\begin{definition}[Definition:Best-Response Function]
Let a strategic game $G$ be modelled by:
:$G = \left\langle{N, \left\langle{A_i}\right\rangle, \left\langle{\succsim_i}\right\rangle}\right\rangle$
Let $a^*$ be a Nash equilibrium of $G$:
:$\forall i \in N: \forall a_i \in A_i: \left({a^*_{-i}, a^*_i}\right) \succsim_i \left({a^*_{-i}, a_i}\right)$
For any $a_{-1} \in A_{-i}$, let $B_i \left({a_{-i} }\right)$ be the set of player $i$'s best moves, defined as:
:$B_i \left({a_{-i} }\right) = \left\{ {a_i \in A_i: \forall a'_i \in A_i: \left({a_{-i}, a_i}\right) \precsim_i  \left({a_{-i}, a'_i}\right)}\right\}$
Then $B_{-i}$ is known as the '''best-response function''' of player $i$.
\end{definition}