一种不完全信息相互威慑讨价还价模型

理性威慑理论将相互威慑看作是一种讨价还价过程，但鲁宾斯坦经典讨价还价模型无法直接用于相互威慑讨价还价研究。本文将不完全信息引入相互威慑讨价还价之中，探讨了相互威慑中博弈方单边不完全信息和双边不完全信息条件下的威慑可信性与冲突可能性。     

三方相互体谅讨价还价模型

对于较重要的三方合作利益分配博弈问题,将相互体谅作为基本遵循并基于适应性预期模型,建立三方相互体谅讨价还价模型.运用这个模型,可以把三方相互体谅讨价还价达成均衡,归结为单调有界数列收敛与常系数非齐次线性差分方程组求解的结合运用.三方相互体谅讨价还价属于不完全信息动态合作博弈.对模型求解,一般地揭示三方相互体谅讨价还价达成均衡的过程与结果,阐明讨价还价有满足初始条件的唯一解和充要条件,以及充要条件的经济含义和数学意义.三方相互体谅讨价还价模型是对于两方相互体谅讨价还价模型的拓展,可以为建立更多方相互体谅讨价还价模型提供借鉴.     

基于进化博弈方法的相互威慑稳定性分析

在危机管理和冲突分析中,力量对等冲突方之间的相互威慑是否具有稳定性问题,一直存在疑义。本文基于进化博弈论视野,给出了直接求解3×3和4×4鹰—鸽博弈扩展模型进化稳定策略ESS(EvolutionaryStableStrategy)的方法,画出了3×3鹰—鸽扩展博弈的相位图,得出了威慑策略是进化稳定策略的结论,从而对上述问题进行了有说服力的解释。     

基于Rubinstein讨价还价博弈的农地流转价格研究

针对农地流转市场存在双边信息不对称议价的现实,基于Rubinstein讨价还价博弈刻画了农地流转双方的议价过程,根据子博弈精炼纳什均衡得到了均衡流转价格,最后利用有关数据进行了算例分析.研究发现:均衡流转价格与流入方议价能力负相关、与流出方议价能力正相关;在流出方先出价的不完全信息讨价还价博弈中,当流出方对流入方的策略空间了解的越准确,或者流入方对流出方的策略空间了解的越少时,均衡交易价格越高;另外,流转双方的心理预期价格越高,均衡交易价格也越高.将流转双方的讨价还价过程、信息结构、破裂点纳入到农地流转价格的研究,既兼顾了流出方和流入方的利益,为双方谈判和议价提供了理论上的指导,也为农地流转价格的研究提供了新的视角.     

供应商竞争下的供应链多边谈判

探讨了单买方多供应商基于供应链利润分配的多边谈判,其中的供应商具有不同讨价还价力.多边谈判程序为买方与单个供应商轮流进行双边谈判.此种情形下,供应商参与双边谈判的顺序影响供应商所获谈判利润,同时基于讨价还价力供应商通过向买方支付排位费用竞争双边谈判位置.结果给出了供应商竞争下多边谈判的唯一均衡,以及均衡状态下各方所获利润.本文构建了供应商讨价还价力不同情形下供应链多边谈判分析框架,并指出讨价还价力的不同使能力强的供应商通过竞争双边谈判位置而获利.     

能源经济环境冲突中利益相关者的博弈分析——以能源重镇宁波市镇海区为例

当前城市冲突之一表现在能源经济环境利益各方的争执上,以可持续发展为根本理念,如何实现三者的协调发展已经成为人们关注的焦点问题.为此,围绕宁波市镇海发电厂、当地市民和当地政府的三方利益冲突,分别构建了单策略和多策略的冲突博弈模型,其中多策略又分为发电厂技术升级和搬迁为导向的冲突博弈模型,并用GMCR_Ⅱ软件求解模型的最强纳什均衡解.模型的计算结果符合三方博弈的实际情况,体现出当地政府注重民生和环境的同时,通过搬迁镇海电厂、技术升级改造,促进当地经济的发展.研究结果对我国能源重镇在能源经济环境冲突中的决策具有一定的指导意义.     

“讨价还价”的“纳什解”的形成路径与结论拓展

建立了一个"讨价还价"的双边适应性预期模型,并利用这个模型的二元常系数线性差分方程组,揭示"纳什讨价还价解"的形成路径.对于不是"纳什讨价还价解"的一般讨价还价的成交结果,同样可以运用这样一个模型来揭示.基于这个模型,当买、卖双方希望成交,各方的出价通过逐次调整会最终收敛到同一个常数,因此能够从理论上保证讨价还价最终成交.双方当中有一方不肯让价而成交的情形,可以作为这个模型退化成为单边适应性预期模型的情形.举例计算说明了一个讨价还价问题的收敛过程与结果.     

碳减排政策下多周期供应链网络均衡决策

为研究碳减排政策对多周期供应链网络均衡决策的影响,分析了供应链网络结构中各层的最优条件,建立了多周期碳减排供应链网络均衡模型.首先将其转化为等价的变分不等式问题,然后利用变分不等式的投影收缩算法进行求解.并通过模型仿真分析了在不同周期下不同碳限额、单位碳排放量对供应链网络均衡的影响结果发现企业在环境绩效和经济绩效之间存在冲突,适当的控制碳税和调整产品的单位碳排放量可以缓解这种冲突.同时,政府对于碳限额的值过于宽松,对于碳减排的实施起不到明显作用.     

运输问题的合作对策求解方法

产地间或销地间往往存在竞争,在这种情况下,使用运输问题最优化方法是不合理的。因此,从个体理性的视角提出运输问题的合作对策求解方法,方法将运输问题看作是一个博弈问题,各个产地或销地是博弈的局中人,求解其纳什均衡与纳什讨价还价解。在此基础上,说明了运输问题的非合作形式是一个指派问题,并证明指派问题的最优解是一个纳什均衡点。接着,通过实验验证运输问题的最优解是一个纳什讨价还价解,满足产地或销地的自身利益。在此基础上,针对纳什讨价还价解不唯一的问题,从决策者的视角给出最大可能激励成本的计算方法。最后,为弥补纳什讨价还价解不唯一及纳什讨价还价解不允许出现子联盟的缺陷,给出运输收益分配或成本分摊的Shapely值计算方法。     

基于博弈论的小煤矿安全问题分析

安全事故频繁发生是我国小煤矿的现状和特点.文章从小煤矿的内部管理、政府监管及矿工举报三个方面入手,分析了小煤矿安全监管体系中由于行为原因而引起的问题,从而建立了小煤矿安全监管体系中基于监管部门、小煤矿及矿工三方之间的两两博弈模型.并根据博弈模型的纳什均衡解得出能使三方达到均衡并可加强安全监管的几点政策建议.     

The price of fairness with the extended Perles–Maschler solution

In Nash bargaining problem, due to fairness concerns of players, instead of maximizing the sum of utilities of all players, an implementable solution should satisfy some axioms or characterizations. Such a solution can result in the so-called price of fairness, because of the reduction in the sum of utilities of all players. An important issue is to quantify the system efficiency loss under axiomatic solutions through the price of fairness. Based on Perles–Maschler solution of two-player Nash bargaining problem, this paper deals with the extended Perles–Maschler solution of multi-player Nash bargaining problem. We give lower bounds of three measures of the system efficiency for this solution, and show that the lower bounds are asymptotically tight.     

An attrition game on an acyclic network

This paper deals with noncooperative games in which two players conflict on a network through an attrition phenomenon. The associated problem has a variety of applications, but we model the problem as a military conflict between an attacker and a defender on an acyclic network. The attacker marches from a starting node to a destination node, expecting to keep his initial members untouched during the march. The defender deploys his forces on arcs to intercept the attacker. If the attacker goes through an arc with deployed defenders, the attacker incurs casualties according to Lanchester’s linear law. In this paper, we discuss two games having the number of remaining attackers as the payoff and propose systems of linear programming formulations to derive their equilibrium points. One game is a two-person zero-sum (TPZS) one-shot game with no information and the other is a TPZS game with two stages separated by information acquisition about players’ opponents.     

Sequential share bargaining

This paper presents a new extension of the Rubinstein-St?hl bargaining model to the case with n players, called sequential share bargaining. The bargaining protocol is natural and has as its main feature that the players’ shares in the surplus are determined sequentially rather than simultaneously. The protocol also assumes orderly voting, a restriction on the order in which players respond to a proposal. The bargaining protocol requires unanimous agreement for proposals to be implemented. Unlike all existing bargaining protocols with unanimous agreement, the resulting game has unique subgame perfect equilibrium utilities for any value of the discount factor. The result builds on the analysis of so-called one-dimensional bargaining problems. We show that also one-dimensional bargaining problems have unique subgame perfect equilibrium utilities for any value of the discount factor.     

Divide the dollar and conquer more: sequential bargaining and risk aversion

We analyze the problem of dividing a fixed amount of a single commodity between two players on the basis of the Nash bargaining solution (NBS). For one-shot negotiations, a cornerstone result of Roth (Axiomatic models of bargaining. Springer, Berlin, 1979) establishes that the more risk averse player will obtain less than half the total amount. In the present paper, we assume that the bargaining procedure occurs over several rounds. In each round, an increasing share of the total amount is negotiated over in accordance with the NBS, the disagreement point being determined by the outcome of the previous round. In line with Roth’s result, the final amount received by the more risk averse player is still bounded by half the total amount. As a new feature, however, this player does not lose from bargaining for more rounds if his opponent exhibits non-increasing absolute risk aversion. What is more, both players’ risk profiles become essentially irrelevant if successive bargaining takes place over sufficiently small commodity increments. Each player then gets approximately half of the commodity.     

A bargaining game model for measuring performance of two-stage network structures

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs), where the internal structures of DMUs are treated as a black-box. Recently DEA has been extended to examine the efficiency of DMUs that have two-stage network structures or processes, where all the outputs from the first stage are intermediate measures that make up the inputs to the second stage. The resulting two-stage DEA model not only provides an overall efficiency score for the entire process, but also yields an efficiency score for each of the individual stages. The current paper develops a Nash bargaining game model to measure the performance of DMUs that have a two-stage structure. Under Nash bargaining theory, the two stages are viewed as players and the DEA efficiency model is a cooperative game model. It is shown that when only one intermediate measure exists between the two stages, our newly developed Nash bargaining game approach yields the same results as applying the standard DEA approach to each stage separately. Two real world data sets are used to demonstrate our bargaining game model.     

Relative impatience determines preference between contract bargaining and repeated bargaining

In this paper we consider the effect of the `impatience ratio' I (of the worker discount factor to the firm discount factor) on the preferences of the players between two bargaining schemes in an asymmetric information wage bargaining context. The firm has private information about the worker's value and the worker makes wage demands. In the contact bargaining scheme, a wage demand which is accepted in one period is binding for all future periods (and hence the bargaining ends after acceptance of a wage demand). In the repeated bargaining scheme, the parties continue to bargain irrespective of whether the worker has been hired or not, and any accepted wage demand is only valid for the period in which it was accepted. We establish the following results under the assumption that the worker's value is uniformly distributed on an interval: When the firm is more patient than the worker (I<1) both parties prefer contract bargaining, and when the worker is more patient than the firm (I >1) both prefer repeated bargaining. For any value of I, the preferred type of bargaining gives the lower unemployment.  The work of Bae has already shown that when players are equally patient (I=1) the players are indifferent between the two schemes, regardless of the distribution of the worker's value. This paper shows that Bae's indifference result (Bae, 1991) cannot be extended to unequally patient players. Received: December 1996/Final version: October 1998     

Three-person multi-objective conflict decision in reservoir flood control

Reservoir flood control decisions are often compromised by various parties with conflicting benefits. In this paper, a three-person multi-objective conflict decision model is presented for reservoir flood control. In order to obtain the group decision, the ideal bargaining solution is first sought by two stages satisfying programming and then the decision alternative is chosen using the fuzzy pattern recognition. The advantages of this model are simple and more adaptable to the real problem. The model is demonstrated by application to Fengman Reservoir in China.     

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。     

Collusive game solutions via optimization

A Nash-based collusive game among a finite set of players is one in which the players coordinate in order for each to gain higher payoffs than those prescribed by the Nash equilibrium solution. In this paper, we study the optimization problem of such a collusive game in which the players collectively maximize the Nash bargaining objective subject to a set of incentive compatibility constraints. We present a smooth reformulation of this optimization problem in terms of a nonlinear complementarity problem. We establish the convexity of the optimization problem in the case where each player's strategy set is unidimensional. In the multivariate case, we propose upper and lower bounding procedures for the collusive optimization problem and establish convergence properties of these procedures. Computational results with these procedures for solving some test problems are reported. It is with great honor that we dedicate this paper to Professor Terry Rockafellar on the occasion of his 70th birthday. Our work provides another example showing how Terry's fundamental contributions to convex and variational analysis have impacted the computational solution of applied game problems. This author's research was partially supported by the National Science Foundation under grant ECS-0080577. This author's research was partially supported by the National Science Foundation under grant CCR-0098013.