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.     

Robust Predictions for Bilateral Contracting with Externalities

The paper studies bilateral contracting between one principal and N agents when each agent's utility depends on the principal's unobservable contracts with other agents. We show that allowing deviations to menu contracts from which the principal chooses bounds equilibrium outcomes in a wide class of bilateral contracting games without imposing ad hoc restrictions on the agents' beliefs. This bound yields, for example, competitive convergence as N →∞ in environments in which an appropriately‐defined notion of competitive equilibrium exists. We also examine the additional restrictions arising in two common bilateral contracting games: the “offer game” in which the principal makes simultaneous offers to the agents, and the “bidding game” in which the agents make simultaneous offers to the principal.     

The Coalitional Nash Bargaining Solution

The coalitional Nash bargaining solution is defined to be the core allocation for which the product of players' payoffs is maximal. We consider a non‐cooperative model with discounting in which one team may form and every player is randomly selected to make a proposal in every period. The grand team, consisting of all players, generates the largest surplus. But a smaller team may form. We show that as players get more patient if an efficient and stationary equilibrium exists, it must deliver payoffs that correspond to the coalitional Nash bargaining solution. We also characterize when an efficient and stationary equilibrium exists, which requires conditions that go beyond the nonemptiness of the core.     

The Mirrlees Approach to Mechanism Design with Renegotiation (with Applications to Hold‐up and Risk Sharing)

The paper studies the implementation problem, first analyzed by Maskin and Moore (1999), in which two agents observe an unverifiable state of nature and may renegotiate inefficient outcomes following play of the mechanism. We develop a first‐order approach to characterizing the set of implementable utility mappings in this problem, paralleling Mirrlees's (1971) first‐order analysis of standard mechanism design problems. We use this characterization to study optimal contracting in hold‐up and risk‐sharing models. In particular, we examine when the contracting parties can optimally restrict attention to simple contracts, such as noncontingent contracts and option contracts (where only one agent sends a message).     

MORAL HAZARD AND CAPITAL STRUCTURE DYNAMICS

We base a contracting theory for a startup firm on an agency model with observable but nonverifiable effort, and renegotiable contracts. Two essential restrictions on simple contracts are imposed: the entrepreneur must be given limited liability, and the investor's earnings must not decrease in the realized profit of the firm. All message game contracts with pure strategy equilibria (and no third parties) are considered. Within this class of contracts/equilibria, and regardless of who has the renegotiating bargaining power, debt and convertible debt maximize the entrepreneur's incentives to exert effort. These contracts are optimal if the entrepreneur has the bargaining power in renegotiation. If the investor has the bargaining power, the same is true unless debt induces excessive effort. In the latter case, a nondebt simple contract achieves efficiency—the noncontractibility of effort does not lower welfare. Thus, when the noncontractibility of effort matters, our results mirror typical capital structure dynamics: an early use of debt claims, followed by a switch to equity‐like claims. (JEL: D820, L140, O261)     

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)     

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.     

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.     

Stable and Coordinating Contracts for a Supply Chain with Multiple Risk‐Averse Suppliers

We analyze a decentralized supply chain with a single risk‐averse retailer and multiple risk‐averse suppliers under a Conditional Value at Risk objective. We define coordinating contracts and show that the supply chain is coordinated only when the least risk‐averse agent bears the entire risk and the lowest‐cost supplier handles all production. However, due to competition, not all coordinating contracts are stable. Thus, we introduce the notion of contract core, which reflects the agents' “bargaining power” and restricts the set of coordinating contracts to a subset which is “credible.” We also study the concept of contract equilibrium, which helps to characterize contracts that are immune to opportunistic renegotiation. We show that, the concept of contract core imposes conditions on the share of profit among different agents, while the concept of contract equilibrium provide conditions on how the payment changes with the order quantity.     

Moral Hazard Contracting and Private Credit Markets

This paper studies the impact of credit markets on optimal contracting, when the agent's “interim preference” over upcoming contracts is private information because personal financial decisions affect it via the wealth effect. The main result is a severe loss of incentive provision: equilibrium contracts invariably cause the agent to shirk (i.e., exert minimal effort) if the agent's private financial decision precedes moral hazard contracting. The basic intuition is that committing on another private variable, other than the effort level, exposes the parties to further exploitation of efficient risk‐sharing by relaxing the incentive constraint that was binding ex ante, unless the risk‐sharing was fully efficient to begin with.     

Optimal Contracts when Enforcement is a Decision Variable

This paper analyzes choice‐theoretic costly enforcement in an intertemporal contracting model with a differentially informed investor and entrepreneur. An intertemporal contract is modeled as a mechanism in which there is limited commitment to payment and enforcement decisions. The goal of the analysis is to characterize the effect of choice‐theoretic costly enforcement on the structure of optimal contracts. The paper shows that simple debt is the optimal contract when commitment is limited and costly enforcement is a decision variable (Theorem 1). In contrast, stochastic contracts are optimal when agents can commit to the ex‐ante optimal decisions (Theorem 2). The paper also shows that the costly state verification model can be viewed as a reduced form of an enforcement model in which agents choose payments and strategies as part of a perfect Bayesian Nash equilibrium.     

A Theory of the Firm with Non‐binding Employment Contracts

This paper examines an employment relation in which individual workers enjoy some bargaining power vis‐a‐vis the firm although they are not unionized. The main elements of the situations studied here are that the employment contracts are non‐binding across periods of production and that the firm has opportunities to replace workers. The paper analyzes a dynamic model in which the processes of contracting and recontracting between the firm and its workers are intertwined with the dynamic evolution of the firm's workforce. The analysis of the model is somewhat complicated because the employment level is a nondegenerate state variable that evolves over time and is affected by past decisions. The main analytical results characterize certain important equilibria: the profit maximizing and stationary equilibria. The unique stationary equilibrium is markedly inefficient: it exhibits inefficient over‐employment and the steady state wages coincide with the workers' reservation wage. It confirms earlier results derived by Stole and Zwiebel (1996a, b) in the context of a static model and shows that they are very robust even when the firm has nearly frictionless hiring opportunities. In contrast, in the profit maximizing equilibrium the outcome is nearly efficient and the wage exhibits a mark‐up over the reservation wage.     

Stability and Preference Alignment in Matching and Coalition Formation

We study matching and coalition formation environments allowing complementarities and peer effects. Agents have preferences over coalitions, and these preferences vary with an underlying, and commonly known, state of nature. Assuming that there is substantial variability of preferences across states of nature, we show that there exists a core stable coalition structure in every state if and only if agents' preferences are pairwise‐aligned in every state. This implies that there is a stable coalition structure if agents' preferences are generated by Nash bargaining over coalitional outputs. We further show that all stability‐inducing rules for sharing outputs can be represented by a profile of agents' bargaining functions and that agents match assortatively with respect to these bargaining functions. This framework allows us to show how complementarities and peer effects overturn well known comparative statics of many‐to‐one matching.     

Adverse Selection in Competitive Search Equilibrium

We study economies with adverse selection, plus the frictions in competitive search theory. With competitive search, principals post terms of trade (contracts), then agents choose where to apply, and they match bilaterally. Search allows us to analyze the effects of private information on both the intensive and extensive margins (the terms and probability of trade). There always exists a separating equilibrium where each type applies to a different contract. The equilibrium is unique in terms of payoffs. It is not generally efficient. We provide an algorithm for constructing equilibrium. Three applications illustrate the usefulness of the approach, and contrast our results with those in standard contract and search theory.     

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.     

基于讨价还价的私募基金机制比较研究

作为私募基金的主要形式，有限合伙制具有比公司制更高的激励作用，原因可能是两者在契约设计上的不同。本文引入讨价还价模型对公司制与有限合伙制进行分析，求解了两种机制下的均衡契约。研究发现，股东(或有限合伙人)和经理(或普通合伙人)之间的博弈等价于包含外部选择的讨价还价博弈，当经理保留收益不断提高，有限合伙制将逐步取代公司制。进一步地，有限合伙制将给出更高的分成比例，进而实现更高的激励，更有效地利用人力资本。     

Temporary Contracts,Employment Protection,and Collective Bargaining

This paper examines the effect of employment protection in a matching model with endogenous job destruction, collective bargaining, and two types of employment contracts. Using this framework, we show that (i) the impact on job creation and job destruction caused by reducing the firing costs associated with temporary jobs depends on the labour unions' bargaining strength and the gap in firing costs between contracts; (ii) reducing the firing costs associated with permanent jobs unambiguously decreases equilibrium unemployment if labour unions have strong bargaining power; and (iii) the impact caused by the firing costs differs between collective and individual bargaining.     

Provider-sponsored networks. Physicians organize for direct contracting

The Provider Service Network (PSN) concept is part of a wider movement by physicians to restructure for managed care to improve bargaining leverage for America's more than 600,000 active medical practitioners. Direct contracting has a simple appeal--no intermediaries. Imagine managed care contracts without the costs or hassles of an HMO or third-party intermediary. The PSN is a new form of managed care organization, but without the middleman. Savvy, self-insured employers, business coalitions, and government health programs are the potential "buyers." Doctors and hospitals are the "sellers," organizing provider networks on a regional and statewide basis. Up for grabs are over 225 million consumers whose health benefits are currently managed by insurance plans, HMOs, and third parties. This new marketplace of direct contracting may sound to doctors like the Garden of Eden, but there is plenty of opposition. PSNs will not become a national trend without a fight.     

力量不对等供应链中不同定价权下的契约选择

寄存契约为供应商管理库存运营模式中的一种,零售商偏好寄存契约从而把库存风险转移给供应商,而供应商则偏好传统模式从而不需承担库存风险.从批发价格的定价权出发,探讨力量不对等供应链中成员偏好某种契约的务件.分析在力量不对等的供应链中,当批发价格为外生批发价格,即批发价格由外部市场决定时,供应链中成员在传统模式和寄存契约下的决策问题,并分析外生批发价格的大小如何影响供应链中成员的契约选择;当批发价格为内生批发价格,即批发价格由供应链中强势方(零售商或供应商)决定时,分别分析供应链中成员在传统模式和寄存契约下的决策问题,并横向分析不同力量对比度的供应链中,供应链成员如何选择契约和供应链的最终运行模式,从而为供应链成员的运营模式选择提供一定的科学指导.     

售电侧改革、市场主体变化与电价红利:基于讨价还价博弈

本文通过构建“一对多”和“多对多”讨价还价博弈模型,研究了售电侧改革前后,发电商和售电公司之间关于消费者剩余分配的博弈过程。具体来说,文章从售电侧改革带来的博弈主体与博弈机制变化角度,揭示了售电侧改革对用户电价红利的影响。研究发现:售电侧放开后,电力市场交易机制由“一对多”竞价上网变为“多对多”讨价还价匹配,造成了售电侧博弈主体的议价能力下降,发电侧博弈主体相对议价能力上升。发电商群体将索取更多的消费者剩余,从而推动发电侧整体报价的上涨,挤压了售电侧的利润空间,导致售电公司被迫抬高市场电价,最终剥夺了用户的电价红利。研究揭示了售电侧改革未能带来电价下降的根本原因。