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.     

Reputational Bargaining and Deadlines

I highlight how reputational concerns provide a natural explanation for “deadline effects,” the high frequency of deals prior to a deadline in bargaining. Rational agents imitate the demands of obstinate behavioral types and engage in brinkmanship in the face of uncertainty about the deadline's arrival. I also identify how surplus is divided when the prior probability of behavioral types is vanishingly small. If behavioral types are committed to fixed demands, outcomes converge to the Nash bargaining solution regardless of agents' respective impatience. If behavioral types can adopt more complex demand strategies, outcomes converge to the solution of an alternating offers game without behavioral types for the deadline environment.     

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.     

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.     

Revisiting the relationship between ownership and control in international business operations: Lessons from transition economies

This article develops a conceptual model linking two interrelated dimensions of foreign business operations in transition economies: resources committed to the entry in terms of ownership, and resources committed to control the operations. The model outlines four types of foreign operations in transition economies: 1) arm's length contractor (low degree of foreign ownership and low level of foreign control over the operations); 2) hands-on contractor (low ownership and high control); 3) brand protector (high ownership and control); and 4) market share maximizer (high ownership and low control). These types are illustrated with examples of companies in four sectors of the Russian economy: metals, textiles, oil products, and beverages.We contribute to the literature on ownership and control in foreign operations, and their linkage to resource commitment at different stages of operations. In particular, we explicate situations characteristic of transition economies where ownership and control are not positively correlated. Moreover, we illustrate that the (financial) resources committed at the entry stage do not necessarily correlate with the managerial resources committed to the operations. For example, contractual collaborations in transition economies typically require few financial resources but more managerial resource commitment than in more developed market economies. On the other hand, operations with major commitment in the form of foreign equity investment may be managed autonomously by a local manager or a minority shareholder.     

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.     

Explaining the Desire for Local Bargaining: Evidence from a Finnish Survey of Employers and Employees

Abstract. This paper describes divergences in employers’ and employees’ opinions on the proper share of local bargaining in contract wage gains in Finland. Employers want the locally bargained wage share to be approximately half of the total wage rise, while the majority of employees would prefer this share to be in the region of 1–24 per cent. Employers in firms that are large, foreign owned or operate in the financial services industry desire the largest locally bargained share of contract wages. Employees in large firms, on the other hand, resist local bargaining. When the firm uses performance‐related pay, employees would prefer a large role for local bargaining in contract wage gains.     

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。     

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.     

Bargaining and Cooperation in Strategic Form Games

In this paper we view bargaining and cooperation as an interaction superimposed on a game in strategic form. A multistage bargaining procedure for N players, the “proposer commitment” procedure, is presented. It is inspired by Nash's two‐player variable‐threat model; a key feature is the commitment to “threats.” We establish links to classical cooperative game theory solutions, such as the Shapley value in the transferable utility case. However, we show that even in standard pure exchange economies, the traditional coalitional function may not be adequate when utilities are not transferable. (JEL: C70, C71, C78, D70)     

专利技术授权、生产外包与合同设计

专利授权及其授权协议是知识产权转化为现实生产力的关键。本文针对由一个专利技术提供商、一个品牌制造商和一个OEM组成的供应链,考虑市场需求信息不对称以及OEM存在规模经济效应,研究了专利技术提供商最优专利授权合同设计问题,考察了不对称信息、规模经济效应等因素对专利授权合同设计、供应链利润、消费者剩余和社会福利的影响。研究结果表明：在不对称信息下,专利技术提供商通过设计一组合同菜单可以有效甄别市场需求信息;OEM会有动机去提升其规模经济效应,但却不一定有利于其他供应链成员和消费者;不对称信息的存在会影响供应链成员企业的利润水平以及消费者剩余,并总是会导致供应链系统利润的损失,但若满足一定条件,则专利技术提供商与品牌制造商可以达成信息共享谈判,实现"双赢"。     

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.     

顾客策略行为下基于CVaR和回购契约的供应链决策模型

依据条件风险值CVaR度量准则,建立了顾客策略行为下基于回购契约的供应链决策模型,分析了集中式供应链系统和分散式供应链系统中,风险规避供应商和风险规避零售商的决策行为。在此基础上,通过理论求解和数值分析,进一步探讨了顾客策略行为、成员风险规避性和供应链回购契约的交互影响。主要研究结论如下:第一,当供应链成员均为风险规避时,价格承诺可成为顾客策略行为的完美应对策略;第二,最优回购价格受到零售商和供应商的风险规避度的共同影响,零售商的最优订货量随产品回购价格的增加而增加;第三,当且仅当零售商与供应商的风险规避度相当时,回购契约能够实现分散式供应链系统的协调和利润在不同成员间的任意分配,否则回购契约不能实现供应链利润在不同成员间的任意分配。第四,当供应链成员风险规避不等时,零售商的利润分成随顾客对产品估价的增加而增加。同时,风险规避度较小方需要出让部分利润给风险规避度较大方才能够保证契约的实施。     

实报还是谎报——双边信息激励与供应链效率

探讨了双边不对称信息下供应链信息真实分享和谎报对效率的影响。首先,给出完全信息下的最优商品交易量和供应链利润作为比较基准。其次,构建双方信息真实分享的激励模型。研究发现激励双方信息真实共享所需的信息租金降低交易量和供应链利润。再次,构建允许信息谎报的交易量谈判模型。研究发现,供销双方都偏好高报自己的信息类型。个体谎报信息的幅度随着谈判力增加而减小。拥有绝对谈判力的一方不会谎报信息。供应链效率与谎报信息的幅度、成本上界以及销售价格相关。最后,通过数值算例对实报信息和谎报信息下交易量、供应链个体利润及效率进行对比分析。研究结果为管理实践提供一定的洞见:供应链企业是否激励双边信息分享可根据双方成本大小进行选择。     

TRADE QUOTAS AND BUYER POWER,WITH AN APPLICATION TO THE E.U. NATURAL GAS MARKET

We consider a market in which domestic buyers negotiate contracts with foreign sellers, and explore how trade quotas can help to increase the buyers' countervailing power. We use the Shapley value to describe bargaining power and the distribution of the trade surplus in such a bilateral oligopoly. By exploiting strategic externalities among the buyers, bilateral trade quotas can improve the buyers' bargaining positions. In contrast, aggregate trade restrictions on all buyers' trade never improve buyer surplus. Minimum quotas on imports from fringe suppliers can benefit nonaffected buyers, as these enjoy positive externalities. We apply these insights to the E.U. market for natural gas and show that the effects of trade quotas on E.U. gas importers' power can be significant.     

On the Limitations of Redundancies in the Improvement of System Reliability

Some program managers share a common belief that adding a redundant component to a system reduces the probability of failure by half. This is true only if the failures of the redundant components are independent events, which is rarely the case. For example, the redundant components may be subjected to the same external loads. There is, however, in general a decrease in the failure probability of the system. Nonetheless, the redundant element comes at a cost, even if it is less than that of developing the first one when both are based on the same design. Identical parts save the most in terms of design costs, but are subjected to common failure modes from possible design errors that limit the effectiveness of the redundancy. In the development of critical systems, managers thus need to decide if the costs of a parallel system are justified by the increase in the system's reliability. NASA, for example, has used redundant spacecraft to increase the chances of mission success, which worked well in the cases of the Viking and Voyager missions. These two successes, however, do not guarantee future ones. We present here a risk analysis framework accounting for dependencies to support the decision to launch at the same time a twin mission of identical spacecraft, given incremental costs and risk-reduction benefits of the second one. We illustrate this analytical approach with the case of the Mars Exploration Rovers launched by NASA in 2003, for which we had performed this assessment in 2001.     

消费者退货对在线零售商促销与合同设计的影响研究

针对由制造商和在线零售商组成的供应链系统，在存在消费者退货情形下，考虑在线零售商在线上渠道提供促销与退款保证服务，其中在线零售商促销成本为其私有信息，建立了信息不对称下的供应链博弈模型，研究了在线零售商的最优促销策略与供应链合同设计问题；进而分析了不对称信息对供应链均衡的影响，考察了退款保证对供应双方期望利润、信息价值以及消费者剩余的影响。研究发现，当制造商在决策合同参数（设计合同）时，需要在在线零售商信息租金与供应链系统绩效损失之间进行权衡；若满足一定条件，制造商和在线零售商之间进行谈判并能够实现信息共享而分享整个系统的利润；当退货产品总是会给供应链成员造成损失时，退款保证会导致制造商和零售商期望利润的损失，但在一定条件下却能提升消费者剩余。     

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.