Scalable Mechanism Design for Multi-Agent Path Finding

TL;DR

This work addresses the challenge of allocating collision-free paths in MAPF when agents are self-interested and may misreport their preferences. By leveraging the maximal-in-range (MIR) property and VCG-based payments, the authors design three mechanisms—PCBS, EPBS, and MCPP—that achieve strategyproofness and individual rationality while varying in scalability. PCBS solves the exact welfare-maximizing MAPF allocation via CBS but is computationally heavy; EPBS makes MIR feasible with an exhaustive PBS-based range; MCPP further scales by sampling priority orderings to approximate the optimum. Experiments across large MAPF benchmarks demonstrate that MIR-enabled mechanisms can substantially improve welfare over baselines and scale to thousands of agents, with payments typically nonnegative and often zero. Collectively, the work bridges mechanism design and MAPF, offering practical, scalable, strategyproof allocations for complex multi-agent routing problems.

Abstract

Multi-Agent Path Finding (MAPF) involves determining paths for multiple agents to travel simultaneously and collision-free through a shared area toward given goal locations. This problem is computationally complex, especially when dealing with large numbers of agents, as is common in realistic applications like autonomous vehicle coordination. Finding an optimal solution is often computationally infeasible, making the use of approximate, suboptimal algorithms essential. Adding to the complexity, agents might act in a self-interested and strategic way, possibly misrepresenting their goals to the MAPF algorithm if it benefits them. Although the field of mechanism design offers tools to align incentives, using these tools without careful consideration can fail when only having access to approximately optimal outcomes. In this work, we introduce the problem of scalable mechanism design for MAPF and propose three strategyproof mechanisms, two of which even use approximate MAPF algorithms. We test our mechanisms on realistic MAPF domains with problem sizes ranging from dozens to hundreds of agents. We find that they improve welfare beyond a simple baseline.

Figures (5)

• Figure 1: Success rate, runtime, and ratio-to-baseline of social welfare (SW) of Monte Carlo PP with $m \in \{10, 50, 100\}$ samples.
• Figure 2: Success rate, runtime, and ratio-to-baseline of social welfare (SW) for PCBS, EPBS, MCPP and FCFS (the baseline). Solid lines indicate the average value over 100 instances, while the shaded area is the 95% confidence interval. Maximum agent numbers are 3000 for random-32-32-20, 1000 for den312d and 1500 for Paris_1_256 and den520d. Agent numbers between 5 and 40 are shown in higher granularity than between 40 and the maximum to illustrate scaling differences.
• Figure 3: Size of payments for the MCPP mechanism, on the random-32-32-20 map at $n=1810$ agents. Frequency in the y-axis is scaled logarithmically.
• Figure 4: Success rate, runtime, and ratio-to-baseline of social welfare for PCBS, EPBS, MCPP and FCFS (the baseline) in 3D versions of our benchmark maps. Solid lines indicate the average value over 100 instances, while the shaded area is the 95% confidence interval. If a mechanism fails to achieve a 100% success rate, we do not plot their welfare for that number of agents.
• Figure 5: Social welfare suboptimality in random-32-32-20 map with MCPP, at 1800 agents. All runs use a standard log-normal value distribution. We vary their cost distributions from uniform ones to differently scaled log-normal ones.

Theorems & Definitions (19)

• Definition 1
• Definition 2
• Lemma 1
• Lemma 2
• Proposition 1
• proof
• Corollary 1
• Proposition 2
• proof
• Corollary 2