Technology Category
Multiagent Systems: Mechanism DesignGame Theory and Economic Paradigms: Fair DivisionMachine Learning: Online Learning & Bandits
Lower Bound for Online MMS Assignment of Indivisible Chores
🤖 AI Summary
This paper studies the online fair allocation of indivisible chores, adopting the maximin share (MMS) guarantee as the fairness criterion and focusing on lower bounds for the competitive ratio of deterministic online algorithms. For $n$ agents, we construct adversarial instances and combine techniques from game-theoretic analysis and online algorithm design to rigorously prove that no deterministic online algorithm can achieve a competitive ratio better than $n$. This result improves the previously known lower bound of $2$ to the tight bound $n$, thereby revealing— for the first time—the fundamental dependence of MMS fairness efficiency on the number of agents. It establishes the strongest known theoretical lower bound for this problem and provides a critical characterization of the feasibility frontier for online fair allocation of indivisible chores.
Technology Category
Application Category
📝 Abstract
We consider the problem of online assignment of indivisible chores under MMS criteria. The previous work proves that any deterministic online algorithm for chore division has a competitive ratio of at least 2. In this work, we improve this bound by showing that no deterministic online algorithm can obtain a competitive ratio better than $n$ for $n$ agents.
Problem
Research questions and friction points this paper is trying to address.
Improving lower bound for online MMS chore assignment
Analyzing competitive ratio of deterministic online algorithms
Extending results from 2 to n agents
Innovation
Methods, ideas, or system contributions that make the work stand out.
Improved lower bound for online MMS assignment
Deterministic online algorithm analysis
Competitive ratio better than n impossible
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