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 takes those into consideration when optimizing his own strategy.

Key Takeaways

  • According to game theory, the dominant strategy is the optimal move for an individual regardless of how other players act.
  • A Nash equilibrium describes the optimal state of the game where both players make optimal moves but now consider the moves of their opponent.
  • A well-known example of where the Nash equilibrium plays out in game theory is the prisoner's dilemma.

Dominant Strategy Solution

It's possible that a dominant strategy solution is also 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.

Game theory is the science of strategy in situations that involve more than one actor. This can include actual games, military battles, business interactions, or managerial economics.

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.

John Nash's life and discovery of his equilibrium state was documented in the 2001 Hollywood film, A Beautiful Mind.

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.