  We study Stackelberg equilibria in finitely repeated games, where the leader
commits to a strategy that picks actions in each round and can be adaptive to
the history of play (i.e. they commit to an algorithm). In particular, we study
static repeated games with no discounting. We give efficient algorithms for
finding approximate Stackelberg equilibria in this setting, along with rates of
convergence depending on the time horizon $T$. In many cases, these algorithms
allow the leader to do much better on average than they can in the single-round
Stackelberg. We give two algorithms, one computing strategies with an optimal
$\frac{1}{T}$ rate at the expense of an exponential dependence on the number of
actions, and another (randomized) approach computing strategies with no
dependence on the number of actions but a worse dependence on $T$ of
$\frac{1}{T^{0.25}}$. Both algorithms build upon a linear program to produce
simple automata leader strategies and induce corresponding automata
best-responses for the follower. We complement these results by showing that
approximating the Stackelberg value in three-player finite-horizon repeated
games is a computationally hard problem via a reduction from balanced vertex
cover.
