What if we told you there is a way to predict how other people will behave? Imagine owning a company that makes electronic devices and deciding whether or not to increase production. The benefit you get from increasing the output also depends on what your main competitor is doing. If you increase the production while the other company doesn't, you make 5 billion dollars. If you increase the production simultaneously, you earn 2 billion dollars. What is your dominant strategy in such a case? How about your competitor?
The dominant strategy is a strategy that provides the highest outcomes when compared to other strategies. A dominant strategy allows you to predict your competitor's moves and decide accordingly.
Knowing dominant strategy and how players decide will help you win in any game, and not only the ones you play with your friends. Read on and become the smartest in the room who knows everybody else move because you read our explanation on dominant strategies.
Dominant Strategy Definition
Before diving into the dominant strategy definition, let's consider a strategy.
A strategy refers to a general plan outlining the specific actions one needs to take to achieve a particular goal.
Now an example to demonstrate an economic strategy.
For instance, a person could plan to pay off the house loan they have taken out. They may decide to increase the hours they work and thus the money they make. Or they might choose to reduce the amount they spend in other aspects of their life, which would free up more income that might be put into the principal of the loan.
In game theory, a strategy refers to a rule or a plan of action when playing a certain game.
A dominant strategy is one of the strategies that maximize the player's payoffs which makes it the dominant strategy. As the name suggests, this strategy dominates the other strategies regarding the gains it provides to the player.
The dominant strategy is a strategy that provides optimal outcomes for the player regardless of what the other player does.
When an individual has a dominant strategy, it means that there are also other strategies that the individual could choose from.
Let's consider that a player can choose between strategy A and strategy B. Well, look specifically at two different scenarios and where the quality of strategy A is being considered.
In a separate scenario consider that:
Interested in learning more about game strategy? Consider reading this explanation on Game Theory.
Dominant Strategy Payoff Matrix
The dominant strategy payoff matrix is a matrix that shows the outcome of each strategy for each player.
The payoff is the value that is associated with each possible outcome.
Fig. 1 - Payoff matrix of two companies choosing whether to advertise or not
Figure 1 shows two companies that are choosing whether to advertise or not and their respective outcomes.
The right-hand number provides the outcome for Company 1, and the left-hand number provides the outcome for Company 2.
The following is how to read the payoff matrix for both companies.
For Company 1, the payoffs are:
If Company 1 decides to advertise while Company 2 decides to advertise, Company 1 makes a revenue of $6 billion in a year.
If company 1 decides to advertise while company 2 decides not to, Company 1 makes a revenue of $8 billion a year.
If Company 1 doesn't advertise and Company 2 advertises, Company 1 makes $4 billion in revenue.
If Company 1 doesn't advertise and Company 2 doesn't advertise, Company 1 makes 7 billion a year.
For Company 2, the payoffs of each strategy are as follows.
If Company 2 decides to advertise and Company 1 decides to advertise too, Company 2 makes $4 billion in revenue.
If Company 2 chooses to advertise and Company 1 doesn't, Company 2 earns $6 billion.
If Company 2 decides not to advertise when Company 1 advertises, Company 2 makes $1 billion.
If Company 2 decides not to advertise and Company 1 doesn't advertise as well, Company 2 makes 3 billion.
Dominant Strategy Example
As a dominant strategy example, let's consider two companies competing and have to decide whether to advertise or not.
Fig. 2 - Dominant strategy example
The payoff matrix in Figure 2 shows the outcomes we've just mentioned for each company.
The right-hand number provides the outcome for Company 1, and the left-hand number provides the outcome for Company 2.
Now, what is the dominant strategy for Company 1?
Notice that Company 1 makes the highest revenue when it advertises, regardless of whether or not Company 2 advertises. When it advertises, it makes 6 billion if company 2 advertises as well and makes 8 billion if company 2 does not advertise.
On the other hand, company 1 makes only 4 billion if it doesn't advertise when Company 2 does and makes only 7 billion when Company 2 doesn't advertise too.
Hence, advertising for Company 1 strictly dominates the other option not advertising, no matter what Company 2 does.
For Company 2, advertising also strictly dominates not advertising. When Company 2 advertises, it makes 4 billion if it advertises at the same time as Company 1 does, and 6 billion if Company 1 doesn't.
On the other hand, it makes only 1 billion if it chooses not to advertise while Company 1 does, and it makes only 3 billion if both don't advertise. Hence, advertising provides a better outcome for Company 2 as well.
When both players have a dominant strategy, it is known as equilibrium in the dominant strategy.
Equilibrium in dominant strategy is the outcome of a game where all players achieve their best outcome regardless of what their competitors are doing.
The outcome of a game in which each firm is doing the best it can, regardless of what its competitors are doing. There are also cases when equilibrium in the dominant strategy doesn't occur. In other words, not both players have dominant strategies.
Weakly Dominant Strategy
A weakly dominant strategy is a strategy that never provides a lower payoff than the other strategy, and at the same time, there exists at least one combination of strategies for which the payoffs for both strategies are equal.
For example, strategy 1 weakly dominates strategy 2 if strategy 1 has no outcome, which is lower than strategy 2. Additionally, there exist at least one combination of strategies for which the payoffs are equal.
Fig. 3 - Weakly dominant strategy
Figure 3 shows the payoff matrix of two companies choosing whether to advertise; however, in this case, there is no dominant strategy for company 2. In other words, Company 2 does not have a strategy with all outcomes greater than the other strategy's outcomes.
When Company 1 doesn't advertise, Company 2 makes the same revenue whether it advertises or not. Company 2 has a weakly dominant strategy, which is advertising. That's because it has a combination of movement, which is greater than not advertising. When company 1 advertises, company 2 is better off advertising.
So what Company 2 does in such a case looks at whether Company 1 has a dominant strategy. Company 1 has a dominant strategy which is to advertise, as advertising's outcomes are higher than not advertising.
In such a case, Company 2 will know that Company 1 chooses to advertise; hence it will have to choose between advertising or not advertising. Advertising, in this case, provides a better outcome; hence Company 2 will choose to advertise as well.
Dominant Strategy Prisoner's Dilemma
Dominant strategy in the prisoner's dilemma helps us understand how a player chooses to stick to one strategy regardless of what the other player does. That's because the dominant strategy is the strategy that provides the individual with the highest outcome.
A prisoner dilemma occurs when two individuals are caught committing a crime.
Let's assume that two best friends, Mike and John, owned a business, and after some time, the business went bankrupt. Not having any other source of income, the two best friends decide to rob a bank.
Shortly after having robbed the bank, the two best friends are caught by the police. They are brought to the station and placed in two separate rooms.
They are given the following options.
- If one of them confesses, the one that confesses gets 1 year in prison while the other that remains silent gets to prison for 10 years.
- If both of them confess, they will have to spend 5 years in prison.
- If none confess, they will have to spend 3 years in prison.
Fig. 4 - Dominant strategy Prisoner's Dilemma
Figure 4 shows the payoff matrix for both Mike and John. Notice that confessing is a strategy, and not confessing is another strategy. That is, they are two different strategies that the player can play.
So think about what is Mike's best choice, to confess or to remain silent.
If John remains silent, Mike's best strategy is to confess since he gets 1 year instead of 5 for both confessings.
If John confesses, Mike's best strategy is still to confess since he gets 5 years in prison instead of 10 for not admitting.
So Mike's dominant strategy in such a case is to confess.
John has the same outcome as Mike and decides to confess.
Both of them decide to confess, and this is known as Nash Equilibrium.
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