Epsilon Equilibrium

For $\epsilon\ge 0$, a profile $s\in S$ is an $\epsilon$-equilibrium if every player is within $\epsilon$ of a best response: $$ g_i(t_i,s_{-i})\le g_i(s)+\epsilon \quad\text{for all } i\in I,\ t_i\in S_i. $$ A Nash equilibrium is the special case $\epsilon=0$.

References

• [MFoGT, Def. 4.5.2] Laraki, Renault, and Sorin, Mathematical Foundations of Game Theory. epsilon-equilibrium in a strategic game.