Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2305.00818

On-demand Mobility-as-a-Service platform assignment games with guaranteed stable outcomes

Bingqing Liu·Joseph Y. J. Chow
View original source ↗Read source document ↗Export metadata ↓

Abstract

Mobility-as-a-Service (MaaS) systems are two-sided markets, with two mutually exclusive sets of agents, i.e., travelers/users and operators, forming a mobility ecosystem in which multiple operators compete or cooperate to serve customers under a governing platform provider. This study proposes a MaaS platform equilibrium model based on many-to-many assignment games incorporating both fixed-route transit services and mobility-on-demand (MOD) services. The matching problem is formulated as a convex multicommodity flow network design problem under congestion that captures the cost of accessing MOD services. The local stability conditions reflect a generalization of Wardrop's principles that include operators' decisions. Due to the presence of congestion, the problem may result in non-stable designs, and a subsidy mechanism from the platform is proposed to guarantee local stability. A new exact solution algorithm to the matching problem is proposed based on a branch and bound framework with a Frank-Wolfe algorithm integrated with Lagrangian relaxation and subgradient optimization, which guarantees the optimality of the matching problem but not stability. A heuristic which integrates stability conditions and subsidy design is proposed, which reaches either an optimal MaaS platform equilibrium solution with global stability, or a feasible locally stable solution that may require subsidy. For the heuristic, a worst-case bound and condition for obtaining an exact solution are both identified. An expanded Sioux Falls network test with 82 nodes and 748 links derives generalizable insights about the model for coopetitive interdependencies between operators sharing the platform, handling congestion effects in MOD services, effects of local stability on investment impacts, and illustrating inequities that may arise under heterogeneous populations.

Explore related subjects

cs.GTcs.CY

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Bingqing Liu, Joseph Y. J. Chow. 2023-05-01. On-demand Mobility-as-a-Service platform assignment games with guaranteed stable outcomes. https://doi.org/10.1016/j.trb.2024.103060

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

MMS Allocation for Chores with Online Agent Arrivals

We study the fair allocation of $m$ indivisible chores to $n$ agents with subadditive cost functions arriving online in an arbitrary order. Upon an agent's arrival, we are informed of her cost function and must irrevocably assign her a set of chores. We focus on the Maximin Share (MMS) fairness notion and aim to compute an allocation in which all items are assigned, and no agent incurs a cost more than $\alpha$ times her MMS. Without any prior information about the instance (other than $n$ and $m$), we design an algorithm with a competitive ratio of $O(\min\{n, k\log^{1+\epsilon}k, \log m\})$ for any constant $\epsilon > 0$, where $k$ denotes the number of cost function types. Our bound matches the best known offline approximation guarantees for MMS under subadditive costs and is nearly optimal with respect to all three parameters: we show that even for binary additive cost functions, no online algorithm can achieve a competitive ratio of $o(\min\{n, k\log k, \log m\})$. We then consider the setting in which the $k$ cost function types are known in advance (though the realized types of arriving agents are not). For additive cost functions, we provide an algorithm with a competitive ratio of $O(\min\{\log k, \log(kn)/\log\log(kn)\})$, and show that constant-competitive algorithms do not exist for general $k$, even for the binary additive setting. For binary additive functions when $k \le n$, we propose a $3$-competitive algorithm and establish a lower bound of $2$.

cs.GT↗
arXiv2026

Truncated Noisy Best-Response Algorithms: Toward Game Theoretic Learning with Safety Guarantees

We consider a game theoretic approach to solve multi-agent coordination problems with submodular maximization objectives. It is known for such problems that the Nash equilibria for the corresponding game are always within 50% of the optimal, but that the equilibria which achieve this worst-case bound are not stable. To exploit this instability, we propose a family of algorithms which we call Truncated Noisy Best-Response (TNBR) Algorithms. These algorithms are flexibly characterized by agents asynchronously and stochastically selecting actions from a neighbourhood of their best response payoffs. We compute bounds on the recurrent classes of TNBR algorithms' associated Markov chains. Our bounds fall into two categories: first, "Performance" bounds ensure that TNBR algorithms always have a high-value recurrent state; second, "Safety" bounds ensure that TNBR algorithms never have arbitrarily-bad recurrent states. Furthermore, these two types of bounds are linked by a waterbed-like effect: every game with a poor Safety guarantee necessarily has a favorable Performance guarantee.

cs.GT↗
arXiv2026

Existence of the Core in Approval-Based Committee Elections

We settle the main open question in the theory of approval-based multi-winner elections: we show that there always exists a committee in the core. The core is a stability and group fairness concept. The proof introduces a new voting rule that optimizes an entropy-like objective function over committees and payment systems. All local optima of this objective function lie in the core, which implies that a core committee can be found in polynomial time.

cs.GT↗