3层供应链VMI集成的短期效果与博弈分析

提出了S-F-R型3层供应链的VMI集成策略,并将DONG等的单层VMI模型扩展到S-F-R型3层供应链(2级VMI)上,分析了S-F-R型3层供应链VMI集成在短期内的实施效果。此外,进一步讨论了S-F-R型3层供应链的VMI联盟博弈核心的存在性,从而证实了各方均可接受的收益分配方案是存在的,并且供应链各方所结成的VMI联盟是稳定的。     

基于合作博弈模型的公共河流水资源分配方案研究

水资源的稀缺性使得公共河流的水资源分配问题中存在着各种冲突与矛盾。为了确定公共河流流经的各用水主体之间分配水资源的合理方案，本文建立具有外部性的合作博弈模型来分析公共河流流经的各用水主体之间在竞争与合作并存情况下的水资源分配问题。使用动态博弈的方法来确定联盟之间通过竞争产生的均衡水资源分配量，然后在各联盟之内通过Nash协商的方式来分配联盟的均衡水资源分配量，比较各种方案下用水主体产生的总效用，进而得到公共河流用水主体之间竞争与合作并存时的最优水资源分配方案和各用水主体之间形成联盟的具体形式。研究表明：受到外部性环境的影响，公共河流用水主体之间部分合作可能比完全合作产生更大的总效用，合作与竞争并存时的最优分配方案优于完全合作时的最优分配方案。     

碳交易机制下零售商合作的费用分配研究

在一个由单供应商和多个零售商组成的二阶供应链中，研究碳交易机制下多零售商合作的订货决策问题。对完全信息下零售商合作的费用分配问题，应用合作博弈理论建立了费用分配的博弈模型，证明了博弈为子模博弈且设计了属于核心的费用分配方案，该方案不仅可通过总体单调分配机制实现而且可使大联盟长远稳定。对不完全信息下零售商合作的费用分配问题，证明了纯策略纳什均衡的存在性。研究结果表明，零售商的合作不仅能降低总费用，而且能降低碳排放量；各零售商在不完全信息下分担的费用大于完全信息下分担的费用。     

模糊合作对策的Shapley值

考虑合作对策中支付函数是模糊数的情形,利用模糊数学相关理论,对Shapley提出的三条公理进行拓广,并构造了模糊Shapley值.针对局中人在合作完成后需要对具体的联盟收益进行分配的情况,文中利用构造的模糊Shapley值隶属函数给出了确定的收益分配方案.最后将该方法应用到动态联盟伙伴企业收益分配的实例中.     

Duality Approaches to Economic Lot‐Sizing Games

Sharing common production, resources, and services to reduce cost are important for not for profit operations due to limited and mission‐oriented budget and effective cost allocation mechanisms are essential for encouraging effective collaborations. In this study, we illustrate how rigorous methodologies can be developed to derive effective cost allocations to facilitate sustainable collaborations in not for profit operations by modeling the cost allocation problem arising from an economic lot‐sizing (ELS) setting as a cooperative game. Specifically, we consider the economic lot‐sizing (ELS) game with general concave ordering cost. In this cooperative game, multiple retailers form a coalition by placing joint orders to a single supplier in order to reduce ordering cost. When both the inventory holding cost and backlogging cost are linear functions, it can be shown that the core of this game is non‐empty. The main contribution of this study is to show that a core allocation can be computed in polynomial time under the assumption that all retailers have the same cost parameters. Our approach is based on linear programming (LP) duality. More specifically, we study an integer programming formulation for the ELS problem and show that its LP relaxation admits zero integrality gap, which makes it possible to analyze the ELS game by using LP duality. We show that there exists an optimal dual solution that defines an allocation in the core. An interesting feature of our approach is that it is not necessarily true that every optimal dual solution defines a core allocation. This is in contrast to the duality approach for other known cooperative games in the literature.     

非合作-合作两型博弈的Shapley值纯策略纳什均衡解求解方法

在合作中又有竞争的"经济全球化"时代背景下,经济实体之间越来越多地体现出竞争与合作交织的特点,既有策略的选择,同时也有利益的分配或者成本的分摊,即竞争与合作相互联系。为此,Brandenburger和Stuart提出了非合作-合作两型博弈模型为这类博弈提供了有效的工具。目前非合作-合作两型博弈研究较少,且Brandenburger和Stuart提出的非合作-合作两型博弈存在一些不足：合作博弈用核心求解可能为空或者不唯一。Shapley值是一种重要的合作博弈单值解,满足匿名性、有效性、可加性和虚拟性,表达形式简单且唯一,对一些成本分摊问题和利益分配问题,给决策者提供了一个公平满意的分配方案。因此本文研究将Shapley值作为合作博弈的解时非合作-合作两型博弈解存在的条件。为了分析本文提出的基于Shapley值的非合作-合作两型博弈的新理论框架,首先给出了其特征函数满足的联盟无外部性条件。在满足此条件下,我们进一步证明了非合作-合作两型博弈解存在的条件及性质。结合数值实例比较分析合作博弈用核心和Shapley值求解非合作-合作两型博弈解的优缺点。研究表明：当用Shapley值求解合作博弈解,降低了非合作-合作两型博弈解存在条件。因此,本文的研究不仅弥补了Brandenburger和Stuart提出的非合作-合作两型博弈中合作博弈的核心为空或者不唯一的情况,而且为非合作-合作两型博弈的解提供新的理论框架,从而为既有竞争又有合作的博弈问题提供新的求解方法,因此,本文的研究具有一定的理论价值和应用价值。     

Coalition Formation and Cost Allocation for Joint Replenishment Systems

This paper focuses on the issues of coalition formation and cost allocation in a joint replenishment system involving a set of independent and freely interacting retailers purchasing an item from one supplier to meet a deterministic demand. The papers dealing with this problem are mainly focused on supperadditive games, where the cost savings associated with a coalition increase with the number of players in the coalition. The most relevant question addressed then is how to allocate the savings to the players. In this paper, we propose to go further by dealing with a non‐supperadditive game, where a set of independent retailers have the common understanding to share the cost savings according to the cost‐based proportional rule. In this setting, the global cost optimization is no longer a relevant approach to identify appealing coalitions for any retailer. Here, we provide an iterative procedure to form the so‐called efficient coalition structure and we show that this coalition structure has the nice properties of being (i) weakly stable in the sense of the coalition structure core and (ii) strongly stable under a given assumption. An exact fractional programming based solution is also given to generate such efficient coalitions.     

Harsanyi power solution for games with restricted cooperation

This paper discusses the Harsanyi power solution for cooperative games in which cooperation among players is based on an arbitrary collection of feasible coalitions. We define the Harsanyi power solution as a value which distributes the Harsanyi dividends such that the dividend shares of players in each feasible coalition are proportional to the corresponding players’ participation index, (i.e., a power measure for players in the cooperation restrictions). When all coalitions can be formed in a game, the Harsanyi power solution coincides with the Shapley value. We provide two axiomatic characterizations for the Harsanyi power solution: one uses component efficiency and participation fairness, and the other uses efficiency and participation balanced contributions. Meanwhile, we show that the axioms of each axiomatization are logically independent. The study also shows that the Harsanyi power solution satisfies several other properties such as additivity and inessential player out. In addition, the Harsanyi power solution is the unique value that admits the \(\lambda \)-potential.     

Multiperson Bargaining and Strategic Complexity

We investigate the effect of introducing costs of complexity in the n‐person unanimity bargaining game. As is well‐known, in this game every individually rational allocation is sustainable as a Nash equilibrium (also as a subgame perfect equilibrium if players are sufficiently patient and if n & 2). Moreover, delays in agreement are also possible in such equilibria. By limiting ourselves to a plausible notion of complexity that captures length of memory, we find that the introduction of complexity costs (lexicographically with the standard payoffs) does not reduce the range of possible allocations but does limit the amount of delay that can occur in any agreement. In particular, we show that in any n‐player game, for any allocation z, an agreement on z at any period t can be sustained as a Nash equilibrium of the game with complexity costs if and only if t≤n. We use the limit on delay result to establish that, in equilibrium, the strategies implement stationary behavior. Finally, we also show that ‘noisy Nash equilibrium’ with complexity costs sustains only the unique stationary subgame perfect equilibrium allocation.     

The influence of mutations: an evolutionary inspection game with three strategic actors

Suboptimal business decisions lead to corporate cost increases. The basis of the following study is a game theoretical model of Fandel and Trockel (Eur J Oper Res 226:85–93, 2013a), which analyses the relationship between bonuses and financial penalties in a three-person inspection game and the measures that counteract suboptimal decisions. In the present article we investigate from evolutionary perspectives whether the strategic behaviour of the actors described in an inspection game can be invaded by mutants and what risks emerge as a result. In a first step each of the three decision variables of the players will be discussed. It will become apparent that corporate optimal behaviour is realised when the actions of the business management or the controlling department are fixed. In a second step it will be shown that in games with three strategic variables mutations can undermine the solutions. In a third step we will investigate the model in consideration of monotonic payment and monotonic positive payment functions and divide the area of the solutions into octants to which we will allocate the influence of the mutations and demonstrate the circumstances under which a solution tending towards optimal corporate behaviour can be generated.     

基于M型组织结构的企业内部激励机制与兼并效应

在寡头竞争环境下,引入企业内部激励机制激励参数变量,建立了一个替代性产品M型制下企业兼并二阶段Cournot竞争博弈模型:第一阶段,兼并企业采用M型制并选择基于利润和销售收入内部激励机制的激励参数;在第二阶段,兼并后各企业的决策者根据企业提供的内部激励机制进行产量竞争。在此基础上,分析了兼并对各企业利润、产量与价格带来的影响。证明对于替代性产品行业,存在一个兼并临界规模(1)只有当兼并规模小于临界规模时,兼并企业才适合采用M型组织结构;且企业普遍存在兼并动机,产品替代化程度越高,兼并动力越大;(2)当兼并企业采用M型组织结构且兼并规模小于临界规模时,兼并对外部企业产生负外部性,但对消费者带来有利影响。本文还进一步讨论了兼并企业采用M型组织结构时内部激励机制激励参数的选择问题,证明激励参数受行业利润率、兼并规模与产品替代性程度的影响。     

基于Choquet延拓n人模糊对策的Shapley值

由于n人对策任意联盟可由它的特征向量来等价地表示,利用Choquet积分,将n人对策从集合{0,1}n延拓到[0,1]n上,通过建立公理化体系,对具有Choquet延拓形式n人模糊对策的Shapley值进行深入研究,证明了这类n人模糊对策Shapley值存在性与惟一性,并给出了此模糊对策Shapley值的解释表达式.最后将此模糊对策的Shapley值作为收益分配方案应用到供应链协作企业收益分配的实例中.     

基于Agent和进化博弈的服务商动态联盟协同管理策略研究

基于进化博弈理论,实现了用于服务商动态联盟协同管理工作的多智能体模拟系统,并进行模拟数据分析。扩展传统对称静态博弈为含惩罚参数和协同效率参数的离散进化博弈情形,设计一种含历史信息和近邻特征的群体进化学习规则;在Repast基础上,用java编程实现了多加盟企业进化博弈Agent模拟系统并进行分析。结果表明:agent规模数对平均收益影响小,具有不同决策特征的agent的比例分布能改变企业的平均收益,不同协同率、沟通方式和惩罚参数对期望收益有影响。为电子商务和移动商务环境下的动态联盟管理决策提供参考。     

Penalizing passenger’s transfer time in computing airlines revenue

Airline strategic alliances result in a form of cooperation where firms can access the resources of others network members in order to create added value for their passengers. The shortcoming of this process is that each member of the network makes individual revenue management decisions to maximize its own income, resulting in a sub-optimal income for the network members.To deal with this problem, this paper suggests a resource allocation based on a transfer pricing mechanism, to cooperatively divide the revenue of a passenger between network members. The method penalizes the total time that a passenger takes for reaching the final destination. The model takes into consideration that the profit is independent of the number of available seats (with a maximum determined for each airline). The method computes the optimal transfer pricing and, at the same time, optimizes the quantity of seats (the booking limits). The solution results in a strong Nash equilibrium, which incorporate both the transfer prices and booking limits. We describe the transfer pricing process using an ergodic, finite and continuous-time Markov game model for multiple players. The revenue of each airline in the supply chain will depend on the number of flight transfers and the transit time of the passenger at the airports: the longer the time to the final destination, the lower the price. We compute a collaborative equilibrium point, useful for understanding the resulting revenue of each member of the network. For solving the game, we employ an iterative method based on a proximal approach that involves time penalization. In our final contribution, we present results from a numerical example, which validates the proposed Markov game model and measures the benefits of the transfer pricing resource allocation.     

Collaborative job scheduling in the wine bottling process

This paper proposes a horizontal collaborative approach for the wine bottling scheduling problem. The opportunities for collaboration in this problem are due to the fact that many local wine producers are usually located around the same region and that bottling is a standard process. Collaboration among wineries is modeled as a cooperative game, whose characteristic function is derived from a mixed integer linear programming model. Real world instances of the problem are, however, unlikely to be solved to optimality due to its complex combinatorial structure and large dimension. This motivates the introduction of an approximated version of the original game, where the characteristic function is computed through a heuristic procedure. Unlike the exact game, the approximated game may violate the subadditivity property. Therefore, it turns relevant not only to find a stable cost allocation but also to find a coalition structure for selecting the best partition of the set of firms. We propose a maximum entropy methodology which can address these two problems simultaneously. Numerical experiments illustrate how this approach applies, and reveal that collaboration can have important positive effects in wine bottling scheduling decreasing delay by 33.4 to 56.9% when improvement heuristic solutions are used. In contrast to the exact game in which the grand coalition is always the best outcome, in the approximated game companies may be better forming smaller coalitions. We also devise a simple procedure to repair the characteristic function of the approximated game so that it recovers the subadditivity property.     

The Farsighted Stable Set

Harsanyi (1974) criticized the von Neumann–Morgenstern (vNM) stable set for its presumption that coalitions are myopic about their prospects. He proposed a new dominance relation incorporating farsightedness, but retained another feature of the stable set: that a coalition S can impose any imputation as long as its restriction to S is feasible for it. This implicitly gives an objecting coalition complete power to arrange the payoffs of players elsewhere, which is clearly unsatisfactory. While this assumption is largely innocuous for myopic dominance, it is of crucial significance for its farsighted counterpart. Our modification of the Harsanyi set respects “coalitional sovereignty.” The resulting farsighted stable set is very different from both the Harsanyi and the vNM sets. We provide a necessary and sufficient condition for the existence of a farsighted stable set containing just a single‐payoff allocation. This condition roughly establishes an equivalence between core allocations and the union of allocations over all single‐payoff farsighted stable sets. We then conduct a comprehensive analysis of the existence and structure of farsighted stable sets in simple games. This last exercise throws light on both single‐payoff and multi‐payoff stable sets, and suggests that they do not coexist.     

具有联盟优先关系的模糊合作博弈的目标规划求解模型

用合作博弈研究实际管理问题中的分配方案时，常常存在一些不重要联盟或无效联盟，这些联盟影响公平合理的分配方案。因此，联盟的重要程度成为求解合作博弈必不可少的因素。本文考虑了联盟的重要性和局中人参与联盟的不确定性，研究了具有优先关系的模糊联盟合作博弈(简称为模糊合作博弈)。首先，借助于目标规划模型的优先因子可以表征联盟重要程度的思想，通过构建多优先级目标规划模型，得到模糊合作博弈新的解。其次，证明了构建的多优先级目标规划模型的解和模糊合作博弈的核心之间具有重要对应关系。最后，通过数值实例和比较分析，说明本文提出的多优先级目标规划模型求解模糊合作博弈问题的合理性和有效性。研究表明：(1)本文提出的多优先级目标规划模型考虑不同联盟重要程度，得到的解符合“多劳多得”原则，能够更公平合理解决实际管理中的分配问题。(2)本文的目标规划模型同时适用于求解存在联盟特征函数值缺失的合作博弈。与已有合作博弈的解进行比较分析，该模型无需估算无效联盟的特征函数缺失数据得到的分配值更为准确。从而，说明本文给出的目标规划求解模糊合作博弈解的模型，更符合许多管理学问题的实际情况。(3)通过多优先级目标规划模型最优解是否存在可判断模糊合作博弈的核心存在情况，若核心存在则该模型通过目标规划软件包可得到核心内的一个解，这样也得到了一个判断合作博弈核心是否存在的标准。(4)目标规划模型可弥补已有合作博弈解的一些不足，如核心可能为空集，Shapley值和最小二乘预核仁可能不满足个体合理性等。本文构建的多优先级目标规划模型不仅能求解联盟具有优先关系的模糊合作博弈，而且能够求解一般合作博弈的解，该目标规划模型作为合作博弈一种新的求解方法，能更有效地解决实际管理中的分配问题，具有更加广泛的应用价值。     

Fast Equilibrium Selection by Rational Players Living in a Changing World

We study a coordination game with randomly changing payoffs and small frictions in changing actions. Using only backwards induction, we find that players must coordinate on the risk‐dominant equilibrium. More precisely, a continuum of fully rational players are randomly matched to play a symmetric 2×2 game. The payoff matrix changes according to a random walk. Players observe these payoffs and the population distribution of actions as they evolve. The game has frictions: opportunities to change strategies arrive from independent random processes, so that the players are locked into their actions for some time. As the frictions disappear, each player ignores what the others are doing and switches at her first opportunity to the risk‐dominant action. History dependence emerges in some cases when frictions remain positive.     

A Simple Adaptive Procedure Leading to Correlated Equilibrium

We propose a new and simple adaptive procedure for playing a game: ‘regret‐matching.’ In this procedure, players may depart from their current play with probabilities that are proportional to measures of regret for not having used other strategies in the past. It is shown that our adaptive procedure guarantees that, with probability one, the empirical distributions of play converge to the set of correlated equilibria of the game.     

Profit Sharing and the Firm‐Size Wage Premium

This study analyzes the relationships among wages, firm size, and profit sharing schemes. We develop a simple theoretical model and explore the relationship empirically using high‐quality panel data. The theoretical model shows that the firm‐size wage premium decreases in the presence of profit sharing. The empirical results based on rich matched employee‐employer data for private sector wage earners in Finland show that the firm‐size wage premium is modest, and it becomes negligible when we account for profit sharing and covariates describing assortative matching and monopsony behavior. The analysis suggests that profit sharing schemes embody effects of firm‐specific unobservables that raise productivity, support rent sharing, and boost wages.