Leadership Inference for Multi-Agent Interactions

TL;DR

This work addresses inferring leadership in two-agent interactive scenarios to enhance long-horizon intent and behavior prediction. It develops SILQGames, an iterative solver that linearizes nonlinear dynamic Stackelberg games into sequence of tractable problems, and SLF, an online Stackelberg leadership filter based on particle filtering. Empirical results show SILQGames converges in nonlinear settings and SLF can infer the correct leader from noisy observations in driving-like tasks, including realistic passing and merging. The approach enables principled, leadership-aware motion planning and highlights practical considerations for real-time deployment and extending to more agents.

Abstract

Effectively predicting intent and behavior requires inferring leadership in multi-agent interactions. Dynamic games provide an expressive theoretical framework for modeling these interactions. Employing this framework, we propose a novel method to infer the leader in a two-agent game by observing the agents' behavior in complex, long-horizon interactions. We make two contributions. First, we introduce an iterative algorithm that solves dynamic two-agent Stackelberg games with nonlinear dynamics and nonquadratic costs, and demonstrate that it consistently converges. Second, we propose the Stackelberg Leadership Filter (SLF), an online method for identifying the leading agent in interactive scenarios based on observations of the game interactions. We validate the leadership filter's efficacy on simulated driving scenarios to demonstrate that the SLF can draw conclusions about leadership that match right-of-way expectations.

Figures (5)

• Figure 1: Agents $\mathcal{A}_{1}$ (red) and $\mathcal{A}_{2}$ (blue) initially proceed along the same lane of a two-way road at similar speeds. While $\mathcal{A}_{2}$ is behind $\mathcal{A}_{1}$, the SLF infers that $\mathcal{A}_{1}$ is the leader. During $\mathcal{A}_{2}$'s passing maneuver, the SLF captures the leadership probability shifting to $\mathcal{A}_{2}$. The dashed line in the inset indicates the probabilities at the current time. We display the current expected measurements generated by the measurement model $h$. The blue coloring indicates that most particles in the SLF believe $\mathcal{A}_{2}$ is the leader.
• Figure 2: Each particle in the Stackelberg leadership filter has context $c_{t}^{k} = [\tilde{x}_{t}^{k}, H_{t}^{k}]^\intercal$, where continuous RV $x_{t} \in \mathbb{R}^n$ describes the state and discrete RV $H_{t} \in \{1, 2\}$ indicates the leader. 1. At $t-1$, we have a prior distribution over the filter context. For $H_{t-1}$, the prior is Bernoulli distributed. 2. The continuous state transitions according to game dynamics $f_{t-1}$. Leadership state evolves stochastically based on a two-state Markov chain. 3. We play a Stackelberg game from each particle's previous state and extract the game state at the current time $t$ as the expected measurement. 4. The algorithm uses a standard particle filter measurement update thrun2002probabilistic. Resampling eliminates unlikely particles and reweights the particle set towards those that are similar to the measurement. Finally, we marginalize over the continuous state and produce a probability of leadership.
• Figure 3: We run 100 SILQGames simulations on the non-LQ shepherd and sheep game with leader $\mathcal{A}_{2}$. The simulations converge in $1133 \pm 367$ iterations. (a) shows the number of unconverged simulations and (b) shows the solution for one instance.
• Figure 4: We run 100 SLF simulations on analytic solutions to the LQ shepherd and sheep game. (a) indicates that the SLF initially misidentifies the leader but then identifies the leader correctly as $\mathcal{A}_{1}$ before becoming uncertain due to noise. (b) and (c) are associated with a particular simulation and show the Stackelberg measurement trajectories at $t=0.54s$ and $t=2.04s$, respectively. The color of a particle's measurement trajectory indicates leading agent $H_{t-1}^{k}$, and the insets show the expected measurements for each particle, the actual measurement, and the ground truth.
• Figure 5: In this merge, $\mathcal{A}_{2}$ starts ahead in its lane and $\mathcal{A}_{1}$ yields to $\mathcal{A}_{2}$. We see a high leadership likelihood for $\mathcal{A}_{2}$, as expected because it merges first. The inset indicates the current probabilities with a vertical dashed line.