碳税机制下考虑不同低碳策略的动态博弈模型及复杂性研究

考虑碳排放税,建立双寡头制造商分别实施废品回收和绿色低碳广告投入策略的动态博弈模型。通过系统稳定域,分岔图,功率谱等分析了博弈模型纳什均衡解处的稳定性及参数对系统稳定域的影响,同时对系统的复杂性特征进行了研究。结果表明,消费者回收价格敏感性增加会使整个系统稳定域缩小,而绿色低碳广告投入水平增加只会使实施该策略的企业自身稳定域扩大;当制造商价格调整速度过快时,系统会进入混沌状态;混沌状态下,对比实施广告策略的制造商,实施废品回收策略的制造商价格调整行为对市场造成的震荡更大。最后使用反馈控制策略对系统混沌状态进行了有效的控制,研究结果对制造商低碳策略选择及价格决策有着较好的借鉴意义。     

Establishing Nash equilibrium of the manufacturer–supplier game in supply chain management

We study a game model of multi-leader and one-follower in supply chain optimization where n suppliers compete to provide a single product for a manufacturer. We regard the selling price of each supplier as a pre-determined parameter and consider the case that suppliers compete on the basis of delivery frequency to the manufacturer. Each supplier's profit depends not only on its own delivery frequency, but also on other suppliers' frequencies through their impact on manufacturer's purchase allocation to the suppliers. We first solve the follower's (manufacturer's) purchase allocation problem by deducing an explicit formula of its solution. We then formulate the n leaders' (suppliers') game as a generalized Nash game with shared constraints, which is theoretically difficult, but in our case could be solved numerically by converting to a regular variational inequality problem. For the special case that the selling prices of all suppliers are identical, we provide a sufficient and necessary condition for the existence and uniqueness of the Nash equilibrium. An explicit formula of the Nash equilibrium is obtained and its local uniqueness property is proved.     

基于在线评论的多个竞争制造商和零售商的产品定价策略

在线评论作为一种产品信息传播载体,越来越受到网上电商及消费者的重视,并在很大程度上影响消费者的购买决策。本文在多个竞争性制造商为在线零售商提供可替代性产品并通过零售商销售给网络消费者的电子商务环境下,研究在线评论信息如何影响网络消费者购买决策及在线零售商和制造商的定价策略。以neo-Hoteling模型为基础,构建了依赖零售渠道在线评论的消费者选择模型,并通过模型求解定量分析了二级供应链结构分散系统下在线评论对多个竞争性制造商及零售商最优决策的影响。得到当制造商基于评论制定最优定价策略时,在线评论对市场竞争强度没有影响,但决定潜在市场大小;各产品的均衡批发价及销售价按一定的比例随评论揭示的该产品与其他产品质量均值之差(正或负)增加或减少,评论信息通常会使制造商因好评而获利,由于评论增加了不同产品需求的不对称性,零售商因而具有更大的调价空间,往往通过提高(降低)占据有利(不利)评论的产品价格获得更高的利润。     

Approximating Nash equilibrium for production control with sticky price

We study a mean field game problem arising from the production control for multiple firms with price stickiness in the commodity market. The price dynamics for each firm is described as a (controlled) jump-diffusion process with mean-field interaction. Each firm aims to maximize her expectation of cumulative net profit coupled with each other through price processes. By solving the limiting control problem and a fixed-point problem, we construct an explicit approximating Nash equilibrium when the number of firms grows large.     

线上商品与多种快递服务的组合优化研究

针对网上销售的商品所捆绑的快递服务无法满足顾客多样化需求,而快递服务商又失去了市场空间的问题,提出一种“线上商品+多种快递服务”的组合销售模式,以扩大电商的市场规模,提高快递服务商的利润和差异化竞争水平。在市场细分和顾客需求调查的基础上,综合考虑电商、快递服务商、网购顾客三方的利益,以快递服务商收益最大为目标,构建基于顾客选择行为的“线上商品+多种快递服务”组合销售模式优化模型。以SP调查为数据基础,优化线上商品与多种快递服务的组合销售模式及确定各组合销售模式的均衡价格。模型的求解结果准确地揭示了顾客在网上购物时的快递服务选择行为、快递服务商的末端利润与组合模式之间的关系。     

A note on price and quality competition between asymmetric firms

This paper analyzes the impact of asymmetry between firms on the outcome of price and quality competition from a microeconomic viewpoint. Consumers purchase a product based on not only its price but also its quality level; therefore, two firms compete in determining their prices and quality levels to maximize their profits. The asymmetry arises from the difference in consumers’ loyalty to each firm; that asymmetry then determines a character of differentiation between firms. Our purpose is to show how asymmetry influences competition under varying consumers’ price- and quality-sensitivity. In doing so, we extend earlier work in the area of price and quality competition. We show that in both the moderately quality-sensitive and price-sensitive markets, higher consumers’ sensitivity as well as lower consumers’ loyalty to any firm leads to intense competition, resulting in a decrease of both firms’ equilibrium profits. On the other hand, in highly quality-sensitive market, asymmetry compels the smaller firm to change its competitive strategy. In general, this is more beneficial to the larger firm, as the smaller firm’s profit tends to decline. In the worst case, the smaller firm is driven out of business under equilibrium.     

The information value of logistics platforms in a freight matching market

The information asymmetry in the freight matching of the long-haul trucking industry usually pushes shippers to join a logistics platform that has better knowledge of truckers’ cost information. A logistics platform that is plugged into a freight transportation system helps shippers overcome their information disadvantage but produces the double marginalization effect. We investigate the equilibrium characteristics of a shipper and logistics platform in the freight matching market and find that the shipper prefers to cooperate with the logistics platform in a small-scale sales market but searches for truckers by himself in a large-scale sales market. We show that the information value of a logistics platform for the freight system consists of two aspects: (i) employ low-cost truckers for the shipper and avoid the shipper’s inefficient expansion of the selling quantity in a moderate-scale sales market with greatly heterogeneous truckers, and (ii) improve both the total profit and social welfare of the freight system in a small-scale sales market. We further find that the shipper’s private information may hurt the logistics platform and the logistics platform can mitigate her double marginalization disadvantage by improving value-added services or lowering the logistics price in a large-scale market. Our findings provide guidelines for the shipper and logistics platform on how to choose the appropriate transportation strategy and employment strategy in different logistics markets.     

具有不完全信息的内部交易动态博弈

在Kyle模型中的线性均衡假设进行了修正的基础上,针对内部交易者只具有资产价值不完全信息情况,建立两期风险厌恶型内部交易均衡模型,并求得该模型的子博弈纳什均衡解.由此发现资产价值不完信息中噪音对市场干扰程度愈小(波动程度愈小),就愈有利于内部交易者的收益;内部交易者的交易就愈活跃;交易均衡价格包含资产价值信息就愈多.     

The risk and information sharing of application services supply chain

We study an application services supply chain consisting of one application service provider (ASP) and one application infrastructure provider (AIP). The AIP supplies the computer capacity to the ASP that in turn sells the value-added application services to the market. The market is characterized by a price-sensitive random demand. The ASP’s objective is to determine the optimal price of its service to the market and the optimal capacity to purchase from the AIP. The AIP’s goal on the other hand is to maximize its profit from selling the capacity to the ASP.     

Competition among providers in loss networks

Communication networks are becoming ubiquitous and more and more competitive among revenue-maximizing providers, operating on potentially different technologies. In this paper, we propose to analyze thanks to game theory the competition of providers playing with access prices and fighting for customers. Considering a slotted-time model, the part of demand exceeding capacity is lost and has to be resent. We consider an access price for submitted packets, thus inducing a congestion pricing through losses. Customers therefore choose the provider with the cheapest average price per correctly transmitted unit of traffic. The model is a two-level game, the lower level for the distribution of customers among providers, and the upper level for the competition on prices among providers, taking into account what the subsequent repartition at the lower level will be. We prove that the upper level has a unique Nash equilibrium, for which the user repartition among different available providers is also unique, and, remarkably, efficient in the sense of social welfare (with a so-called price of anarchy equal to one). Moreover, even when adding a higher level game on capacity disclosure with a possibility of lying for providers, providers are better off being truthful, and the unique Nash equilibrium is thus unchanged.     

Nonlinear duopoly games with positive cost externalities due to spillover effects

A Cournot duopoly game is proposed where the interdependence between the quantity-setting firms is not only related to the selling price, determined by the total production through a given demand function, but also on cost-reduction effects related to the presence of the competitor. Such cost reductions are introduced to model the effects of know-how spillovers, caused by the ability of a firm to take advantage, for free, of the results of competitors' Research and Development (R&D) results, due to the difficulties to protect intellectual properties or to avoid the movements of skilled workers among competing firms. These effects may be particularly important in the modeling of high-tech markets, where costs are mainly related to R&D and workers' training. The results of this paper concern the existence and uniqueness of the Cournot–Nash equilibrium, located at the intersection of non-monotonic reaction curves, and its stability under two different kinds of bounded rationality adjustment mechanisms. The effects of spillovers on the existence of the Nash equilibrium are discussed, as well as their influence on the kind of attractors arising when the Nash equilibrium is unstable. Methods for the global analysis of two-dimensional discrete dynamical systems are used to study the structure of the basins of attraction.     

Pricing and advertisement in a manufacturer–retailer supply chain

We use a game theoretical approach to study pricing and advertisement decisions in a manufacturer–retailer supply chain when price discounts are offered by both the manufacturer and retailer. When the manufacturer is the leader of the game, we obtained Stackelberg equilibrium with manufacturer’s local allowance, national brand name investment, manufacturer’s preferred price discount, retailer’s price discount, and local advertising expense. For the special case of two-stage equilibrium when the manufacturer’s price discount is exogenous, we found that the retailer is willing to increase local advertising expense if the manufacturer increases local advertising allowance and provides deeper price discount, or if the manufacturer decreases its brand name investment. When both the manufacturer and retailer have power, Nash equilibrium in a competition game is obtained. The comparison between the Nash equilibrium and Stackelberg equilibrium shows that the manufacturer always prefers Stackelberg equilibrium, but there is no definitive conclusion for the retailer. The bargaining power can be used to determine the profit sharing between the manufacturer and the retailer. Once the profit sharing is determined, we suggest a simple contract to help the manufacturer and retailer obtain their desired profit sharing.     

Equilibria of a two-stage market with chance outcome in the spot market

We address the problem of how to improve the efficiency of markets of similar goods (electric power, gas, and other resources). One way to undermine the market dominance of some companies is the possibility of forward contracts. Here a model of the spot and forward markets functioning as Curnout auctions is studied using the example of symmetrical oligopoly. Suppliers try to maximize their profit by this two-stage game’s strategies of traded subgame equilibrium (TSE). The conditions for equilibrium achieved by correlated mixed strategies are elucidated: either a “bull” or “bear” market is established according to a chance factor. The optimum strategies of rational bidders are found to depend on the reserve price and a risk-avoiding parameter. TSE is compared to the Nash equilibria for one-stage models.     

Alliance or no alliance—Bargaining power in competing reverse supply chains

This work investigates how bargaining power affects negotiations between manufacturers and reverse logistics providers in reverse supply chains under government intervention using a novel three-stage reverse supply chain model for two scenarios, a reverse logistics provider alliance and no reverse logistics provider alliance. Utilizing the asymmetric Nash bargaining game, this work seeks equilibrium negotiation solutions. Analytical results indicate that the reverse logistics provider alliance increases the bargaining power of reverse logistics providers when negotiating with a manufacturer for a profitable recycled-component supply contract; however, manufacturer profits are often reduced. Particularly in the case of an recycled-component vender-dominated market, a reverse logistics alliance with extreme bargaining power may cause a counter-profit effect that results in the decreases of profits for all players involved, including buyers (i.e., manufacturers) and allied recycled-component venders (i.e., reverse logistics providers). Additional managerial insights are provided for discussion.     

Complex dynamics and chaos control of duopoly Bertrand model in Chinese air-conditioning market

A dynamic duopoly Bertrand model with quadratic cost function which is closer to reality and different from previous researches is discussed. The model is applied into air-conditioning market where the boundary equilibrium point is locally stable. Numerical simulations illustrate that the stability of Nash equilibrium strongly depends on the speed of adjustment of bounded rational player. The adjustment speeds and the degree of substitutability may undermine the stability of the equilibrium and cause a market structure to behave chaotically. The Lyapunov dimension of the chaos attractor is 1.9585 under some conditions. The stabilization of the chaotic behavior can be obtained by reducing the degree of substitutability. The results have an important theoretical and practical significance to Chinese air-conditioning market.     

规模不经济下基于一致定价和促销努力的双渠道供应链协调策略

在制造商存在规模不经济环境下,分别针对集中决策模式和分散决策模式,建立了基于一致定价和促销努力的双渠道供应链协调策略模型,分析了规模不经济和服务负溢出效应对供应链运营决策的影响,得到了集中和分散决策下各企业最优运作策略和收益。研究指出,规模不经济的双渠道供应链在分散决策批发价契约下无法实现供应链协调;而分散决策网络渠道收益共享契约能够实现双渠道总收益等于集中决策模式下供应链收益,但无法保证各主体始终获得高于批发价合同下的收益;进一步,设计了带有固定补偿的网络渠道收益共享契约,通过对固定补偿值的有效设计,不仅可以保证双渠道总收益等于集中决策模式下供应链收益,且可以始终保证各主体收益不低于分散决策批发价契约下其所得收益,从而实现各主体利益双赢以及供应链的有效协调。     

考虑地位效应时炫耀性虚拟商品的最优定价与普及版本化

考虑地位效应的影响,针对炫耀性虚拟商品,决策最优定价和普及版本化。建立了单标准版策略、双版本免费普及策略和双版本销售策略等三种模型,求解得到企业在对应策略下对单版本或双版本的炫耀性虚拟商品的最优定价,在此基础上分析得到地位效应对虚拟商品价格、企业利润和最优普及版本化策略的影响。研究发现地位效应是导致标准版炫耀性虚拟商品价格和企业利润提升的因素;当存在地位效应时,双版本销售策略是炫耀性虚拟商品的最优普及版本化策略;但双版本销售策略相比于单标准版策略的优势在一定条件下因网络外部性增强而削弱。     

The stability of a Cournot oligopoly: the effects of adaptive expectations

It is crucial to characterize the long-term behaviour for oligopolistic firms by the analysis of asymptotic stability of the equilibrium. Convergent trajectories are usually preferred in the traditional market since unstable orbits may make the behaviour unpredictable. Under some fairly general and reasonable assumptions in an oligopolistic industry, a Cournot oligopoly model is constructed where each firm maximizes its profit in consideration of adaptive expectations with respect to its rivals' choices. We finally arrive at the conclusion that the introduction of adaptive expectations can contribute largely to the convergence to Nash equilibrium, making the long-run market behaviour more predictable.     

Competitive Price Equilibrium with Consumer Reservation Utility

This paper studies a competitive price equilibrium in the market of a product category where consumers are homogeneous with a reservation utility below which they will not purchase the product. The impact of the reservation utility on the price equilibrium is of particular interest, because the reservation utility may change according to the business cycle and economic environments. Using multinomial logit model to describe market response, we study the comparative statics of the prices, profits and market shares of firms, each of which produces one brand in the product category, with respect to the reservation utility in the Nash equilibrium. It is shown that, as the reservation utility increases, the prices as well as the profits at Nash equilibrium decrease. Also, in the case of duopoly market, the firm with lower cost structure will increase its market share as the reservation utility increases.