Equilibrium Point

An equilibrium point in Game Theory is a set of strategies $\{\hat x_1, \dots, \hat x_n\}$ such that the $i$th payoff function $K_i({\bf x})$ is larger or equal for any other $i$th strategy, i.e.,

$$K_i(\hat x_1, \ldots, \hat x_n)\geq K_i(\hat x_1, \ldots, \hat x_{i-1}, x_i, \hat x_{i+1}, \ldots, \hat x_n).$$

See Nash Equilibrium