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We study the problem of efficiently computing optimal strategies inasymmetric leader-follower games repeated a finite number of times, whichpresents a different set of technical challenges than the infinite-horizonsetting. More precisely, we give efficient algorithms for finding approximateStackelberg equilibria in finite-horizon repeated two-player games, along withrates of convergence depending on the horizon $T$. We give two algorithms, onecomputing strategies with an optimal $\frac{1}{T}$ rate at the expense of anexponential dependence on the number of actions, and another (randomized)approach computing strategies with no dependence on the number of actions but aworse dependence on $T$ of $\frac{1}{T^{0.25}}$. Both algorithms build upon alinear program to produce simple automata leader strategies and inducecorresponding automata best-responses for the follower. We complement theseresults by showing that approximating the Stackelberg value in three-playerfinite-horizon repeated games is a computationally hard problem via a reductionfrom the balanced vertex cover problem.

Efficient Stackelberg Strategies for Finitely Repeated Games