考虑全局投标者后悔心理行为的组合拍卖的投标均衡策略

许多实验研究表明投标者在拍卖过程中往往表现出预期后悔心理行为,并且投标者的预期后悔心理行为将会对投标策略产生影响,但以往大多是针对单物品拍卖研究考虑投标者后悔心理行为的投标均衡策略,而针对多物品拍卖情形的研究较少关注。本文着重研究了考虑投标者后悔心理行为的组合拍卖的投标均衡策略问题,在全局投标者存在预期后悔心理行为的假设下,依据Engelbrecht-Wiggans和Katok提出的后悔函数刻画了投标者的后悔心理行为,在此基础上,构建了组合拍卖模型,通过分析给出了全局投标者投标均衡策略需要满足的充分和必要条件。进一步地,依据构建的模型,通过数值实验分析了局部投标者人数、组合效应系数和全局投标者后悔参数对全局投标者投标策略的影响。最后,通过一个关于无线电频谱组合拍卖的算例说明了本文给出的模型及投标均衡策略确定方法的潜在应用和优越性。     

基于价格歧视策略的多单元逆向多属性英式拍卖机制

针对现有的多单元逆向多属性拍卖机制的市场分配效率都比较低,不利于社会效益最大化和采购双方长期合作等问题,设计了高效率的基于价格歧视策略的多单元逆向多属性英式拍卖机制,利用线性混合整数规划建立了赢者确定模型,并基于新建立的拍卖机制给出了拍卖流程和投标策略,为供应商提供投标决策支持。然后通过设计数值实例和对比模拟实验收集数据,采取统计分析的方法验证了新设计的拍卖机制市场分配效率和采购方的效益都比较高。上述研究结果适用于通过逆向多属性拍卖与信息技术相结合的网上自动化多单元商品采购。     

第一密封价格逆向拍卖机制博弈研究

在供应商对拟投标项目成本估计独立、不同分布的条件下,通过建立不公开保留价的第一价格逆向拍卖机制博弈模型,推导了供应商的最优报价策略,博弈均衡存在时采购者最优保留价满足的条件,发现供应商的报价高于他的成本估计,进一步得到了与该采购机制资源配置效率有关的结论:参与投标的人数越多供应商报价溢出成本部分越少;成本越低的供应商期望支付越大.这对于现实采购拍卖的政策建议为:设法让更多供应商参与竞标,能有效选择优势供应商、降低采购成本、增加社会福利.     

一类搜索型随机格斗的获胜概率研究

把随机过程分析引入Lanchester方程就形成了随机格斗理论.运用随机格斗理论研究了潜艇协同隐蔽攻击水面舰艇编队获胜概率的数学模型,利用状态转移图和Laplace变换的性质推导出了2对2搜索型随机格斗中双方的获胜概率公式,并结合潜艇协同隐蔽攻击水面舰艇的实际,计算分析了格斗双方的获胜概率.利用这一公式可以得到概率上的精确解,能够被用来定量评估潜艇协同隐蔽攻击水面舰艇编队的作战效能.     

基于高斯分布的在线采购机制设计及竞争分析

依附于互联网电子商务的在线采购拍卖交易, 对传统的贝叶斯离线拍卖理论提出新的挑战, 因为面对不同时间点的投标, 采购电商必须即可决策出是否中标以及购买价格。鉴于此, 对于诸如石油、煤、粮食等无限可分商品的电子采购, 本文基于投标具有高斯分布特征设计了一种激励相容的在线采购策略, 演绎出在线采购的数学模型, 利用Runge-Kutta数值算法, 通过Matlab编程求解出采购电商在线定价策略的需求曲线及其对应的竞争比, 最后, 利用数值模拟, 将在线采购机制策略与纯竞争分析得到的在线采购策略比较, 结果显示利用了高斯分布信息的在线采购策略的竞争性能由于利用了投标的统计信息而得到了提高。     

一类多对多随机格斗的获胜概率

为了计算出多对多随机格斗的获胜概率,首先推导出多对多随机格斗的状态转移速率,然后应用拉普拉斯变换的性质,分别计算出在不带搜索和带搜索两种情形下,三对二随机格斗中双方各自获胜概率的实用公式.     

一类多对一随机格斗的获胜概率

本研究多对一搜索型随机格斗模型，求出了计算格斗双方各自获胜概率的实用公式。     

预算约束下广义第二价格关键字拍卖均衡分析

在关键字拍卖中,广告主预算约束是影响投标策略均衡的重要因素。针对广泛应用的广义第二价格机制,分析了预算约束下的关键字拍卖均衡性质。按照广告主的点击估价和预算分布情况,将广告主划分为天然完全赢家、天然部分赢家和天然输家这三种类型,提出了广告主投标临界值与关键值的概念,基于关键字拍卖不断重复进行的特点,分别从长期视角与短期视角建立了静态模型与动态模型,研究结果表明:静态环境下拍卖存在唯一的纯策略纳什均衡;动态环境下当广告主采用最优反应投标策略时拍卖将收敛至唯一的纳什均衡点,并且动态环境下拍卖商收入不低于静态环境下的拍卖收入。数值算例的结果表明在动态环境下不同的初始报价会导致拍卖收敛至不同的均衡点。研究结果为拍卖商提供了拍卖收入预测和拍卖机制优化的决策依据。     

两种记分函数下多属性拍卖投标均衡策略

以拍卖人期望收益最大化为机制设计目标,讨论两种不同偏好的记分函数条件下,最高得分密封投标拍卖和连续完全信息多属性英式拍卖中,卖者的最优投标策略和买者的最优拍卖设计问题,主要结论是:1)无论选择哪种拍卖方式和记分函数,拍卖人均有动机隐瞒自己的真实偏好,除非竞价人是同质的或参与人数足够多.2)竞价人最优属性策略qi*与拍卖...     

基于网上拍卖的共同价值托投标分析

基于信息不对称条件下的共同价值模型,刻画了网上拍卖过程中可能存在的托投标行为,并运用博弈理论结合竞价关系求解了竞标者的赢标概率和最优竞价策略．研究发现,在共同价值模型下,参与竞标的人数与嬴者诅咒的发生存在联系;在最高出价者赢标的概率模型基础上,分别建立了是否存在托投标行为时的竞标者收益模型,并求解了竞标者的均衡竞价策略．     

Probability of Winning at Tennis I. Theory and Data

The probability of winning a game, a set, and a match in tennis are computed, based on each player's probability of winning a point on serve, which we assume are independent identically distributed (iid) random variables. Both two out of three and three out of five set matches are considered, allowing a 13-point tiebreaker in each set, if necessary. As a by-product of these formulas, we give an explicit proof that the probability of winning a set, and hence a match, is independent of which player serves first. Then, the probability of each player winning a 128-player tournament is calculated. Data from the 2002 U.S. Open and Wimbledon tournaments are used both to validate the theory as well as to show how predictions can be made regarding the ultimate tournament champion. We finish with a brief discussion of evidence for non-iid effects in tennis, and indicate how one could extend the current theory to incorporate such features.     

基于次大值标杆的秘书问题研究

秘书问题的实质是决定何时停止观察选项、而不是哪一个选项被选择,已有解决秘书问题的策略,其主要特征是以取样选项中的一个最大值作为标杆。该策略的优点是能保证命中概率最大,然而其不足是很少考虑决策者的有限理性与启发式偏见,因此本文提出了次大值标杆的设想,然后从理论上计算出该策略的最优截止阀值与命中概率,并通过计算机仿真实验验证与比较了该策略的特征与规律。研究结果发现在最大化命中概率的条件下,标杆降低导致取样观察选项的数量不断增加,但命中概率却逐渐降低。     

A necessary 4-cycle condition for dice representability of reciprocal relations

The comparison of independent random variables can be modeled by a set of dice and a reciprocal relation expressing the winning probability of one dice over another. It is well known that dice transitivity is a necessary 3-cycle condition for a reciprocal relation to be dice representable, i.e. to be the winning probability relation of a set of dice. Although this 3-cycle condition is sufficient for a rational-valued reciprocal relation on a set of three elements to be dice representable, it has been shown that this is no longer the case for sets consisting of four or more elements. In this contribution, we provide a necessary 4-cycle condition for dice representability of reciprocal relations. Moreover, we show that our condition is sufficient in the sense that a given rational-weighted 4-cycle and reciprocally weighted inverse cycle, both fulfilling the 4-cycle condition, can be extended to a winning probability graph representing a dice-representable reciprocal relation on four elements.     

Eliciting and Developing Teachers' Conceptions of Random Processes in a Probability and Statistics Course

The purpose of this study is to examine prospective mathematics specialists' engagement in an instructional sequence designed to elicit and develop their understandings of random processes. The study was conducted with two different sections of a probability and statistics course for K-8 teachers. Thirty-two teachers participated. Video analyses within a collaborative course design were used to support a teaching experiment about teachers' conceptions of random processes. In particular, teachers were asked whether the outcomes of Rock-Paper-Scissors (RPS) are generated randomly or not, were presented with a definition for random selection, and were asked to come to a conclusion about RPS. Teachers struggled to reconcile the equality of winning outcomes for each player with the potential for human interference in the process of generating outcomes. Ultimately, teachers concluded the outcomes were not generated randomly, but encountered a variety of unexpected obstacles along the way.     

To bat or not to bat: An examination of match outcomes in day-night limited overs cricket

The tradition of tossing a coin to decide who bats first in a cricket match introduces a randomly assigned advantage to one team that is unique in sporting contests. The potential importance of the toss rule in determining cricket match results has been the subject of some investigation, which is further advanced in this paper that utilizes a data set relating to the increasingly popular, but contentious, day-night form of limited overs cricket as played at international level. We employ logit regression models to examine the effects of winning the toss and choice of batting order on the likelihood of a match victory, while controlling for home advantage and (relative) team quality. Our findings suggest that winning the toss and batting first increases the probability of winning whereas winning the toss and bowling first does not.     

A note on Bayesian Nash equilibria in imperfectly discriminating contests

The literature on imperfectly discriminating contests has almost exclusively focused on complete information. We study such contests assuming players have private information. We identify a general class of imperfectly discriminating contests for which findings by  Athey (2001) imply the existence of a Bayesian Nash equilibrium in monotone pure strategies. The main assumptions are that a player’s valuation of winning is increasing in the signal he observes and that a player’s probability of winning is continuous in the efforts of all players as well as increasing in his own effort.     

Using Lotteries to Improve Students' Number Sense and Understanding of Probability

This article examines ways in which a discussion of lotteries can be integrated into a classroom lesson on combinatorics and probability and be used to enhance the teaching and learning of number sense and probability of winning various lottery games, and facts and myths about lotteries. Instructional tips for incorporating discussions of lotteries into lesson plans are also given.     

Recurrent Competitive Bidding

A competitive bidding policy can be formulated if prior probability distributions of competitors' bids for future contracts have been determined. A method for determining these prior probability distributions is described for markets where there are a large number of customers. The identity of each winning company and its bid are assumed to be available to competitors and other customers so that the market reacts quickly to changes. A real example of the use of the method is given. The suppliers' general levels of bidding and their variation with individual types of customer are evaluated quantitatively. The results are consistent with qualitative knowledge of the market.