Strategyproof methods improve pathway building between blocked regions
Strategyproof Mechanisms for Connecting Impassable Regions
Computer Science and Game Theory
Summary
This paper looks at how to build a route connecting two separated areas when there's an obstacle between them, with agents whose exact positions are private information. The challenge is to design systems that encourage truthful reporting of locations while keeping travel costs low, either for the worst-off agent or for everyone combined. The authors find best possible trade-offs for deterministic methods and also explore randomized approaches with guaranteed performance. They further improve known results from earlier research in this area.
What this means in practice
- •For network planners: Help design truthful incentive schemes for connecting network regions separated by failures or obstacles with predictable cost guarantees.
- •For logistics coordinators: Improve routing strategies to fairly allocate costs when connecting separated delivery zones considering unknown agent locations.
Authors
Hau Chan, Jianan Lin, Chenhao Wang
Abstract
We study strategyproof mechanisms for building a pathway between two regions of a line segment separated by an obstacle. Each of the $n$ agents has a private location within its region and may use either its original route to a facility or the new pathway, whose traversal cost is a fraction $k\in[0,1)$ of its length. We seek strategyproof (SP) and group-strategyproof (GSP) mechanisms that approximately minimize maximum cost or social cost. After characterizing optimal pathways for both objectives, we establish a tight deterministic maximum-cost approximation ratio of $\frac{2}{1+k}$ and a deterministic social-cost upper bound of $\frac{n}{1+k(n-1)}$, together with complementary lower bounds. Both upper bounds are achieved by GSP mechanisms. We then study randomized mechanisms under strategyproofness in expectation. A power-proportional mechanism achieves a social-cost approximation ratio at most $5$, independent of $n$ and $k$, with a tight guarantee of $3$ for this mechanism when $k=0$. We prove randomized lower bounds of $\frac{3+2k}{2+3k}$ for maximum cost and $\max\big\{1,\frac{285}{263+385k}\big\}$ for social cost, the latter for $n\ge7$. Finally, we improve several bounds for the real-line pathway model of [Chan and Wang, AAMAS 2023]. Our deterministic maximum-cost lower bound of $2$ matches the upper bound obtainable from [Qin, Fang, and Liu, COCOA 2024]. We strengthen the deterministic social-cost lower bound from $\frac32$ to $2$ under SP and to $\max\{2,n-1\}$ under GSP. For randomized social cost, we sharpen the guarantee of Chan and Wang's proportional mechanism from $6$ to $3$ and raise their lower bound from $1.02$ to $\frac{285}{263}\approx1.08365$ for $n\ge7$.