Comparing a Dominant Strategy Solution vs. Nash Equilibrium Solution

Dominant Strategy Solution vs. Nash Equilibrium Solution: An Overview

Game theory is the science of strategic decision-making in situations that involve more than one actor. These can include actual games or real-life situations like military battles, business interactions, or managerial decisions. According to game theory, the best strategy for an individual may or may not be the same depending on the stakes of the game and given the likely move of the other player involved.

Sometimes, the best strategy will be the same no matter how other players act. This is known as the dominant strategy. On the other hand, there exists the so-called Nash equilibrium, which does not describe a particular strategy per se, but rather a sort of mutual understanding—each player understands the other player's optimal strategies and considers those when optimizing their own strategy.

Dominant Strategy Solution

A dominant strategy solution may also be in Nash equilibrium, although the underlying principles of a dominant strategy render Nash analysis somewhat superfluous. In other words, the cost and benefit incentives don't change based on other actors.

In the dominant strategy, each player's best strategy is unaffected by the actions of other players. This renders the critical assumption of the Nash equilibrium—that each actor knows the optimal strategy of the other players—possible but almost pointless.

Nash Equilibrium Solution

The Nash equilibrium is named after John Forbes Nash, Jr., who authored a one-page article in 1950 (and a longer follow-up in 1951) describing a stable-state equilibrium in a multi-person situation where no participant gains by a change in his strategy as long as the other participants also remain unchanged.

In other words, a Nash equilibrium takes place when each player remains in the same position as long as no other player would take a different action. Each player would be worse off and, therefore, chooses not to move.

The most famous example of Nash equilibrium is the prisoner's dilemma. In the prisoner's dilemma, two criminals are captured and interrogated separately. Even though each would be best off by not cooperating with police, each expects the other criminal to confess and reach a plea deal. Thus, there is a conflict between group rationality and individual rationality, and each criminal is likely to rat out the other.

This example has caused some confusion about the Nash equilibrium. The theory is not used exclusively for situations where there is a defecting party; the Nash equilibrium can exist where all members of a group cooperate or where none do. In fact, many games can have multiple Nash equilibria.

Nash Equilibrium vs Dominant Strategy FAQs 

Is the Dominant Strategy the Same As the Nash Equilibrium?

With dominant strategy, each player is unaware of the other's optimal strategy. Each player chooses the best strategy among all options. Nash equilibrium occurs when each player knows the strategy of their opponent and uses that knowledge to form their own strategy. The dominant strategy may be the Nash equilibrium, however.

Why Is an Equilibrium Stable in Dominant Strategies?

The dominant strategy is the best strategy chosen by players. When both parties have dominant strategies, equilibrium is stable as neither party has a motive to change.

How Do You Find the Dominant Strategy and Nash Equilibrium?

Nash equilibrium takes place when players don't change their positions, knowing that a change in positions would create a worse outcome. Dominant strategy occurs when each player chooses the best strategy, independent of the opponent's move.

What Is the Solution in Dominant Strategies?

The solution in dominant strategies is when both players have chosen the best strategy and those choices are unaffected or not influenced by the choice of the opposing party.