Robust commitments and partial reputation

How should agents shape a finite “reputational" history to their advantage knowing that others will be learning from that history? We focus on one leader interacting with multiple followers and show that in most non-zero-sum games, the traditional Stackelberg mixed commitment is very fragile to observational uncertainty. We propose robust commitment rules that anticipate being learned and show that these approximately preserve Stackelberg-level performance. Further, we show that any leader advantage over and above Stackelberg is only realized in a small-sample regime relative to the effective dimension of the game. Thus we can approximate the optimal payoff in the non-asymptotic regime where learnability matters. We corroborate our theory with illustrative examples and extensive simulations on random ensembles of security games.