The Optimal Design of Research Contests

采购武器系统、运输系统或新车型等新产品往往需要供应商付出大量的创新努力。然而，通过双边合同获得这种努力可能很困难，因为这些努力可能是“无法核实的”和“合作的”。也就是说，努力的程度无法由第三方核实，所产生的价值的很大一部分可能会归买家所有。此外，对破产的担忧和法律限制限制了采购人收取入场费的能力(即“有限责任”)。在这样的环境中，采购者往往依靠竞争来获得创新成果。特别是，研究竞赛一直是由各种政府机构(特别是国防部)以及私营公司赞助的研发采购竞赛的重要组成部分。拟议的研究将研究当不可验证性、协作性和有限责任非常重要时，最佳采购方法。我们将首先提出用竞争取代双边合同的理由。其次，我们将研究采购商应如何选择一组公司参加比赛。最后，也是最重要的，我们将描述最优竞赛设计的特征。在这样做的过程中，我们考虑到了大量的奖品结构，其中包括拍卖(参赛者竞标他们的奖品)和锦标赛(奖品是固定的)作为特殊情况。这些问题的一些方面以前已经研究过。例如，拍卖文献对拍卖的事后绩效(即如何分配货物或合同以及如何分配盈余)产生了实质性的见解，表明拍卖可能是一种最佳机制。然而，对最佳机制的探索并没有扩大到包括事前投资激励措施。最近关于研究竞赛和进入拍卖的工作已经纳入了事前维度，但它仍然被认为是给定的竞赛形式(拍卖或锦标赛)。这项拟议的研究将首先考虑广泛的竞赛类别，使奖金结构内生化，并确定在事前和事后表现都很重要的情况下的最佳竞赛。完成的研究将分为两部分。在第一部分中，我们将给出均衡投资和竞价策略的闭式表达式，即使在非对称企业(即具有不同投资技术的企业)的情况下也是如此。第二部分将使用一种新颖的二元性论证来确定最优竞赛设计。(标准的机制设计方法在这里行不通。)如果两家公司是对称的，那么只有两家公司且没有保留价的第一价格拍卖是最优的。如果两家公司拥有不同的技术，则两家公司的拍卖似乎是最优的，但效率更高的公司会受到阻碍。这一研究将对一般竞争，特别是拍卖的文献做出重大贡献。它还将通过调查竞争在激励合作投资方面的特殊作用，为不完全合同文献做出贡献。最后，它将被证明是有用的，以竞争设计师。考虑到管理拍卖的简便性，只有两家公司的第一价格拍卖的最佳性尤为重要。

The procurement of new products such as weapons systems, transportation systems, or new car models often requires substantial innovative effort by suppliers. Procuring such efforts through bilateral contracts may be difficult, however, since the efforts may be "unverifiable" and "cooperative." That is, the level of effort cannot be verified by a third party, and a substantial fraction of the value generated may accrue to the buyer. Also, bankruptcy concerns and legal restrictions limit the ability of the procurer to charge entry fees (i.e., "limited liability" ). Procurers have often relied on contests to procure innovative effort in such an environment. In particular, research contests have been an important part of R&D procurement competitions sponsored by various government agencies (notably the Department of Defense) as well as private firms.The proposed research will study the optimal method of procurement when unverifiability,cooperativeness and limited liability are important. We will first make the case for using contests in place of bilateral contracts. Second, we will study how the procurer should select the set of firms to participate in the contest. Finally, and most importantly, we will characterize the optimal contest design. In doing so, we allow for a vast array of prize structures, which includes auctions (contestants bid their prizes) and tournaments (the prize is fixed) as special cases.Some aspects of these issues have been studied previously. For instance, the auctions literature has yielded substantial insights into the en post performance of auctions (i.e., how the good or Contract is allocated, and how the surplus is divided), showing that auctions may be an optimal mechanism. The search for an optimal mechanism has not been extended to incorporate en ante investment incentives, however. Recent work on research contests and entry into auctions has incorporated an ex ante dimension, but it still takes as given the form of contest (auction or tournament). The proposed research will be the first to consider a broad class of contests, to endogenize the prize structure, and to identify the optimal contest when ex ante and ex post performance considerations are important.The completed research will be presented in two parts. In the first part, we will provide closed-form expressions for equilibrium investment and bidding strategies, even with asymmetric firms (i.e., firms with different investment technologies). The second part will identify the optimal contest design, using a novel duality argument. (The standard mechanism design approach does not work here.) A first-price auction with just two firms and no reserve price is optimal if the firms are symmetric. If the firms have different technologies, an auction with two firms appears to be optimal, but with the more efficient firm being handicapped.This research will make a signficant contribution to the literature on contests in general, and auctions in particular. It will also contribute to the incomplete contracts literature by investigating the special role of contests in motivating cooperative investments. Finally, it will prove useful to contest designers. The optimality of first-price auctions with just two firms is particularly important, given the ease of administering auctions.