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

When interacting with other decision-making agents in nonadversarial scenarios, it is critical for an autonomous agent to have inferable behavior. The agent's actions must convey its 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 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, which encourages the use of inferable strategies with lower stochasticity levels. We also analyze bimatrix Stackelberg games and identify a set of games in which the leader's near-optimal strategy may potentially suffer from a large inferability gap.