# When Should a Leader Act Suboptimally? The Role of Inferability in Repeated Stackelberg Games

arXiv: https://arxiv.org/abs/2310.00468 · HTML: https://mlsanity.com/paper/2310.00468/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 43 references that are in the map.
- First posted on arXiv 30 Sep 2023.

## Builds on (most cited first, 10 of 10)

- [CARLA: An Open Urban Driving Simulator](https://mlsanity.com/paper/1711.03938/) (2017)
- [On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning](https://mlsanity.com/paper/1704.00805/) (2017)
- [Maximum-Entropy Multi-Agent Dynamic Games: Forward and Inverse Solutions](https://mlsanity.com/paper/2110.01027/) (2021)
- [On Stackelberg Mixed Strategies](https://mlsanity.com/paper/1705.07476/) (2017)
- [Stochastic Conditional Gradient++](https://mlsanity.com/paper/1902.06992/) (2019)
- [Least Inferable Policies for Markov Decision Processes](https://mlsanity.com/paper/1809.06482/) (2018)
- [On the Sample Complexity of Vanilla Model-Based Offline Reinforcement Learning with Dependent Samples](https://mlsanity.com/paper/2303.04268/) (2023)
- [Ensuring Privacy with Constrained Additive Noise by Minimizing Fisher Information](https://mlsanity.com/paper/1808.09565/) (2018)
- [Robust Commitments and Partial Reputation](https://mlsanity.com/paper/1905.11555/) (2019)
- [Liability Design for Autonomous Vehicles and Human-Driven Vehicles: A Hierarchical Game-Theoretic Approach](https://mlsanity.com/paper/1911.02405/) (2019)

## Abstract (arXiv)

When interacting with other decision-making agents in non-adversarial scenarios, it is critical for an autonomous agent to have inferable behavior: The agent's actions must convey their intention and strategy. We model the inferability problem using Stackelberg games with observations where a leader and a follower repeatedly interact. During the interactions, the leader uses a fixed mixed strategy. The follower does not know the leader's strategy and dynamically reacts to the statistically inferred strategy based on the leader's previous actions. In the inference setting, the leader may have a lower performance compared to the setting where the follower has full information on the leader's strategy. We refer to the performance gap between these settings as the inferability gap. For a variety of game settings, we show that the inferability gap is upper-bounded by a function of the number of interactions and the stochasticity level of the leader's strategy, encouraging the use of inferable strategies with lower stochasticity levels. We also analyze bimatrix Stackelberg games and identify a set of games where the leader's near-optimal strategy may potentially suffer from a large inferability gap.