Blockchain protocols often seek to procure computationally challenging work from a decentralized set of participants. While there are simple procurement auctions that result in the minimal cost of acquisition and maximal efficiency, they also lead to concentration in the provider set due to the winner-take-all market structure. We design and analyze single-good procurement auctions that balance social-cost minimization (at the extreme, a winner-take-all auction) with decentralization (at the extreme, a uniform allocation). We first give a dominant-strategy incentive-compatible (DSIC) mechanism explicitly designed to implement non-winner-take-all allocations. Our allocation rule uniquely solves an optimization with respect to a modified social-cost metric that penalizes large, single-player concentrations and is parameterized with a curvature value, $α$, with $α\rightarrow 0$ implementing the uniform allocation and $α\rightarrow \infty$ implementing the winner-take-all allocation. We further quantify the loss in social cost of this mechanism as a function of $α$. We then propose two alternative mechanisms, each addressing a limitation of the DSIC mechanism, namely a lack of Sybil-resistance and a complex payment rule. First, we examine a variation of Tullock contests to achieve a non-winner-take-all Sybil-proof procurement mechanism. Second, we consider a mechanism with the same allocation rule as the DSIC mechanism but with an alternative payment rule in which producers are simply paid proportionally to their bids. This provides a much simpler payment rule which, while not DSIC, still results in the mechanism being ex-post ``safe'' (where there exists a bidding strategy that is guaranteed to result in non-negative utility) for participating bidders. For both non-DSIC mechanisms, we characterize the equilibrium allocations and prove price of anarchy bounds.

翻译：区块链协议常需从去中心化的参与者集合中采购计算密集型工作。虽然存在实现最小采购成本与最大效率的简单采购拍卖，但胜者全得的市场结构会导致供应商集中化。我们设计并分析了在最小化社会成本（极端情况下为胜者全得拍卖）与去中心化（极端情况下为均匀分配）之间取得平衡的单物品采购拍卖。首先给出一个显式设计用于实现非胜者全得分配的占优策略激励兼容（DSIC）机制。该分配规则唯一解出基于修正社会成本度量的优化问题，该度量通过曲率参数α惩罚大规模单参与者集中化，其中α→0实现均匀分配，α→∞实现胜者全得分配。我们进一步量化该机制社会成本损失关于α的函数关系。随后提出两种替代机制，分别针对DSIC机制的局限性：缺乏女巫攻击抵抗性与复杂支付规则。首先研究图洛克竞赛的变体以实现非胜者全得的女巫证明采购机制；其次考虑采用与DSIC机制相同分配规则但替代支付规则的机制——生产者仅按其报价比例获得报酬。这种更简单的支付规则虽非DSIC，但能保证参与投标者的事后"安全性"（存在能够确保非负效用的投标策略）。针对两种非DSIC机制，我们刻画了均衡分配并证明其无政府状态价格的界限。