Game theory book by Tirole,Fudenberg, zero up to first order of $\epsilon$,equilibrium

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In this book on Game Theory, on page 186,I do not understand the very end of the page:

[T]he incentive to deviate$-$the left hand side of equation 5.18$-$ is $0$ in first order of $\epsilon$, so that preventing deviations require only a probability of punishment that is $0$ to first order as well.

Can someone clarify to me what is meant technically by these two sentences separately, and also why it is the case that they hold?