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arXiv · 2402.09246

Who Plays First? Optimizing the Order of Play in Stackelberg Games with Many Robots

Haimin Hu·Gabriele Dragotto·Zixu Zhang·Kaiqu Liang·Bartolomeo Stellato·Jaime F. Fisac
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Abstract

We consider the multi-agent spatial navigation problem of computing the socially optimal order of play, i.e., the sequence in which the agents commit to their decisions, and its associated equilibrium in an N-player Stackelberg trajectory game. We model this problem as a mixed-integer optimization problem over the space of all possible Stackelberg games associated with the order of play's permutations. To solve the problem, we introduce Branch and Play (B&P), an efficient and exact algorithm that provably converges to a socially optimal order of play and its Stackelberg equilibrium. As a subroutine for B&P, we employ and extend sequential trajectory planning, i.e., a popular multi-agent control approach, to scalably compute valid local Stackelberg equilibria for any given order of play. We demonstrate the practical utility of B&P to coordinate air traffic control, swarm formation, and delivery vehicle fleets. We find that B&P consistently outperforms various baselines, and computes the socially optimal equilibrium.

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Haimin Hu, Gabriele Dragotto, Zixu Zhang, Kaiqu Liang, Bartolomeo Stellato, Jaime F. Fisac. 2024-06-25. Who Plays First? Optimizing the Order of Play in Stackelberg Games with Many Robots. https://arxiv.org/abs/2402.09246

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