Core Concepts
The key idea is to efficiently compute the socially optimal order of play and its associated Stackelberg equilibrium for multi-agent trajectory games, where the order of play crucially affects the overall system performance.
Abstract
The paper presents a novel algorithm called Branch and Play (B&P) to efficiently compute the socially optimal order of play and its associated Stackelberg equilibrium for N-player trajectory games.
Key highlights:
- B&P is an iterative branch-and-bound method that implicitly explores the search space of all possible orders of play to avoid the costly enumeration.
- As a subroutine, B&P employs and extends sequential trajectory planning (STP), a popular multi-agent control approach, to scalably compute valid local Stackelberg equilibria for any given order of play.
- The authors prove that STP yields a local Stackelberg equilibrium in a single pass for games with aligned interaction preferences (e.g., collision avoidance).
- B&P is deployed in simulated air traffic control, quadrotor swarm formation, and hardware experiments for delivery vehicle fleet coordination, outperforming baseline approaches.
The paper provides a principled game-theoretic framework to optimize the order of play, a key factor influencing the overall system performance in multi-agent coordination tasks.
Stats
The system dynamics are governed by the nonlinear equation xt+1 = ft(xt, ut).
The individual cost for each player i is gi
t(xt, ui
t) = ¯
gi
t(xi
t, ui
t) + ℓi
t(xt), where ¯
gi
t(xi
t, ui
t) is the individual cost and ℓi
t(xt) is the interactive safety cost.
The social cost is J(γ) := P
i∈I Ji(γ), where Ji(γ) = PT
k=0 gi
k(xk, ui
k).
Quotes
"The key challenge for the regulator is determining an optimal order of play that is socially optimal, i.e., that maximizes the sum of the agents' utilities."
"Unlike the existing approaches, we do not assume that the order of play is given."