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.     

Unobservable Investment and the Hold‐Up Problem

We study a two‐person bargaining problem in which the buyer may invest and increase his valuation of the object before bargaining. We show that if all offers are made by the seller and the time between offers is small, then the buyer invests efficiently and the seller extracts all of the surplus. Hence, bargaining with frequently repeated offers remedies the hold‐up problem even when the agent who makes the relation‐specific investment has no bargaining power and contracting is not possible. We consider alternative formulations with uncertain gains from trade or two‐sided investment.     

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.     

Optimal Offer Strategies in Mergers and Acquisitions*

This paper models the corporate takeover process as a bargaining game under certainty. During the takeover process, an acquirer is generally uncertain about the minimum price the target shareholders will accept. Normally, a takeover is concluded after a sequence of offers have been made. This paper derives optimal offer strategies for the buyer at each stage of this bargaining game under uncertainty. Uncertainty about the target's minimum acceptable price is represented by a probability distribution. Optimal offer strategies depend on the probability distribution of the minimum acceptable price, which can change during the offer process.     

REFERENCE POINTS,SOCIAL NORMS,AND FAIRNESS IN CONTRACT RENEGOTIATIONS

How does an ex‐ante contract affect behavior in an ex‐post renegotiation game? We address this question in a canonical buyer–seller relationship with renegotiation. Our paper provides causal experimental evidence that an initial contract has a highly significant and economically important impact on renegotiation behavior that goes beyond the effect of contracts on bargaining threat points. We compare situations in which an initial contract is renegotiated to strategically equivalent bargaining situations in which no ex‐ante contract was written. The ex‐ante contract causes sellers to ask for markups that are 45% lower than in strategically equivalent bargaining situations without an initial contract. Moreover, buyers are more likely to reject given markups in renegotiations than in negotiations. These effects do not depend on whether the contract was written under competitive or monopolistic conditions. Our results provide strong evidence supporting the hypothesis that contracts serve as reference points that shape and coordinate the expectations of the contracting parties.     

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.     

A Dynamic Reinterpretation of Nash Bargaining With Endogenous Threats

This paper concerns the two‐stage game introduced in Nash (1953). It formalizes a suggestion made (but not pursued) by Nash regarding equilibrium selection in that game, and hence offers an arguably more solid foundation for the “Nash bargaining with endogenous threats” solution. Analogous reasoning is then applied to an infinite horizon game to provide equilibrium selection in two‐person repeated games with contracts. In this setting, issues about enforcement of threats are much less problematic than in Nash's static setting. The analysis can be extended to stochastic games with contracts.     

Revenue management with minimax regret negotiations

We study the dynamic bilateral price negotiations from the perspective of a monopolist seller. We first study the classical static problem with an added uncertainty feature. Next, we review the dynamic negotiation problem, and propose a simple deterministic “fluid” analog. The main emphasis of the paper is in analyzing the relationship of the dynamic negotiation problem and the classical revenue management problems; and expanding the formulation to the case where both the buyer and seller have limited prior information on their counterparty valuation. Our first result shows that if both the seller and buyer are bidding so as to minimize their maximum regret, then it is optimal for them to bid as if the unknown valuation distributions were uniform. Building on this result and the fluid formulation of the dynamic negotiation problem, we characterize the seller’s minimum acceptable price at any given point in time.     

Mechanism Design with Collusion and Correlation

In a public good environment with positively correlated types, we characterize optimal mechanisms when agents have private information and can enter collusive agreements. First, we prove a weak‐collusion‐proof principle according to which there is no restriction for the principal in offering weak‐collusion‐proof mechanisms. Second, with this principle, we characterize the set of allocations that satisfy individual and coalitional incentive constraints. The optimal weakly collusion‐proof mechanism calls for distortions away from first‐best efficiency obtained without collusion. Allowing collusion restores continuity between the correlated and the uncorrelated environments. When the correlation becomes almost perfect, first‐best efficiency is approached. Finally, the optimal collusion‐proof mechanism is strongly ratifiable.     

AMBIVALENT INVESTMENT AND THE HOLD‐UP PROBLEM

In this paper we add to the foundations of incomplete contracting literature. We study the hold‐up problem with ambivalent investment, where investment benefits the investing party if ex post the right decision is undertaken but harms the investing party if the wrong decision is made. In this context, we show that the power of contracts to provide investment incentives depends on three factors: the commitment value of contracts, the amount of quasirents that the investing party can expect in the case of out‐of‐contract renegotiation, and the degree of ambivalence of investment. First, contracts provide first‐best investment incentives when parties can commit to a contract regardless of the type of investment. Second, with sufficiently ambivalent investment, if parties cannot commit not to renegotiate a contract and if the investing party's bargaining power is intermediate, contracts cannot improve investment incentives above those provided by no contract. In contrast, a simple buyer or seller option contract is optimal when the investing party's bargaining power is extreme. (JEL: D23, K12, L22)     

Supply Chain Contracting Under Competition: Bilateral Bargaining vs. Stackelberg

We analyze contracting behaviors in a two‐tier supply chain system consisting of competing manufacturers and competing retailers. We contrast the contracting outcome of a Stackelberg game, in which the manufacturers offer take‐it‐or‐leave‐it contracts to the retailers, with that of a bargaining game, in which the firms bilaterally negotiate contract terms via a process of alternating offers. The manufacturers in the Stackelberg game possess a Stackelberg‐leader advantage in that the retailers are not entitled to make counteroffers. Our analysis suggests that whether this advantage would benefit the manufacturers depends on the contractual form. With simple contracts such as wholesale‐price contracts, which generally do not allow one party to fully extract the trade surplus, the Stackelberg game replicates the boundary case of the bargaining game with the manufacturers possessing all the bargaining power. In contrast, with sophisticated contracts such as two‐part tariffs, which enable full surplus extraction, the two games lead to distinct outcomes. We further show that the game structure being Stackelberg or bargaining critically affects firms' preferences over contract types and thus their equilibrium contract choices. These observations suggest that the Stackelberg game may not be a sufficient device to predict contracting behaviors in reality where bargaining is commonly observed.     

Reputational Bargaining With Minimal Knowledge of Rationality

Two players announce bargaining postures to which they may become committed and then bargain over the division of a surplus. The share of the surplus that a player can guarantee herself under first‐order knowledge of rationality is determined (as a function of her probability of becoming committed), as is the bargaining posture that she must announce in order to guarantee herself this much. This “maxmin” share of the surplus is large relative to the probability of becoming committed (e.g., it equals 30% if the commitment probability is 1 in 10 and equals 13% if the commitment probability is 1 in 1000), and the corresponding bargaining posture simply demands this share plus compensation for any delay in reaching agreement.     

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。     

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.     

Coopetitive Buyer–Supplier Relationship: An Investigation of Bargaining Power,Relational Context,and Investment Strategies

This study proposes an analytical approach combined with a behavioral experiment for a joint examination of the competitive and cooperative (i.e., coopetitive) relationship between a buyer and a supplier. Specifically, the article considers the scenario in which the buyer and the supplier invest in strategic capabilities to increase their relative bargaining power. The article examines how dynamic investments in strategic assets are influenced by the locus of bargaining power and by the underlying context (synergistic vs. adversarial) of the interfirm relationship. The dynamic evolution of bargaining power is also examined. A dynamic game model is considered to examine the evolution of investment strategies in critical resources and to investigate the issues of bargaining power in a buyer–supplier dyad. Equilibrium expressions for the investment strategies of the buyer and the supplier are presented and their implications for buyer–supplier relationships are examined. The behavioral experiment complements the analytical model and examines the correspondence between optimal behavior suggested by the analytical model and the boundedly rational behavior of decision makers in an experimental context. The results from the model and behavioral experiments suggest that the strategies are a function of the risk‐adjusted returns obtained from investments. The experiment shows that, in a synergistic relational context when the buyer maintains bargaining power, the investment shifts of the buyer and the supplier accord well with theoretical predictions. In an adversarial relational context, the results of the experimental study do not correspond well with that predicted by the theoretical model. The implications of the results are discussed and directions for future research are presented.     

Co‐opetition and Investment for Supply‐Chain Resilience

This paper considers the problem of disruption risk management in global supply chains. We consider a supply chain with two participants, who face interdependent losses resulting from supply chain disruptions such as terrorist strikes and natural hazards. The Harsanyi–Selten–Nash bargaining framework is used to model the supply chain participants' choice of risk mitigation investments. The bargaining approach allows a framing of both joint financing of mitigation activities before the fact and loss‐sharing net of insurance payouts after the fact. The disagreement outcome in the bargaining game is assumed to be the result of the corresponding non‐cooperative game. We describe an incentive‐compatible contract that leads to First Best investment and equal “gain” for all players, when the solution is “interior” (as it almost certainly is in practice). A supplier that has superior security practices (i.e., is inherently safer) exploits its informational advantage by extracting an “information rent” in the usual spirit of incomplete information games. We also identify a special case of this contract, which is robust to moral hazard. The role of auditing in reinforcing investment incentives is also examined.     

Procurement with Reverse Auction and Flexible Noncompetitive Contracts

This article investigates a hybrid procurement mechanism that combines a reverse auction with flexible noncompetitive contracts. A buyer adopts such mechanism to procure multiple units of a product from a group of potential suppliers. Specifically, the buyer first offers contracts to some suppliers who, if accepting the contract, do not participate in the auction while committing to selling a unit to the buyer at the price of the subsequent auction. For the suppliers rejecting the offers, they can join the subsequent auction with the other suppliers to compete on the remaining units. When the buyer offers only one flexible noncompetitive contract, we find that the selected supplier may accept the offer regardless of whether he knows his exact cost information. Meanwhile, the buyer can benefit from offering such a contract, as opposed to solely conducting a regular reverse auction or offering a noncompetitive contract that does not allow suppliers declining offers to join the subsequent auction. Moreover, we find that the suppliers' information about their own costs has a significant impact on the buyer's decision. When the buyer makes multiple offers, we analyze the resulting game behavior of the selected suppliers and demonstrate that the buyer can benefit more than just offering one such contract. Therefore, the hybrid procurement mechanism can be mutually beneficial for both the buyer and the selected suppliers.     

PROPERTY RIGHTS AND THE EFFICIENCY OF BARGAINING

We show that efficient bargaining is impossible for a wide class of economic settings and property rights. These settings are characterized by (i) the existence of “adverse efficient opt‐out types”, whose participation does not change the efficient allocation and who, when they opt out, are the worst type other agents can face, and (ii) non‐existence of the “marginal core”, and its multivaluedness with a positive probability. We also examine the optimal allocation of property rights within a given class that satisfies (i), such as simple property rights, liability rules, and dual‐chooser rules. We characterize property rights that minimize the expected subsidy required to implement efficiency. With two agents, simple property rights that are optimal in this way maximize the expected surplus at the status quo allocation, but this no longer holds with more agents. We also study “second‐best” budget‐balanced bargaining under a liability rule. The optimal “second‐best” liability rule may differ from, but is often close to, the expectation of the victim's harm, which would be optimal if there were no bargaining. However, liability rules that are close to a simple property right result in a lower expected surplus than the simple property right they are near.     

Collusion With Persistent Cost Shocks

We consider a dynamic Bertrand game in which prices are publicly observed and each firm receives a privately observed cost shock in each period. Although cost shocks are independent across firms, within a firm costs follow a first‐order Markov process. We analyze the set of collusive equilibria available to firms, emphasizing the best collusive scheme for the firms at the start of the game. In general, there is a trade‐off between productive efficiency, whereby the low‐cost firm serves the market in a given period, and high prices. We show that when costs are perfectly correlated over time within a firm, if the distribution of costs is log‐concave and firms are sufficiently patient, then the optimal collusive scheme entails price rigidity: firms set the same price and share the market equally, regardless of their respective costs. When serial correlation of costs is imperfect, partial productive efficiency is optimal. For the case of two cost types, first‐best collusion is possible if the firms are patient relative to the persistence of cost shocks, but not otherwise. We present numerical examples of first‐best collusive schemes.     

供应链应收账款融资的决策分析与价值研究

根据供应链应收账款融资交易模型,建立了包含供应商、下游厂商和金融机构的多阶段供应链决策模型,研究了包含和不包含融资情况下相关企业的决策问题,得到供应链中各参与方在各阶段的期望收益,并通过数值分析研究了供应链应收账款融资对供应链成员和整个供应链的价值.分析发现:没有其他融资的情况下,中小供应商有可能出现生产不连续的情况,而供应链应收账款融资能够使其进行连续生产,并在快速增长的市场中能在较短的周期内达到最优产量;应收账款融资也能使厂商得到连续供货,收益持续增长,供应商的初始现金越多,厂商的期望收益越高;当供应商的实力较弱时,金融机构能够得到较大融资总收益,当供应商的实力达到一定程度后,金融机构得到的总收益呈下降趋势.供应链应收账款融资对中小供应商、厂商和金融机构都具有很大的应用价值.