Dynamic Matching,Two‐Sided Incomplete Information,and Participation Costs: Existence and Convergence to Perfect Competition

Consider a decentralized, dynamic market with an infinite horizon and participation costs in which both buyers and sellers have private information concerning their values for the indivisible traded good. Time is discrete, each period has length δ, and, each unit of time, continuums of new buyers and sellers consider entry. Traders whose expected utility is negative choose not to enter. Within a period each buyer is matched anonymously with a seller and each seller is matched with zero, one, or more buyers. Every seller runs a first price auction with a reservation price and, if trade occurs, both the seller and the winning buyer exit the market with their realized utility. Traders who fail to trade continue in the market to be rematched. We characterize the steady‐state equilibria that are perfect Bayesian. We show that, as δ converges to zero, equilibrium prices at which trades occur converge to the Walrasian price and the realized allocations converge to the competitive allocation. We also show the existence of equilibria for δ sufficiently small, provided the discount rate is small relative to the participation costs.     

产品异质条件下排污权交易市场支配力对系统均衡的影响研究

日趋臻显的行业细分趋势和显著的外向型经济发展特点等在很大程度上决定了我国区域排污权交易系统内不存在显著的产品竞争。鉴于此,在产品异质条件下,通过考虑产成品市场与排污权交易市场之间的关联影响,首先从理论层面分析了社会最优的排污权配置状态;进而,构建了主导企业与从属企业之间的主从博弈模型,通过分析特定排污权市场价格下从属企业的最优行为特征,深入剖析了主导企业的策略性行为及其对系统均衡的影响。结果表明：市场支配力对系统均衡的影响具有多样性与复杂性;特别是,为了获取更大的额外收益,主导企业存在作为卖家时选择"溢价"与作为买家时"抑价"两种排污权价格操纵形式,并不可避免地导致系统均衡与社会最优配置状态的偏离,而从属企业却会蒙受巨大损失;其中,初始排污权禀赋是影响主导企业最优决策的重要因素。最后,通过量化分析对结论进行了验证,并细致展现了主导企业产污系数和治污成本等变动对系统均衡的影响。     

基于可变供给量的可分离物品拍卖及其应用

本文对统一价格下可分离物品的拍卖问题进行了研究。首先,在买者报价连续、买者和卖者风险中立、卖者采取可变供给量(将供给量看成价格的函数)的策略下,设计了一个新的基于可变供给量的可分离物品统一价格拍卖机制,研究了其信息激励性和分配的有效性,给出了卖者的最佳供给策略和买者的均衡报价策略。然后,将拍卖机制推广到风险中立、风险爱好和风险厌恶三类风险买者共存的情形,并给出了相应的均衡结论,该结论与现有的一些成果相比更具一般性。最后,给出了拍卖机制在环境规划中应用。具体地,结合"十一五"期间获得的"1+8武汉城市圈"环境规划中有关污染物允许排放总量分配数据和统计申报资料,利用拍卖模型来分析和评价了免费分配方案的有效性程度,并据此给出了关于目前排污申报制度和免费分配方法的若干结论和建议。     

基于信号博弈的卖方欺诈行为分析

本文主要基于信号博弈的卖方欺诈行为进行研究，假设拍卖中可能存在欺诈型和诚实型两种卖家，其中欺诈行为有概率发生在第二价格拍卖中：欺诈型卖方冒充竞拍者递交仅次于最高价的报价从而获得额外收益。两种卖家根据各自效用选择拍卖形式：第一价格或者第二价格。而竞买者将卖者的选择作为信号，更新对卖方类型的判断，然后制定报价策略。这是一个买卖方信号交叉影响的过程。考虑到拍卖过程中买方价值相关性，本文在建立模型中参考了关联价值原理。针对该模型进行分析，得出了不同情况下的买卖方策略，并且研究了买方报价、买方判断、卖方收益三者之间的关系。文中利用贝叶斯公式对双方的策略选择问题进行预测，与单纯的概率分布方法相比，更具实践价值。     

Insider Trading,Stochastic Liquidity,and Equilibrium Prices

We extend Kyle's (1985) model of insider trading to the case where noise trading volatility follows a general stochastic process. We determine conditions under which, in equilibrium, price impact and price volatility are both stochastic, driven by shocks to uninformed volume even though the fundamental value is constant. The volatility of price volatility appears ‘excessive’ because insiders choose to trade more aggressively (and thus more information is revealed) when uninformed volume is higher and price impact is lower. This generates a positive relation between price volatility and trading volume, giving rise to an endogenous subordinate stochastic process for prices.     

Strategic Supply Function Competition With Private Information

A finite number of sellers (n) compete in schedules to supply an elastic demand. The cost of each seller is random, with common and private value components, and the seller receives a private signal about it. A Bayesian supply function equilibrium is characterized: The equilibrium is privately revealing and the incentives to rely on private signals are preserved. Supply functions are steeper with higher correlation among the cost parameters. For high (positive) correlation, supply functions are downward sloping, price is above the Cournot level, and as we approach the common value case, price tends to the collusive level. As correlation becomes maximally negative, we approach the competitive outcome. With positive correlation, private information coupled with strategic behavior induces additional distortionary market power above full information levels. Efficiency can be restored with appropriate subsidy schemes or with a precise enough public signal about the common value component. As the market grows large with the number of sellers, the equilibrium becomes price‐taking, bid shading is on the order of 1/n, and the order of magnitude of welfare losses is 1/n². The results extend to inelastic demand, demand uncertainty, and demand schedule competition. A range of applications in product and financial markets is presented.     

Waiting for News in the Market for Lemons

We study a dynamic setting in which stochastic information (news) about the value of a privately informed seller's asset is gradually revealed to a market of buyers. We construct an equilibrium that involves periods of no trade or market failure. The no‐trade period ends in one of two ways: either enough good news arrives, restoring confidence and markets reopen, or bad news arrives, making buyers more pessimistic and forcing capitulation that is, a partial sell‐off of low‐value assets. Conditions under which the equilibrium is unique are provided. We analyze welfare and efficiency as they depend on the quality of the news. Higher quality news can lead to more inefficient outcomes. Our model encompasses settings with or without a standard static adverse selection problem—in a dynamic setting with sufficiently informative news, reservation values arise endogenously from the option to sell in the future and the two environments have the same equilibrium structure.     

MARKET POWER AND INFORMATION REVELATION IN DYNAMIC TRADING

We study a strategic model of dynamic trading where agents are asymmetrically informed over common value sources of uncertainty. There is a continuum of buyers and a finite number n of sellers. All buyers are uninformed, while at least one seller is privately informed about the true state of the world. When n = 1, full information revelation never occurs in equilibrium and the only information transmission happens in the first period. With n > 1 the outcome depends both on the structure of the sellers' information and, even more importantly, on the intensity of competition allowed by the existing trading rules. When there is intense competition (absence of clienteles), information is fully and immediately revealed to the buyers in every equilibrium for n large enough, regardless of the number of informed sellers. On the other hand, for trading arrangements characterized by less intense forms of competition (presence of clienteles), for any n we always have equilibria where information is never fully revealed. Moreover, in that case, when only one seller is informed, for many parameter configurations there are no equilibria with full information revelation, even for large n. (JEL: C72, C78, D82, D83)     

Optimal procurement of long-term contracts in the presence of imperfect spot market

B2B spot market has grown rapidly and become an effective trading channel for commodity products. Besides long-term contract procurement from conventional suppliers (forward and option), a buyer can procure or sell commodities at any time in B2B spot market to adjust her inventory level. However, spot prices are generally volatile and the market is imperfect in the sense that spot trading may be realized with uncertainty in a given period of time and often comes with extra transaction cost. This paper considers a commodity buyer who can order forward and option contracts in advance and trade in a B2B spot market when spot price and demand are observed stochastically. Based on a single-period newsvendor model, we discuss three optimal order strategies and derive respective expected profits when the buyer is risk-neutral. The sensitivity of purchase costs, market liquidity and transaction cost is investigated. We also compare the optimal expected profits for different strategies to illustrate the effects of the two long-term contracts in the presence of the B2B spot market. We then extend our model to a multi-period setting and derive the optimal strategy. Finally, we numerically compute the optimal order strategy for a risk-averse buyer and analyze the impact of spot market, risk aversion, as well as the correlation between customer demand and spot price.     

跟单服务与溢短交易驱动下产能分享供应链均衡策略选择

考虑由于信息不对称等原因导致的产能分享双方订单与实际交付不一致的情形,本文构建了由产能买方,产能卖方和第三方跟单服务商组成的产能分享供应链系统,并研究“溢短交易”和“跟单服务”对产能交付率提升发挥的作用。考虑产能卖方决策是否选择溢短交易模式,产能买方决策是否接受跟单服务,本文采用博弈论分析了产能买卖双方的占优策略以及双方的均衡策略组合。研究发现,溢短交易和跟单服务都可以降低产能分享的加入门槛,使得更多企业加入到产能分享中。当次品率相对较高,或跟单服务效果相对较好时,买卖双方倾向于接受跟单服务,采取普通交易模式;相反,当次品率相对较低,或跟单服务效果相对较差时,买卖双方倾向于采取溢短交易模式,不接受跟单服务。本文进一步给出了溢短交易和跟单服务的均衡策略及其条件,为产能买卖双方对合作对象的选择及相关决策提供了依据。     

Dynamic Monetary Equilibrium in a Random Matching Economy

This article concerns an infinite horizon economy where trade must occur pairwise, using a double auction mechanism, and where fiat money overcomes lack of double coincidence of wants. Traders are anonymous and lack market power. Goods are divisible and perishable, and are consumed at every date. Preferences are defined by utility‐stream overtaking. Money is divisible and not subject to inventory constraints. The evolution of individual and economywide money holdings distributions is characterized. There is a welfare‐ordered continuum of single price equilibria, reflecting indeterminacy of the price level rather than of relative prices.     

Managing the Revenue of Sales Platforms: Insights into Service Fees

Online sales platforms have grown substantially in recent years. These platforms assist sellers to conduct sales, and in return, collect service fees from sellers. We study the fee policies by considering a fee‐setting platform, on which a seller may conduct a sale with a reserve price to a group of potential buyers: the seller retains the object for sale if the final trading price is below the reserve price. The platform may charge two types of fees as in current practice: a reserve fee as a function of the seller's reserve price and a final value fee as a function of the sale's final trading price. We derive the optimality condition for fee policies, and show that the platform can use either just a final value fee or just a reserve fee to achieve optimality. In the former case, the optimal final value fee charged by the platform is independent of the number of buyers. In the latter case, the optimal reserve fee is often a decreasing, instead of increasing, function of the seller's reserve price. An increasing reserve fee may make the seller reluctant to use a positive reserve price and hurt the platform's revenue. In general, the optimal fees are nonlinear functions, but in reality, linear fees are commonly used because of their simplicity for implementation. We show that a linear fee policy is indeed optimal in the case that the seller's valuation follows a power distribution. In other cases, our numerical analysis suggests close‐to‐optimal performance of the linear policy.     

Efficient Competition Through Cheap Talk: The Case of Competing Auctions

We consider a large market where auctioneers with private reservation values compete for bidders by announcing cheap‐talk messages. If auctioneers run efficient first‐price auctions, then there always exists an equilibrium in which each auctioneer truthfully reveals her type. The equilibrium is constrained efficient, assigning more bidders to auctioneers with larger gains from trade. The choice of the trading mechanism is crucial for the result. Most notably, the use of second‐price auctions (equivalently, ex post bidding) leads to the nonexistence of any informative equilibrium. We examine the robustness of our finding in various dimensions, including finite markets and equilibrium selection.     

Relational Contracts and the Nature of Market Interactions

We provide evidence that long‐term relationships between trading parties emerge endogenously in the absence of third party enforcement of contracts and are associated with a fundamental change in the nature of market interactions. Without third party enforcement, the vast majority of trades are initiated with private offers and the parties share the gains from trade equally. Low effort or bad quality is penalized by the termination of the relationship, wielding a powerful effect on contract enforcement. Successful long‐term relations exhibit generous rent sharing and high effort (quality) from the very beginning of the relationship. In the absence of third‐party enforcement, markets resemble a collection of bilateral trading islands rather than a competitive market. If contracts are third party enforceable, rent sharing and long‐term relations are absent and the vast majority of trades are initiated with public offers. Most trades take place in one‐shot transactions and the contracting parties are indifferent with regard to the identity of their trading partner.     

Public Disclosure and Dissimulation of Insider Trades

Regulation requiring insiders to publicly disclose their stock trades after the fact complicates the trading decisions of informed, rent‐seeking insiders. Given this requirement, we present an insider's equilibrium trading strategy in a multiperiod rational expectations framework. Relative to Kyle (1985), price discovery is accelerated and insider profits are lower. The strategy balances immediate profits from informed trades against the reduction in future profits following trade disclosure and, hence, revelation of some of the insider's information. Our results offer a novel rationale for contrarian trading: dissimulation, a phenomenon distinct from manipulation, may underlie insiders' trading decisions.     

双寡头电商平台的收费制度选择博弈

在竞争环境下,考虑两个开放型电商平台寡头主导的电商服务链,两平台对网商的收费制度为注册收费制、交易收费制、两部收费制等三种收费制度构成的策略集,本文构建了两平台的六种收费制度组合模型。通过博弈论逆序求解法和划线法分析发现:当平台的注册服务成本不低于交易服务成本时,两平台对网商的收费制度选择博弈不一定存在均衡,存在则必为其中一方采取交易收费制而另一方采取两部收费制这种分离均衡;反之,两平台对网商的收费制度选择博弈必定存在均衡,且为双方均选择注册收费制这种混同均衡。     

拍卖中的串通出价

本文在扩展的独立私有价值模型下,考虑第二价格和第一价格拍卖机制下的串通出价行为和卖方对串通出价的反映。第二价格串通出价机制和第一价格串通出价机制分别为在这两种拍卖机制下的激励相容、有效的直接显示串通出价机制。我们发现卖方若知道有串通行为,可以提高保留价来减少损失。由于卖方一般情况下不太可能确定是否存在串通行为及参与串通的人数k,但可以确定给定保留价时串通人数的'最优反应',在第二价格串通出价机制下,给定串通人数,增加保留价可以提高卖方的期望收益,对于确定的保留价,串通人数的增加会减少卖方的期望收益。从而存在这样的纳什均衡:所有的投标人串通,即,k=N,而卖方宣布与之相应的保留价r (N)。当然,并不是所有的串通出价对投标人都是有利可图的,在第一价格拍卖机制下,若卖方可以调整保留价,只有当参与竞投的人很多时,串通出价才有利可图。     

基于两阶段决策的封闭式基金价格控制问题研究

在给定相关假设的基础上,考虑了在某一交易时间段的初始时刻,“庄家”型封闭式基金投资者初始持有资金额度有限的状况,将“庄家”型基金投资者的基金价格控制决策分为两个阶段：第一阶段为在确定各时刻期望收益率及其收益离差的条件下求得该投资者在对应时刻的最优投资值,第二阶段以各时刻的最优投资值为约束来获得最优基金价格控制序列。对于第一阶段可建立使“庄家”型基金投资者期望收益最大、收益平均绝对离差最小（风险最小）的双目标模型,变换为一个单目标模型后利用库恩-塔克条件进行求解,从而获得各时刻的最优投资值;对于第二阶段则以第一阶段得到的各时刻最优投资值为约束,以“庄家”型基金投资者在该交易时间段内的现金支付为极小值（现金收益的极大值）建立目标函数,而其为一个带约束的非线性规划问题,对此采用了一种改进的遗传算法进行求解,最终获得基金的最优价格控制序列。     

Strategic Management of Distressed Inventory

It is well known that maximizing revenue from a fixed stock of perishable goods may require discounting prices rather than allowing unsold inventory to perish. This behavior is seen in industries ranging from fashion retail to tour packages and baked goods. A number of authors have addressed the markdown management problem in which a seller seeks to determine the optimal sequence of discounts to maximize the revenue from a fixed stock of perishable goods. However, merchants who consistently use markdown policies risk training customers to “wait for the sale.” We investigate models in which the decision to sell inventory at a discount will change the future expectations of customers and hence their buying behavior. We show that, in equilibrium, a single‐price policy is optimal if all consumers are strategic and demand is known to the seller. Relaxing any of these conditions can lead to a situation in which a two‐price markdown policy is optimal. We show using numerical simulation that if customers update their expectations of availability over time, then optimal sales limit policies can evolve in a complex fashion.     

Robust trading mechanisms over 0/1 polytopes

The problem of designing a trade mechanism (for an indivisible good) between a seller and a buyer is studied in the setting of discrete valuations of both parties using tools of finite-dimensional optimization. A robust trade design is defined as one which allows both traders a dominant strategy implementation independent of other traders’ valuations with participation incentive and no intermediary (i.e., under budget balance). The design problem which is initially formulated as a mixed-integer non-linear non-convex feasibility problem is transformed into a linear integer feasibility problem by duality arguments, and its explicit solution corresponding to posted price optimal mechanisms is derived along with full characterization of the convex hull of integer solutions. A further robustness concept is then introduced for a central planner unsure about the buyer or seller valuation distribution, a corresponding worst-case design problem over a set of possible distributions is formulated as an integer linear programming problem, and a polynomial solution procedure is given. When budget balance requirement is relaxed to feasibility only, i.e., when one allows an intermediary maximizing the expected surplus from trade, a characterization of the optimal robust trade as the solution of a simple linear program is given. A modified VCG mechanism turns out to be optimal.