Repeated precise commitments can outperform the single-round Stackelberg optimum

Establish the existence of a sequence of leader mixed strategies (p_L^t) in an infinitely repeated Stackelberg game such that, when followers best respond each round, the leader’s long-run average payoff liminf_{T→∞} (1/T) ∑_{t=1}^T E_{a_L∼p_L^t}[u(a_L, a_F^t)] exceeds the single-round precise Stackelberg value V^*.

Background

The authors speculate that non-stationary (time-varying) precise commitments in repeated interactions could realize payoffs comparable to those achieved by ambiguous commitments in one-shot games. This conjecture formalizes that intuition by positing a sequence that strictly improves upon the single-shot Stackelberg value.

A proof or counterexample would clarify the relationship between ambiguity in one-shot games and dynamic strategies in repeated settings, and would connect robust commitment analysis to calibrated learning dynamics discussed elsewhere in the paper.