Bargaining without a Common Prior—An Immediate Agreement Theorem

In sequential bargaining models without outside options, each player's bargaining power is ultimately determined by which player will make an offer and when. This paper analyzes a sequential bargaining model in which players may hold different beliefs about which player will make an offer and when. Excessive optimism about making offers in the future can cause delays in agreement. The main result states that, despite this, if players will remain sufficiently optimistic for a sufficiently long future, then in equilibrium they will agree immediately. This result is also extended to other canonical models of optimism.     

Gambling Reputation: Repeated Bargaining With Outside Options

We study the role of incomplete information and outside options in determining bargaining postures and surplus division in repeated bargaining between a long‐run player and a sequence of short‐run players. The outside option is not only a disagreement point, but reveals information privately held by the long‐run player. In equilibrium, the uninformed short‐run players' offers do not always respond to changes in reputation and the informed long‐run player's payoffs are discontinuous. The long‐run player invokes inefficient random outside options repeatedly to build reputation to a level where the subsequent short‐run players succumb to his extraction of a larger payoff, but he also runs the risk of losing reputation and relinquishing bargaining power. We investigate equilibrium properties when the discount factor goes to 1 and when the informativeness of outside options diffuses. In both cases, bargaining outcomes become more inefficient and the limit reputation‐building probabilities are interior.     

Bargaining and Reputation

The paper develops a reputation based theory of bargaining. The idea is to investigate and highlight the influence of bargaining ‘postures’ on bargaining outcomes. A complete information bargaining model a la Rubinstein is amended to accommodate ‘irrational types’ who are obstinate, and indeed for tractability assumed to be completely inflexible in their offers and demands. A strong ‘independence of procedures’ result is derived: after initial postures have been adopted, the bargaining outcome is independent of the fine details of the bargaining protocol so long as both players have the opportunity to make offers frequently. The latter analysis yields a unique continuous‐time limit with a war of attrition structure. In the continuous‐time game, equilibrium is unique, and entails delay, consequently inefficiency. The equilibrium outcome reflects the combined influence of the rates of time preference of the players and the ex ante probabilities of different irrational types. As the probability of irrationality goes to zero, delay and inefficiency disappear; furthermore, if there is a rich set of types for both agents, the limit equilibrium payoffs are inversely proportional to their rates of time preference.     

Multiperson Bargaining and Strategic Complexity

We investigate the effect of introducing costs of complexity in the n‐person unanimity bargaining game. As is well‐known, in this game every individually rational allocation is sustainable as a Nash equilibrium (also as a subgame perfect equilibrium if players are sufficiently patient and if n & 2). Moreover, delays in agreement are also possible in such equilibria. By limiting ourselves to a plausible notion of complexity that captures length of memory, we find that the introduction of complexity costs (lexicographically with the standard payoffs) does not reduce the range of possible allocations but does limit the amount of delay that can occur in any agreement. In particular, we show that in any n‐player game, for any allocation z, an agreement on z at any period t can be sustained as a Nash equilibrium of the game with complexity costs if and only if t≤n. We use the limit on delay result to establish that, in equilibrium, the strategies implement stationary behavior. Finally, we also show that ‘noisy Nash equilibrium’ with complexity costs sustains only the unique stationary subgame perfect equilibrium allocation.     

Bargaining within the Supply Chain and Its Implications in an Industry

Our main objective is to investigate the influence of the bargaining power within a chain on its industry. As a building block, we first discuss the implications of bargaining within a single chain by considering an asymmetric Nash bargaining over the wholesale price (BW). We show that both Manufacturer Stackelberg (MS) and vertical integration (VI) strategies are special cases of the BW contract. We then develop the Nash equilibrium in an industry with two supply chains that use BW. We identify the profit‐maximizing (coordinating) bargaining power within this industry. We show that when a chain is not monopolistic, VI does not coordinate the chain and that the MS contract, where the manufacturer has all the bargaining power, is coordinating when competition is intense. We find that the main determinant of the equilibrium in mature industries is to respond well to the actions of the competing chain rather than to directly maximize the profit of each chain. That is, the equilibrium does not necessarily maximize the profit of the entire industry. While a coordination of the industry could then increase the profitability of both chains, such a coordination is likely against antitrust law. Moreover, if one chain cannot change its actions, the other chain may unilaterally improve its profitability by deviating from the equilibrium. Our results lead to several predictions supported by empirical findings, such as that in competitive industries chains will work “close to” the MS contract.     

非对称信息下产险公司与投保大户之间的二周期讨价还价博弈

将投保人分为投保大户与非大户,认为投保大户能够准确预知自身损失概率,而产险公司却无法知道投保大户损失概率的真值.在这样的信息不对称条件下,构造了产险公司与投保大户之间的二周期讨价还价模型.用博弈论求解该模型,得到了完美贝叶斯均衡解,进而给出了产险公司在谈判中能获得的最大期望收益与投保大户的最优策略.     

基于指令执行延迟的最优交易策略

已有关于最优交易策略的研究尚未注意指令执行延迟的影响。本文主要研究了面对指令执行延迟约束的机构投资者对大额买卖指令进行拆分时所采取的最优策略及其数学性质,并对影响交易策略的各参数敏感性进行分析。研究表明,指令执行延迟导致机构的交易策略向后倾斜,而非均匀的拆分策略,且市场流动性和深度、拆分程度、风险厌恶程度、“价格误估”程度均影响执行延迟所导致的流动性成本。     

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.     

Real‐Time Delay Estimation Based on Delay History in Many‐Server Service Systems with Time‐Varying Arrivals

Motivated by interest in making delay announcements in service systems, we study real‐time delay estimators in many‐server service systems, both with and without customer abandonment. Our main contribution here is to consider the realistic feature of time‐varying arrival rates. We focus especially on delay estimators exploiting recent customer delay history. We show that time‐varying arrival rates can introduce significant estimation bias in delay‐history‐based delay estimators when the system experiences alternating periods of overload and underload. We then introduce refined delay‐history estimators that effectively cope with time‐varying arrival rates together with non‐exponential service‐time and abandonment‐time distributions, which are often observed in practice. We use computer simulation to verify that our proposed estimators outperform several natural alternatives.     

Bargaining,Reputation, and Equilibrium Selection in Repeated Games with Contracts

Consider a two‐person intertemporal bargaining problem in which players choose actions and offers each period, and collect payoffs (as a function of that period's actions) while bargaining proceeds. This can alternatively be viewed as an infinitely repeated game wherein players can offer one another enforceable contracts that govern play for the rest of the game. Theory is silent with regard to how the surplus is likely to be split, because a folk theorem applies. Perturbing such a game with a rich set of behavioral types for each player yields a specific asymptotic prediction for how the surplus will be divided, as the perturbation probabilities approach zero. Behavioral types may follow nonstationary strategies and respond to the opponent's play. In equilibrium, rational players initially choose a behavioral type to imitate and a war of attrition ensues. How much should a player try to get and how should she behave while waiting for the resolution of bargaining? In both respects she should build her strategy around the advice given by the “Nash bargaining with threats” (NBWT) theory developed for two‐stage games. In any perfect Bayesian equilibrium, she can guarantee herself virtually her NBWT payoff by imitating a behavioral type with the following simple strategy: in every period, ask for (and accept nothing less than) that player's NBWT share and, while waiting for the other side to concede, take the action Nash recommends as a threat in his two‐stage game. The results suggest that there are forces at work in some dynamic games that favor certain payoffs over all others. This is in stark contrast to the classic folk theorems, to the further folk theorems established for repeated games with two‐sided reputational perturbations, and to the permissive results obtained in the literature on bargaining with payoffs as you go.     

Simple Finite Horizon Bubbles Robust to Higher Order Knowledge

An asymmetric information model of a finite horizon “nth order” rational asset price bubble is presented, where (all agents know that)ⁿ the asset is worthless. Also, the model has only two agents, so the first order version of the bubble is simpler than other first order bubbles in the literature.     

需求不确定条件下的制造商订单分配模型

制造商的订单分配作为供应链模型微观层面的重要组成部分,对提升整个供应链效率有很大影响,但需求层面的不确定因素加大了订单分配的难度。以按比例分配为原则,讨论在需求不确定条件下完全信息与不完全信息两类多供应商-单制造商的订单分配模型。重点研究完全信息条件下各方的分散决策和集中决策,由于后者能避免各参与方对其他决策方的边际影响,所以能够实现供应链总利润的最大化;其次又将不完全信息引入模型,讨论制造商如何通过折算因子结合已有信息对供应商的私人信息进行估计,进而做出决策。最后以需求服从正态分布为例对两类模型进行验证。     

Public vs. Private Offers in the Market for Lemons

We study the role of observability in bargaining with correlated values. Short‐run buyers sequentially submit offers to one seller. When previous offers are observable, bargaining is likely to end up in an impasse. In contrast, when offers are hidden, agreement is always reached, although with delay.     

风险资本联合投资的激励契约设计

针对风险资本在投资中期或晚期的联合投资激励契约问题,在风险投资家对项目已作了初步融资和了解条件下,建立了风险投资家之间的联合投资契约模型。分对称和非对称信息两种情形,就如何设计最优契约才能使联合投资双方都能真实地显示他们的信号进行了研究,分析了风险投资家的职业能力对联合投资契约的影响,并用算例进行了验证,为风险资本中期或晚期的联合投资提供了决策依据。     

多属性采购拍卖与多属性不对称纳什谈判的比较研究

拍卖与谈判作为采购中有效选择交易对象的常见方式,从最大化采购方收益的角度看,现有理论对这2种方式各有支持。通过运用经典的多属性拍卖模型和多属性不对称纳什谈判模型,将拍卖的期望收益和谈判的收益进行比较,发现2种机制的分界与谈判力量和投标人数这2个指标有关,通过划分谈判力量和投标人数取值的不同区间,找到了拍卖或谈判这2种方式的边界条件以及它们各自的适宜范围。     

基于不对称需求信息的供应链最小订购量决策

在由一个供应商和一个零售商组成的两级分散供应链中,供应商通过制定最小订购量取得规模效应,保障自身利益。当零售商和供应商之间存在需求信息不对称时,即零售商掌握需求信息而供应商仅知道需求信息中价格敏感因子的分布,如何进行最小订购量决策成为供应商面临的一个重要问题。针对这一问题,从营销视角构建了基于Stackelberg博弈的利润最大化模型。假设供应商知道需求的价格敏感因子服从正态分布,通过严密的数学推导确定了模型中的最优最小订购量。将提出的最优最小订购量决策方法应用于云存储的销售供应链中,确定了云存储供应商销售的最优最小存储容量,阐释了方法的合理性与有效性。通过实验研究发现,最小订购量的设置提升了供应商的利润。所提方法对于考虑最小订购量的供应链协调研究具有积极的推动作用。     

信息不对称下零售商自有品牌引入问题研究

零售商引入自有品牌(store brand)已成为商业活动中的常见行为,已有研究表明在信息对称情况下,自有品牌的引入对零售商有利,而对制造商不利.针对信息不对称且零售商可以引入自有品牌的情况,构建制造商和零售商组成的供应链博弈模型,分析在零售商拥有市场信息优势的情形下,零售商引入自有品牌对其订购策略的影响.研究表明:和信息对称情况不同,制造商品牌(national brand)的订购量依赖于两种品牌生产成本之间的关系,并有可能随着自有品牌的引入而增加;此外,通过比较引入自有品牌前后制造商和零售商的相对利润变化,发现在一定的情形下,零售商可以通过共享或不共享市场信息使双方达到"共赢"状态.     

零售商信息禀赋优势下制造商电商直销渠道决策

在供应链中由于零售商相比制造商掌握更多消费者信息,能够对市场需求进行预测,因此制造商在建立直销渠道决策时往往面临着市场需求信息的不对称。本文考虑一个由单个制造商和单个零售商组成的供应链,其中零售商向制造商订购产品并销售给终端市场,制造商可能建立直销渠道将产品直接销售给消费者。通过构建制造商无入侵、对称信息下和不对称信息下制造商入侵三种情形下的博弈模型,本文分析了制造商建立直销渠道决策和零售商的订货决策。研究发现,尽管零售商具有信息禀赋优势,制造商建立直销渠道总是能够获得更多的利润,并且在信息不对称情况下制造商建立直销渠道获得的利润大于在信息对称情况下获得的利润。而零售商与之相反,在制造商掌握市场预测信息的情况下零售商的收益更高,供应链总收益在对称信息的情况下最高。进一步考虑制造商按照自身信息禀赋进行备货量决策的情况,可以得到按照自身信息禀赋与零售商同时决策时制造商建立直销渠道的利润大于信息对称和信息不对称两种情况下的利润。     

Higher Order Uncertainty and Information: Static and Dynamic Games

Weinstein and Yildiz (2007) have shown that in static games, only very weak predictions are robust to perturbations of higher order beliefs. These predictions are precisely those provided by interim correlated rationalizability (ICR). This negative result is obtained under the assumption that agents have no information on payoffs. This assumption is unnatural in many settings. It is therefore natural to ask whether Weinstein and Yildiz's results remain true under more general information structures. This paper characterizes the “robust predictions” in static and dynamic games, under arbitrary information structures. This characterization is provided by an extensive form solution concept: interim sequential rationalizability (ISR). In static games, ISR coincides with ICR and does not depend on the assumptions on agents' information. Hence the “no information” assumption entails no loss of generality in these settings. This is not the case in dynamic games, where ISR refines ICR and depends on the details of the information structure. In these settings, the robust predictions depend on the assumptions on agents' information. This reveals a hitherto neglected interaction between information and higher order uncertainty, raising novel questions of robustness.     

The Role of Quantitative Risk Assessments for Characterizing Risk and Uncertainty and Delineating Appropriate Risk Management Options, with Special Emphasis on Terrorism Risk

The purpose of this article is to discuss the role of quantitative risk assessments for characterizing risk and uncertainty and delineating appropriate risk management options. Our main concern is situations (risk problems) with large potential consequences, large uncertainties, and/or ambiguities (related to the relevance, meaning, and implications of the decision basis; or related to the values to be protected and the priorities to be made), in particular terrorism risk. We look into the scientific basis of the quantitative risk assessments and the boundaries of the assessments in such a context. Based on a risk perspective that defines risk as uncertainty about and severity of the consequences (or outcomes) of an activity with respect to something that humans value we advocate a broad risk assessment approach characterizing uncertainties beyond probabilities and expected values. Key features of this approach are qualitative uncertainty assessment and scenario building instruments.