Selfish Knapsack
Itai Feigenbaum, Matthew P. Johnson

TL;DR
This paper studies a strategic variant of the knapsack problem where agents can misreport item ownership to maximize their own valuation, analyzing the strategic properties and approximation guarantees of various mechanisms.
Contribution
It introduces and analyzes randomized and deterministic mechanisms for strategic knapsack problems, establishing bounds on their approximation ratios and strategyproofness.
Findings
Randomized greedy mechanism has a correlated price of anarchy of 2.
Strategyproof mechanisms have lower bounds on approximation ratios.
Mechanisms are designed for various agent misreporting scenarios.
Abstract
We consider a selfish variant of the knapsack problem. In our version, the items are owned by agents, and each agent can misrepresent the set of items she owns---either by avoiding reporting some of them (understating), or by reporting additional ones that do not exist (overstating). Each agent's objective is to maximize, within the items chosen for inclusion in the knapsack, the total valuation of her own chosen items. The knapsack problem, in this context, seeks to minimize the worst-case approximation ratio for social welfare at equilibrium. We show that a randomized greedy mechanism has attractive strategic properties: in general, it has a correlated price of anarchy of (subject to a mild assumption). For overstating-only agents, it becomes strategyproof; we also provide a matching lower bound of on the (worst-case) approximation ratio attainable by randomized strategyproof…
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Taxonomy
TopicsTeaching and Learning Programming · Modular Robots and Swarm Intelligence
