each game, for instance, and their choices can listed in a matrix that shows how each of their strategies affects the other. Dominant strategies are most often present in so-called zero-sum games, in which one player gains all only at the expense of the other. For example, if the prize for winning is a predetermined amount of money, the only way for one player to win all of it is for the other player to win none of it.

#### Different Types of Strategies

Strategies can be identified as strongly dominant or weakly dominant, depending on the difference between the most benefit that can be achieved and the least benefit — or, alternatively, no benefit at all. If the benefit of a strategy yields only marginally better results, it is considered to be weakly dominant. Depending on the game, the dominant strategy is not always easy to identify because of the various effects that other players' choices can have on different strategies.

#### Domination and its Outcomes

Put simply, when there is a dominant or winning strategy, every other strategy is dominated. This sort of strategy is one that will always earn the player a smaller payoff no matter what the other players do. It is possible for there to be dominated strategies without a single dominant strategy, however, which can make things even more complex.

#### Factoring in the Nash Equilibrium

Even when there are dominant plays available, games can often end up in a tie, with each player ending up on essentially equal footing. Such situations are covered and often predicted by the Nash Equilibrium, which happens when no player would make a different choice unless another player changed his or her strategy. When there is a Nash Equilibrium, players have no desire to change strategies because they would be worse off unless another player also changed strategies.