What is the relationship between a Nash equilibrium and a dominant strategy equilibrium?
A dominant strategy equilibrium is a specific type of Nash equilibrium. It occurs when all players in the game are playing their dominant strategies. Because a dominant strategy is always a best response, the intersection of all players' dominant strategies is guaranteed to be a Nash equilibrium.
Conditions
- All players must have and play a dominant strategy for it to be a dominant strategy equilibrium.
- A Nash equilibrium only requires mutual best responses, which may or may not be dominant strategies.
Reasoning, step by step
- Identify if each player has a dominant strategy.
- Check if all players are playing their dominant strategies in a specific outcome.
- If yes, that outcome is a dominant strategy equilibrium, which is also a Nash equilibrium.
- If no, check for mutual best responses to find standard Nash equilibria.
Example
In the example, UP is a dominant strategy for both Mary and Harley. The outcome (UP, UP) is a dominant strategy equilibrium, and therefore also a Nash equilibrium.
Common misconceptions
- Assuming all Nash equilibria are dominant strategy equilibria.
- Thinking that a game without dominant strategies cannot have a Nash equilibrium.
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