Motivated by many practical applications, in this paper we study budget feasible mechanisms with the goal of procuring an independent set of a matroid. More specifically, we are given a matroid $${\mathcal {M}}=(E,{\mathcal {I}})$$ . Each element of the ground set E is controlled by a selfish agent and the cost of the element is private information of the agent itself. A budget limited buyer has additive valuations over the elements of E. The goal is to design an incentive compatible budget feasible mechanism which procures an independent set of the matroid of largest possible value. We also consider the more general case of the pair $${\mathcal {M}}=(E,{\mathcal {I}})$$ satisfying only the hereditary property. This includes matroids as well as matroid intersection. We show that, given a polynomial time deterministic algorithm that returns an $$\alpha $$ -approximation to the problem of finding a maximum-value independent set in $${\mathcal {M}}$$ , there exists an individually rational, truthful and budget feasible mechanism which is $$(3\alpha +1)$$ -approximated and runs in polynomial time, thus yielding also a 4-approximation for the special case of matroids.

中文翻译：

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拟阵上的预算可行机制

受许多实际应用的启发，在本文中，我们研究了预算可行机制，目的是获得一组独立的拟阵。更具体地说，我们给出了一个拟阵 $${\mathcal {M}}=(E,{\mathcal {I}})$$ 。地面集 E 的每个元素都由一个自私的代理控制，元素的成本是代理本身的私有信息。一个预算有限的买家对 E 的元素有附加的估值。目标是设计一个激励兼容的预算可行机制，该机制采购一组独立的最大可能价值的拟阵。我们还考虑了 $${\mathcal {M}}=(E,{\mathcal {I}})$$ 对仅满足遗传属性的更一般情况。这包括拟阵以及拟阵交集。我们表明，