# Differences between best response, dominant strategy and Nash equilibrium

I can't seem to get the differences of these terms.

I watched this video that has the differences of best response and Nash equilibrium: But then I heard about dominant strategies from another video and searched for differences to land at this quiz question:

Is a​ player's best response in a game the same as his dominant​ strategy? Not necessarily. If a player has a dominant​ strategy, then it is his best​ response; however, every best response is not always a dominant strategy.

Is there a table form that shows the differences of these 3 based on a specific player and what other players would do?

Consider the following game between P1 (row player) and P2 (column player):

$$\begin{array}{|c|c|c|}\hline & L & R \\\hline T& 1,1 & 2,0 \\\hline B& 0,0 & 1,1 \\\hline \end{array}$$

• $$T$$ is P1's dominant strategy
• $$T$$ is P1's best response to both of P2's strategies $$L$$ and $$R$$
• $$L$$ is P2's best response to P1's strategy $$T$$
• $$R$$ is P2's best response to P1's strategy $$B$$
• $$(T,L)$$ is the only Nash equilibrium

Generalizing from the above observations:

1. A strategy is dominant if and only if it is a best response to each of the other player's strategies, e.g. P1's $$T$$.
2. A strategy that is a best response to some but not all of the other player's strategies cannot be a dominant strategy, e.g. P2's $$L$$ and $$R$$.
3. A Nash equilibrium is a pair of mutually best responding strategies, e.g. $$(T,L)$$.