# Robust Commitments and Partial Reputation

## TL;DR

This paper investigates how a leader in Stackelberg games can optimally shape their observable commitment to maximize payoff, proposing robust strategies that perform well under observational uncertainty.

## Contribution

It introduces observation-robust, polynomial-time algorithms for leader commitments that approximate and potentially surpass traditional Stackelberg payoffs in non-zero-sum settings.

## Key findings

- Robust commitment strategies improve leader payoff under observational uncertainty.
- Traditional mixed Stackelberg commitments are not robust to observation errors.
- Proposed methods are computationally efficient and applicable to security and economic scenarios.

## Abstract

Agents rarely act in isolation -- their behavioral history, in particular, is public to others. We seek a non-asymptotic understanding of how a leader agent should shape this history to its maximal advantage, knowing that follower agent(s) will be learning and responding to it. We study Stackelberg leader-follower games with finite observations of the leader commitment, which commonly models security games and network routing in engineering, and persuasion mechanisms in economics. First, we formally show that when the game is not zero-sum and the vanilla Stackelberg commitment is mixed, it is not robust to observational uncertainty. We propose observation-robust, polynomial-time-computable commitment constructions for leader strategies that approximate the Stackelberg payoff, and also show that these commitment rules approximate the maximum obtainable payoff (which could in general be greater than the Stackelberg payoff).