On the implementation of the L-Nash bargaining solution in two-person bargaining games

The “Nash program” initiated by Nash (Econometrica 21:128–140, 1953) is a research agenda aiming at representing every axiomatically determined cooperative solution to a game as a Nash outcome of a reasonable noncooperative bargaining game. The L-Nash solution first defined by Forgó (Interactive Decisions. Lecture Notes in Economics and Mathematical Systems, vol 229. Springer, Berlin, pp 1–15, 1983) is obtained as the limiting point of the Nash bargaining solution when the disagreement point goes to negative infinity in a fixed direction. In Forgó and Szidarovszky (Eur J Oper Res 147:108–116, 2003), the L-Nash solution was related to the solution of multiciteria decision making and two different axiomatizations of the L-Nash solution were also given in this context. In this paper, finite bounds are established for the penalty of disagreement in certain special two-person bargaining problems, making it possible to apply all the implementation models designed for Nash bargaining problems with a finite disagreement point to obtain the L-Nash solution as well. For another set of problems where this method does not work, a version of Rubinstein’s alternative offer game (Econometrica 50:97–109, 1982) is shown to asymptotically implement the L-Nash solution. If penalty is internalized as a decision variable of one of the players, then a modification of Howard’s game (J Econ Theory 56:142–159, 1992) also implements the L-Nash solution.     

Solutions for some bargaining games under the Harsanyi-Selten solution theory,part I: Theoretical preliminaries

Part I of this paper discusses the problem of how to model bargaining behavior, and outlines a few basic ideas of the Harsanyi-Selten solution theory. In particular, we discuss removal of imperfect equilibrium points from the game by using the uniformly perturbed game form. We also describe definition of the solution in terms of payoff-dominance and risk-dominance relations, and in terms of the net strategic distances, between the primitive equilibrium points. Part II of the paper will discuss the actual solutions our theory provides for some important classes of bargaining games.     

Nash refinement of equilibria

A method for choosing equilibria in strategic form games is proposed and axiomatically characterized. The method as well as the axioms are inspired by the Nash bargaining theory. The method can be applied to existing refinements of Nash equilibrium (e.g., perfect equilibrium) and also to other equilibrium concepts, like correlated equilibrium.The authors thank the reviewers for their comments, which led to an improvement of the paper.     

On the value of information sharing and cooperative price setting

We consider a setting of two firms that sell substitutable products under price competition. We show that private signals enable firms to improve market forecast and earn higher profits. Provided that their private signals are not perfectly correlated, firms can benefit from sharing signals with each other. This is irrespective of product substitutability. Moreover, information sharing is a strategic complement to cooperative price setting to improve the profit performance of firms.     

Sufficient conditions for Nash bargaining in differential games

Sufficient conditions for Nash bargaining in differential games are given. These conditions are compared with the sufficient conditions given by Liu (Ref. 1).     

考虑损失厌恶行为与谈判破裂的Rubinstein谈判博弈研究

本文考虑具有损失厌恶行为与破裂风险的Rubinstein谈判博弈。首先构建子博弈完美均衡,并证明子博弈完美均衡的存在性及唯一性。然后分析子博弈完美均衡的性质,结果表明:参与人受益于对手的损失厌恶行为,而因自身具有损失厌恶行为遭受损失;谈判破裂概率对均衡结果的影响取决于贴现因子与参与人的损失厌恶系数;当谈判破裂的概率趋于零时,极限均衡结果收敛于经典的Rubinstein谈判博弈结果。最后建立了与非对称Nash谈判解的关系,其中参与人的议价能力与自身的损失厌恶水平呈负相关性,与对手的损失厌恶水平呈正相关性;参与人的议价能力依赖于谈判破裂概率与出价时间间隔的比值。     

基于CAPM框架下的创业企业风险资本融资契约设计

从组合的视角出发,考虑创业企业家的风险厌恶程度,通过等价利率将创业企业的风险资本融资契约适应到CAPM框架下,利用纳什议价解刻画双方在信息不对称下的均衡解,基于风险-收益的角度建立了最优融资契约设计模型,为创业企业融资提供了契约设计和风险资本类型选择的一个依据,并通过算例说明了模型的可行性。研究还表明,创业企业引入风险资本优于纯债务融资,而股权的分配则取决于双方的议价力。同时,风险厌恶程度越低的创业企业家越趋向于选择独立的风险投资机构;风险厌恶程度越高的创业企业家越趋向于选择公司背景的风险投资机构;而风险厌恶程度不高,考虑后期贷款的创业企业家则趋向于选择银行背景的风险投资机构。     

考虑不公平厌恶偏好与议价能力的交替出价谈判博弈研究

对Fehr和Schmidt的不公平厌恶模型进行修正,考虑议价能力的影响,以Nash谈判解作为参与人的公平参考水平,研究参与人具有不公平厌恶偏好的Rubinstein谈判博弈问题。构建子博弈完美均衡,并在其满足无延迟和稳定性两个性质的条件下,证明该子博弈完美均衡的唯一性,分析子博弈完美均衡的性质。结果表明:当两个参与人的均衡报价使得最先提出报价的参与人的份额低(或高)于其公平参考水平时,该参与人的收益与参与人的不公平厌恶偏好呈正(或负)相关关系;较高的议价能力可能对参与人不利;当两次连续出价之间的时间间隔趋于零时,参与人的均衡份额取决于两个参与人贴现率的比值。     

A bargaining approach to coordination in networks

This paper, presents a model in which players interact via the formation of costly links and the benefits of bilateral interactions are determined by a stag-hunt game. A novel contribution of this paper is that the fraction of the cost borne by each player involved in a bilateral link is not fixed exogenously, but results from bargaining. We analyze the model both in a static and a dynamic setting. Whereas the static game has multiplicity of equilibria, we show that only one is stochastically stable. This is a revised version of Chapter 1 of my Ph.D. Thesis presented at Universidad de Alicante. A previous version of this paper circulated with the title “Network Formation and Coordination: Bargaining the Division of Link Costs” (IVIE WP-AD 2002-27). I am indebted to Fernando Vega-Redondo for many helpful conversations, suggestions and encouragement. I am grateful to Julio González-Díaz, Antonio J. Morales, Ascensión Andina-Díaz and the Associate Editor for valuable suggestions. I also thank Jordi Brandts, Antonio Cabrales, Angel Hernando, Andrea Galeotti, Sanjeev Goyal, Christoph Kuzmics, Ana Lozano-Vivas, Paola Manzini, Juan Mora, Efe Ok, Juana Santamaría-García and José A. Silva for their comments. I gratefully acknowledge the hospitality of New York University, where part of this research was carried out, and the financial support from the Spanish Ministry of Education (ref. BEC2002-02852).     

The partition bargaining problem

Consider the problem of partitioning n items among d players where the utility of each player for bundles of items is additive; so, player r has utility for item i and the utility of that player for a bundle of items is the sum of the 's over the items i in his/her bundle. Each partition S of the items is then associated with a d-dimensional utility vector V^S whose coordinates are the utilities that the players assign to the bundles they get under S. Also, lotteries over partitions are associated with the corresponding expected utility vectors. We model the problem as a Nash bargaining game over the set of lotteries over partitions and provide methods for computing the corresponding Nash solution, to prescribed accuracy, with effort that is polynomial in n. In particular, we show that points in the pareto-optimal set of the corresponding bargaining set correspond to lotteries over partitions under which each item, with the possible exception of at most d(d-1)/2 items, is assigned in the same way.     

A dynamic solution in N-person cooperative game theory

We formulate a cooperative game as an extended form game in which each player in turn proposes payoffs to a coalition over M steps. Payoffs at time t are discounted by a penalty function f(t). If all players in a coalition agree to their payoffs, they receive them. Under a convergence hypothesis verified by computer for three players in many cases, we compute the payoffs resulting from a coalition pattern and give necessary conditions for particular patterns. The resulting solution is related to the Nash bargaining solution and the competitive solution.     

公平偏好下基于回购契约的供应链协调模型

在报童模型的基础上,以一个供应商和一个零售商组成的两级供应链为研究背景,把公平关切引入到回购契约的研究中,并根据Nash讨价还价博弈思想建立公平偏好框架,通过建立效用函数模型,研究了公平关切对回购契约的影响．研究发现,公平关切不会影响回购契约的协调性,公平关切程度也不会影响零售商的最优订购量,进而可以得出,即使供应商在不知道零售商对公平偏好的程度下,依然可以通过制定合适的批发价格和回购价格来做出使自己效用最大化的最优决策．另外,通过灵敏度分析发现,在公平关切时,零售商的最优订购量会随着产品单位生产成本的增加而增加．     

Economic planning based on social preference functions

We argue that the most desirable social welfare functions for practical use (here sometimes called social preference functions) are those determined by Σ_ilog(u_i(x)?α) where u_i(x) is the utility of alternative x to individual i and α is the minimum standard of living decided upon by the society.     

Time-consistent mean–variance hedging of longevity risk: Effect of cointegration

This paper investigates the time-consistent dynamic mean–variance hedging of longevity risk with a longevity security contingent on a mortality index or the national mortality. Using an HJB framework, we solve the hedging problem in which insurance liabilities follow a doubly stochastic Poisson process with an intensity rate that is correlated and cointegrated to the index mortality rate. The derived closed-form optimal hedging policy articulates the important role of cointegration in longevity hedging. We show numerically that a time-consistent hedging policy is a smoother function in time when compared with its time-inconsistent counterpart.