Existence of Equilibria in Bayesian Games, Strategic-Form Games, and Extensive-Form Games with Infinite Action Spaces

拍卖是一种无处不在的资源分配方式，无论是在私营部门还是在公共部门。人们感兴趣的一个关键问题是拍卖是否能够有效地分配资源。至少从20世纪60年代初开始，许多作者就开始研究这个问题。毫不奇怪，只有当竞标者在竞标中谨慎出价，不仅考虑到他们自己对待售物品价值的私人信息，而且考虑到他们在赢得一件或多件物品时推断出的信息时，拍卖才能运作良好。先前的研究表明，当更好的信息导致更高的出价时，拍卖可以产生有效的结果。当这种情况发生时，我们说投标人采用单调的投标策略。策略的单调性导致更有效结果的想法也可以应用于其他设置。例如，人们可能希望在寡头垄断环境中，市场竞争将导致成本较低的公司生产更多的产出。事实上，当公司采用单调策略时，情况就是如此。因此，经济环境中策略的单调性提供了关于市场如何运作的重要信息。本研究的几个目标之一是了解，一般来说，当以战略互动为特征的经济环境具有贝叶斯纳什均衡时，参与者采用单调纯策略。我们期望获得的结果将为这个问题提供迄今为止最一般的答案，因此将提供有关大类经济环境的效率特性的有用信息。

Auctions are a ubiquitous means for allocating resources, both in the private and in the public sectors. A key question of interest is whether auctions are able to allocate resources effciently. This question has been studied by many authors since at least the early 1960s. Not surprisingly, auctions work well only when the bidders competing within them bid carefully, taking into account not only their own private information about the value of the object(s) for sale, but also the information they would infer if they were to win one or more objects. Previous research has shown that auctions can produce effcient outcomes when better information leads to higher bids. When this occurs, wesay that bidders employ monotone bidding strategies. The idea that monotonicity of strategies leads to more effcient outcomes can be applied to other settings as well. For example, one might hope that in an oligopoly setting, the competition of the market will lead firms with lower costs to produce more output. And indeed, this will be the case when firms employ monotone strategies. Thus, monotonicity of strategies in economic settings provide important information about how well markets work. One of several goals of the present research is to understand, quite generally, when economic settings haracterized by strategic interaction possesses Bayesian Nash equilibriain which the participants employ monotone pure strategies. The results we expect to obtain will provide the most general answer to this question to date, and so will provide useful information about the efficiency properties of a large class of economic environments.