Incentives against Max-Min Fairness in a Centralized Resource System

Resource allocating mechanisms draw much attention from various areas, and exploring the truthfulness of these mechanisms is a very hot topic. In this paper, we focus on the max-mm fair allocation in a centralized resource system and explore whether the allocation is truthful when a node behaves strategically. The max-min fair allocation enables nodes receive appropriate resources, and we introduce an efficient algorithm to find out the allocation. To explore whether the allocation is truthful, we analyze how the allocation varies when a new node is added to the system, and we discuss whether the node can gain more resources if it misreports its resource demands. Surprisingly, if a node misrepresents itself by creating several fictitious nodes but keeps the sum of these nodes' resource demands the same, the node can achieve more resources evidently. We further present some illustrative examples to verify the results, and we show that a node can achieve 1.83 times resource if it misrepresents itself as two nodes. Finally, we discuss the influence of node's misrepresenting behavior in tree graph: some child nodes gain fewer resources even if their parent node gains more resources by creating two fictitious nodes.