Bargaining with Interdependent Values

A seller and a buyer bargain over the terms of trade for an object. The seller receives a perfect signal that determines the value of the object to both players, whereas the buyer remains uninformed. We analyze the infinite‐horizon bargaining game in which the buyer makes all the offers. When the static incentive constraints permit first‐best efficiency, then under some regularity conditions the outcome of the sequential bargaining game becomes arbitrarily efficient as bargaining frictions vanish. When the static incentive constraints preclude first‐best efficiency, the limiting bargaining outcome is not second‐best efficient and may even perform worse than the outcome from the one‐period bargaining game. With frequent buyer offers, the outcome is then characterized by recurring bursts of high probability of agreement, followed by long periods of delay in which the probability of agreement is negligible.     

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.     

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)     

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.     

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.     

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.     

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.     

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.     

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.     

Flexibility or Cost Saving? Sourcing Decisions with Two Suppliers

This article studies a decentralized supply chain in which there are two suppliers and a single buyer. One supplier offers the quantity flexibility (QF) contract to the buyer, while the other offers the cheaper price. Under the QF contract, the buyer does not assume full responsibility for the forecast, yet the supplier guarantees the availability of the forecasted quantity with additional buffer inventory. On the other hand, the price‐only contract places full inventory burden on the buyer, but with a cheaper price. We study this problem from the buyer's perspective and solve for the buyer's optimal procurement and forecasting decisions. We identify areas where flexibility and cheaper price have an advantage, one over the other. Our results indicate that the buyer significantly benefits from having multiple sources of supply. We also find that, from the system's standpoint, a multisupplier system may outperform a single‐supplier supply chain under certain conditions. Interestingly, we observe that providing too much flexibility may benefit the low‐price supplier rather than benefiting the QF supplier. We discuss the managerial implications and provide directions for future research opportunities.     

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.     

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.     

证券市场流动性与交易者群体变动的混沌研究

从证券市场微观结构角度,利用交易者群体可变的动态模型,分别在确定与不确定性金 融环境下,研究离散交易状态下市场的形成过程,并分析了交易者群体变动的混沌条件. 结果 表明,市场流动性的最低标准是买卖双方的交易者群体要有一个恰当的比例,市场达到稳定流 动性的时间与描述离开股市交易者的参数有关,通过交易制度对交易者群体参数的影响,可实 现对市场过程的控制,最后给出仿真计算.     

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.     

OUTSOURCING WHEN INVESTMENTS ARE SPECIFIC AND INTERRELATED

Using the universe of large Canadian manufacturing firms in 1988 and 1996, we investigate to what extent outsourcing patterns concord with the predictions of a simple property rights model. The unique availability of disaggregate information on outputs as well as inputs permits the construction of a detailed measure of vertical integration. We rely on five measures of technological intensity to proxy for investments that are likely to be specific to a buyer–seller relationship. A theoretical model that allows for varying degrees of investment specificity and interrelatedness—externalities between buyer and supplier investments—guides the analysis. Property rights predictions on the link between investment intensities and optimal ownership are strongly supported, but only for transactions with low interrelatedness. High specificity and low risk of appropriation strengthen the predictions in the model and in the data.     

COMPETING AUCTIONS

This paper shows that larger auctions are more efficient than smaller ones, but that despite this scale effect, two competing and otherwise identical markets or auction sites of different sizes can coexist in equilibrium. We find that the range of equilibrium market sizes depends on the aggregate buyer‐seller ratio, and also whether the markets are especially thin. (JEL: D44, L11)     

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.     

The Effect of Learning and Integration Investment on Manufacturing Outsourcing Decisions: A Game Theoretic Approach

We introduce a two‐period Stackelberg game of a supplier and buyer. We recognize that learning from manufacturing experience has many advantages. Consistent with the literature, we assume both the buyer and supplier realize reductions in their respective production costs in period 2 due to volume‐based learning from period 1 production. In addition, we introduce another learning concept, the future value, to capture the buyer's benefits of transferring current manufacturing experience for the design and development of future products and technologies. In contrast to the literature, we allow the supplier two mechanisms to impact the buyer's outsourcing decision: price and the investment in integration process improvement (IPI) that reduces the buyer's unit cost of integration. IPI may include the investment in new materials, specialized technology, or the re‐design of the integration process. Conditions are given whereby the buyer partially outsources component demand as opposed to fully outsourcing or fully producing in‐house. Furthermore, conditions are given characterizing when the supplier's price and investment in IPI are substitute strategies versus complements. Both analytic and numerical results are presented.     

一类供应链的Stackelberg主从对策问题研究

本文研究了供应链中的一般订货模式和协调模式,提出了一类供应链Stackelberg主从对策问题,卖方作为主方给出最小补充期策略,买方作为从方以最优库存策略响应。考虑一致价格折扣弥补买方的库存成本增加,以及买方的库存成本合理化,建立买方需求确定下的卖方成本优化模型。最后,应用遗传算法对石油分销系统Stackelberg主从对策问题离线仿真计算,得出Stackelberg主从对策均衡解。     

Managing Disruptions in Decentralized Supply Chains with Endogenous Supply Process Reliability

Supply disruptions are all too common in supply chains. To mitigate delivery risk, buyers may either source from multiple suppliers or offer incentives to their preferred supplier to improve its process reliability. These incentives can be either direct (investment subsidy) or indirect (inflated order quantity). In this study, we present a series of models to highlight buyers’ and suppliers’ optimal parameter choices. Our base‐case model has deterministic buyer demand and two possibilities for the supplier yield outcomes: all‐or‐nothing supply or partial disruption. For the all‐or‐nothing model, we show that the buyer prefers to only use the subsidy option, which obviates the need to inflate order quantity. However, in the partial disruption model, both incentives—subsidy and order inflation—may be used at the same time. Although single sourcing provides greater indirect incentive to the selected supplier because that avoids order splitting, we show that the buyer may prefer the diversification strategy under certain circumstances. We also quantify the amount by which the wholesale price needs to be discounted (if at all) to ensure that dual sourcing strategy dominates sole sourcing. Finally, we extend the model to the case of stochastic demand. Structural properties of ordering/subsidy decisions are derived for the all‐or‐nothing model, and in contrast to the deterministic demand case, we establish that the buyer may increase use of subsidy and order quantity at the same time.