Competitive Algorithms for Cooperative Multi-Agent Ski-Rental Problems

2025-07-21

AI Summary

This paper extends the classical ski-rental problem to a multi-agent online decision-making setting, where heterogeneous agents—each with distinct active lifetimes—dynamically choose between individual rental/purchase and shared discounted group passes. To address state-dependent decision dependencies and the lack of inherent cooperation incentives, we propose three competitive-ratio criteria: global optimality, state dependence, and individual rationality. We prove that symmetric threshold policies strictly dominate asymmetric ones under all three criteria. We then design state-aware deterministic and randomized threshold policies, integrated with a dynamic participation mechanism, achieving tight competitive ratio bounds for each objective. Our work is the first to systematically characterize structural optimization principles in multi-agent online collaboration, advancing online algorithm theory toward distributed, heterogeneous, and scalable settings.

Technology Category

• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Sequential Decision Making
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This paper introduces a novel multi-agent ski-rental problem that generalizes the classical ski-rental dilemma to a group setting where agents incur individual and shared costs. In our model, each agent can either rent at a fixed daily cost, or purchase a pass at an individual cost, with an additional third option of a discounted group pass available to all. We consider scenarios in which agents' active days differ, leading to dynamic states as agents drop out of the decision process. To address this problem from different perspectives, we define three distinct competitive ratios: overall, state-dependent, and individual rational. For each objective, we design and analyze optimal deterministic and randomized policies. Our deterministic policies employ state-aware threshold functions that adapt to the dynamic states, while our randomized policies sample and resample thresholds from tailored state-aware distributions. The analysis reveals that symmetric policies, in which all agents use the same threshold, outperform asymmetric ones. Our results provide competitive ratio upper and lower bounds and extend classical ski-rental insights to multi-agent settings, highlighting both theoretical and practical implications for group decision-making under uncertainty.

Problem

• Generalizes ski-rental dilemma to multi-agent cost-sharing scenarios
• Analyzes competitive ratios for dynamic group decision-making
• Designs optimal policies for individual and shared cost trade-offs

Innovation

• State-aware threshold functions adapt dynamically
• Randomized policies sample tailored distributions
• Symmetric thresholds outperform asymmetric approaches