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

无论是在私营部门还是在公共部门，拍卖都是一种无处不在的资源分配手段。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，许多作家就一直在研究这个问题。不足为奇的是，只有当竞拍者仔细出价时，拍卖才能发挥作用，不仅要考虑他们自己关于待售物品(S)价值的私人信息，还要考虑他们在赢得一件或多件物品时所推断的信息。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，我们说投标人使用单调的投标策略。策略的单调性导致更有效的结果的想法也可以应用到其他环境中。例如，人们可能希望在寡头垄断的环境下，市场的竞争将导致成本较低的公司生产更多的产量。事实上，当公司采用单调战略时，情况就会是这样。因此，经济环境中策略的单调性提供了有关市场运行状况的重要信息。本研究的几个目标之一是，相当普遍地理解，以战略互动为特征的经济环境何时具有参与者使用单调纯策略的贝叶斯·纳什均衡。我们期望获得的结果将为这个问题提供迄今为止最普遍的答案，因此将提供关于一大类经济环境的效率属性的有用信息。

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.