Toward a Strategic Foundation for Rational Expectations Equilibrium

A step toward a strategic foundation for rational expectations equilibrium is taken by considering a double auction with n buyers and m sellers with interdependent values and affiliated private information. If there are sufficiently many buyers and sellers, and their bids are restricted to a sufficiently fine discrete set of prices, then, generically, there is an equilibrium in nondecreasing bidding functions that is arbitrarily close to the unique fully revealing rational expectations equilibrium of the limit market with unrestricted bids and a continuum of agents. In particular, the large double‐auction equilibrium is almost efficient and almost fully aggregates the agents' information.     

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.     

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.     

Reverse Auctions with Multiple Reinforcement Learning Agents*

Reverse auctions in business‐to‐business (B2B) exchanges provide numerous benefits to participants. Arguably the most notable benefit is that of lowered prices driven by increased competition in such auctions. The competition between sellers in reverse auctions has been analyzed using a game‐theoretic framework and equilibria have been established for several scenarios. One finding of note is that, in a setting in which sellers can meet total demand with the highest‐bidding seller being able to sell only a fraction of the total capacity, the sellers resort to a mixed‐strategy equilibrium. Although price randomization in industrial bidding is an accepted norm, one might argue that in reality managers do not utilize advanced game theory calculations in placing bids. More likely, managers adopt simple learning strategies. In this situation, it remains an open question as to whether the bid prices converge to the theoretical equilibrium over time. To address this question, we model reverse‐auction bidding behavior by artificial agents as both two‐player and n‐player games in a simulation environment. The agents begin the game with a minimal understanding of the environment but over time analyze wins and losses for use in determining future bids. To test for convergence, the agents explore the price space and exploit prices where profits are higher, given varying cost and capacity scenarios. In the two‐player case, the agents do indeed converge toward the theoretical equilibrium. The n‐player case provides results that reinforce our understanding of the theoretical equilibria. These results are promising enough to further consider the use of artificial learning mechanisms in reverse auctions and other electronic market transactions, especially as more sophisticated mechanisms are developed to tackle real‐life complexities. We also develop the analytical results when one agent does not behave strategically while the other agent does and show that our simulations for this environment also result in convergence toward the theoretical equilibrium. Because the nature of the best response in the new setting is very different (pure strategy as opposed to mixed), it indicates the robustness of the devised algorithm. The use of artificial agents can also overcome the limitations in rationality demonstrated by human managers. The results thus have interesting implications for designing artificial agents in automating bid responses for large numbers of bids where human intervention might not always be possible.     

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。     

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。     

Repurposing Materials and Waste through Online Exchanges: Overcoming the Last Hurdle

Online material and waste exchanges (OMWEs) provide online channels to repurpose by‐products, unused materials and waste from industrial and commercial facilities. Unfortunately, OMWE's also have challenges. First, sellers may have access to other disposal options and, as a result, may not fully commit to the exchange. Second, buyers can face high uncertainty about the product exchanged and the transaction being undertaken. Overcoming these challenges is the “last hurdle” to making OMWEs successful. This study investigates the factors that reduce the buyers' uncertainty and increase the sellers' commitment to the OMWE. We analyze novel transaction‐level data from an online exchange (MNExchange.org) combined with other archival public records on county‐level repurposing and disposal statistics. First, we find that regional repurposing policies and alternatives have a complementary effect on sellers' commitment toward OMWEs, resulting in increased OMWE exchanges. However, regional disposal policies and alternatives have a substitution effect on sellers' commitment, resulting in reduced exchange success. Further, greater product and transaction information reduce the buyer's uncertainty and increase exchange success. Finally, the analysis shows that users' (buyers and sellers) heavily rely on their prior experience with OMWEs. Specifically, higher familiarity between the buyer–seller pair and familiarity with the OMWE system leads to higher likelihood of exchange success. This study lays the foundation for understanding OMWEs and has important implications for developing policies and operations to increase online transactions of by‐products, materials and wastes.     

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.     

双边市场中平台企业搭售行为分析

搭售是现实中双边平台企业常用的促销策略之一。通过构建一个两阶段完全信息动态博弈模型,将买方分为搭售喜好型和搭售无差异型,从垄断和竞争两种情形研究了双边平台企业采取搭售策略时,具有不同搭售偏好的买方对最优均衡解的影响以及相应的社会福利变化。研究发现:不论是垄断情形还是竞争情形,搭售对买卖双方均衡进入价格的影响都不确定,而搭售产品的定价则按照传统单边市场的定价方式制定;垄断情形下,搭售能增加买方数量、卖方数量及双边平台企业的利润,而竞争情形下,搭售产品成本较小的双边平台企业将获得较大买方数量、卖方数量及利润。在两种情形下的买方总效用、卖方总效用以及社会总福利均随搭售喜好型买方数量的增加而增加。     

Uncertainty about Uncertainty and Delay in Bargaining

We study a one‐sided offers bargaining game in which the buyer has private information about the value of the object and the seller has private information about his beliefs about the buyer's valuation. We show that this uncertainty about uncertainties dramatically changes the set of outcomes. In particular, second order beliefs can lead to a delay in reaching agreement even when the seller makes frequent offers. We show that not all types of second order beliefs lead to a delay. When the buyer assigns positive probability to the seller knowing the buyer's value, then delay not only can occur, but it must occur for a class of equilibria. However, in all other cases delay will never occur.     

Nonexclusive Competition in the Market for Lemons

A seller can trade an endowment of a perfectly divisible good, the quality of which she privately knows. Buyers compete by offering menus of nonexclusive contracts, so that the seller can privately trade with several buyers. In this setting, we show that an equilibrium exists under mild conditions and that aggregate equilibrium allocations are generically unique. Although the good for sale is divisible, in equilibrium the seller ends up trading her whole endowment or not trading at all. Trades take place at a price equal to the expected quality of the good, conditional on the seller being ready to trade at that price. Our model thus provides a novel strategic foundation for Akerlof's (1970) results. It also contrasts with competitive screening models in which contracts are assumed to be exclusive, as in Rothschild and Stiglitz (1976). Latent contracts that are issued but not traded in equilibrium play an important role in our analysis.     

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.     

Modeling Reputation as a Time‐Series: Evaluating the Risk of Purchase Decisions on eBay*

Reputation systems based on buyer feedback play an important role in today's online markets. In this article, we provide a rigorous methodology to establish a relationship between a seller's feedback history and risk of default. We validate this method against eBay's reputation system, using a dataset of terminated users (Not‐A‐Registered‐User or NARU) and the feedback left for them by buyers. By treating feedback rating data as a function of time, we characterize the tendency of change in seller feedback ratings in order to predict the behavior of a seller. We find that NARU sellers have significantly more negative feedback in their final weeks. Applying functional principal component analysis and classification tree methods, we find that when projecting the feedback data to an appropriate space, NARU and non‐NARU sellers can be distinguished at better than 92% accuracy. We use this to provide a quantitative mechanism for evaluating the risk of trading with a seller who has less than perfect feedback, and offer advice on how much a buyer should offer to pay, given an asking price on a commodity item and a seller's feedback history.     

基于好评返现和差评偏好的体验型产品两阶段定价决策研究

假定产品存在发布试销期与正式销售期,在销售商不采取好评返现与采取好评返现两种情形下分别建立考虑消费者差评偏好的两阶段定价决策模型,用KT方法得到相应的最优决策和利润,给出了销售商实施好评返现的条件。基于导函数分析方法与数值仿真技术,分析了好评返现与差评偏好对产品定价、销售商利润和消费者效用的影响,证实了好评返现下消费者重视差评信息的合理性,并针对消费者、平台和销售商提出了对策。研究表明:只有产品质量中等的销售商才会采取好评返现策略,其利润随产品质量的提升而先递增后递减;好评返现提高了销售商第二阶段的市场份额和售价,导致消费者效用损失;消费者越重视差评信息,实施好评返现的高(低)质量产品销售商越多(少),且销售商利润将下降;好评返现扭曲了评价信息的真实性,降低了消费者对在线评价系统的信任度。     

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.     

Group Buying,Buyer Heterogeneity,and Sellers' Bargaining Power*

Group buying enables collective bargaining opportunity that individual buyers lack to negotiate prices with sellers. This potential negotiation capability has two opposing effects. On the one hand, the prospect of the group being able to negotiate price with its rival forces each seller to lower its price offer, as too high a price will induce the group to give its rival an opportunity to undercut its price via negotiation, likely taking away all the buyers. On the other hand, the potential negotiation opportunity may also discourage sellers from competing aggressively in their price offers, as the benefit of charging a low price could be offset by competitors in negotiation, thus yielding overall higher prices for the buyers. In this study, we find that compared to individual purchase, buyers benefit from collective bargaining opportunity by group buying only if sellers’ bargaining power relative to the buyer group is low and/or buyers’ preferences toward the sellers are sufficiently differentiated. Given buyers’ strategic choice of group purchase, sellers may be worse off with a further increase in bargaining power, and so may social welfare.     

电子商务环境下合作采购效益分析

合作采购是一种重要的企业间电子商务应用模式,成功实施合作采购需要供应链成员的积极参与。本文针对供应商采取的两种批发价定价策略,比较分析了协调成本对买主间合作采购动力及其总体采购成本的影响。其结果表明,只要协调成本较小,买主便具有合作采购动力,且无论供应商采取固定价格策略还是采取数量折扣策略,都存在一个协调成本临界值,当协调成本小于该临界值时,合作采购将同时减少买主与供应商的总体成本;当协调成本大于该临界值时,则总有一方的总体成本在合作采购中增加。     

The Affiliation Effect in First‐Price Auctions

We study the monotonicity of the equilibrium bid with respect to the number of bidders n in affiliated private‐value models of first‐price sealed‐bid auctions and prove the existence of a large class of such models in which the equilibrium bid function is not increasing in n. We moreover decompose the effect of a change in n on the bid level into a competition effect and an affiliation effect. The latter suggests to the winner of the auction that competition is less intense than she had thought before the auction. Since the affiliation effect can occur in both private‐ and common‐value models, a negative relationship between the bid level and n does not allow one to distinguish between the two models and is also not necessarily (only) due to bidders taking account of the winner's curse.     

Competing Mechanisms in a Common Value Environment

Consider strategic risk‐neutral traders competing in schedules to supply liquidity to a risk‐averse agent who is privately informed about the value of the asset and his hedging needs. Imperfect competition in this common value environment is analyzed as a multi‐principal game in which liquidity suppliers offer trading mechanisms in a decentralized way. Each liquidity supplier behaves as a monopolist facing a residual demand curve resulting from the maximizing behavior of the informed agent and the trading mechanisms offered by his competitors. There exists a unique equilibrium in convex schedules. It is symmetric and differentiable and exhibits typical features of market‐power: Equilibrium trading volume is lower than ex ante efficiency would require. Liquidity suppliers charge positive mark‐ups and make positive expected profits, but these profits decrease with the number of competitors. In the limit, as this number goes to infinity, ask (resp. bid) prices converge towards the upper (resp. lower) tail expectations obtained in Glosten (1994) and expected profits are zero.     

Large Robust Games

With many semi‐anonymous players, the equilibria of simultaneous‐move games are extensively robust. This means that the equilibria survive even if the simultaneous‐play assumption is relaxed to allow for a large variety of extensive modifications. Such modifications include sequential play with partial and differential revelation of information, commitments, multiple revisions of choices, cheap talk announcements, and more.