The price of anarchy in an exponential multi-server

We consider two criteria for routing selection in a multi-server service station: the equilibrium and social optimization. The ratio between the average mean waiting times in these two routings is called the price of anarchy (PoA). We show that the worst-case PoA is precisely the number of servers.     

Coordination mechanisms for parallel machine scheduling

We consider coordination mechanisms for the distributed scheduling of n jobs on m parallel machines, where each agent holding a job selects a machine to process his/her own job. Without a central authority to construct a schedule, each agent acts selfishly to minimize his/her own disutility, which is either the completion time of the job or the congestion time (defined as the load of the machine on which the job is scheduled). However, the overall system performance is measured by a central objective which is quite different from the agents’ objective. In the literature, makespan is often considered as the central objective. We, however, investigate problems with other central objectives that minimize the total congestion time, the total completion time, the maximum tardiness, the total tardiness, and the number of tardy jobs. The performance deterioration of the central objective by a lack of central coordination, referred to as the price of anarchy, is typically measured by the maximum ratio of the objective function value of a Nash equilibrium schedule versus that of an optimal, coordinated schedule. In this paper we give bounds for the price of anarchy for the above objectives. For problems with due date related objectives, the price of anarchy may not be defined since the optimal value may be zero. In this case, we consider the maximum difference between the objective function value of an equilibrium schedule and the optimal value. We refer to this metric as the absolute price of anarchy and analyze its lower and upper bounds.     

The price of anarchy for non-atomic congestion games with symmetric cost maps and elastic demands

By showing that there is an upper bound for the price of anarchyρ(Γ) for a non-atomic congestion game Γ with only separable cost maps and fixed demands, Roughgarden and Tardos show that the cost of forgoing centralized control is mild. This letter shows that there is an upper bound for ρ(Γ) in Γ for fixed demands with symmetric cost maps. It also shows that there is a weaker bound for ρ(Γ) in Γ with elastic demands.     

The toll effect on price of anarchy when costs are nonlinear and asymmetric

We examine the efficiency of the optimal tolls by establishing the bound for the price of anarchy when the levied tolls are also considered as a part of the cost functions. For linear and nonlinear asymmetric cost functions, we prove that the price of anarchy of the system with tolls is lower than that without tolls. Furthermore, we show that the total disutility caused to the users by the tolls is bounded by a multiple of the original optimal system cost.     

Price of anarchy for supply chains with partial positive externalities

We consider the impact of partial positive externalities (imperfect complementarity) among downstream retailers on supply chain performance. We show that double marginalization may fail to exist in a decentralized setting when some retailers carry multiple imperfect complements. By giving a precise characterization on the degree of complementarity, we prove that a decentralized supply chain loses at least 25% of the optimal profit and that its performance degrades rapidly with the complementarity effect.     

产品差异化、竞争类型与合谋稳定性分析

在分析产品差异化的问题上引入合谋成本,修正了以往认为古诺竞争比伯川德竞争的合谋更容易维持的认识,得出在合谋成本的临界值之上,伯川德竞争比古诺竞争的合谋更容易维持的结论,这为经济参与者和决策制定者分析合谋问题提供一个更加全面的视角.     

差异Bertrand寡占厂商的技术许可策略

利用消费者效用函数推导出产品市场差异Bertrand价格竞争均衡的一般式;结合技术许可的收入效应与租金耗散效应,分析了差异Bertrand多家对称创新厂商与差异Bertrand双寡头中的唯一创新厂商对竞争对手的固定费用许可策略.结果表明:(1)多家对称创新厂商与唯一创新厂商均选择不向潜在进入者发放许可;(2)只要产品差异程度符合一定条件,差异Bertrand双寡头中的唯一创新厂商将向技术劣势在位竞手许可其各种规模的工艺创新.     

A nonnegative extension of the affine demand function and equilibrium analysis for multiproduct price competition

We derive a nonnegative extension of the affine demand function for differentiated substitute products from the optimization problem facing a representative consumer whose utility function is quadratic. We show that the extended demand function reduces to a linear program. The linear program has a simple intuitive interpretation in terms of a shifted price vector. We prove the existence and uniqueness of the Bertrand equilibrium in oligopolies consisting of multiproduct firms under the proposed demand function. The equilibrium, available in closed form, coincides with that obtained when allowing negative demands.     

具有不对称网络外部性和纵向差异化的产品竞争策略

在产品不完全覆盖市场中,研究具有不对称网络外部性的纵向差异化产品的Bertrand价格竞争或Cournot数量竞争策略.研究表明,两产品在Cournot数量竞争中的市场利润和社会福利都大于在Bertrand价格竞争中的市场利润和社会福利.在Bertrand价格竞争或Cournot数量竞争中,当低质量产品的网络外部性较大且满足一定条件时,低质量产品也可以获得较大的市场利润;当高质量产品具有较大网络外部性,或网络外部性虽然较小但满足一定条件条件,网络外部性相等或产品都不具有网络外部性时,高质量产品获得较大的市场利润.随着网络外部性的增强,Cournot-Nash均衡点并不稳定,在重复博弈以后,均衡点向Bertrand-Nash均衡点靠近.     

Coordination mechanisms with hybrid local policies

We study coordination mechanisms for scheduling n jobs on m parallel machines where agents representing the jobs interact to generate a schedule. Each agent acts selfishly to minimize the completion time of his/her own job, without considering the overall system performance that is measured by a central objective. The performance deterioration due to the lack of a central coordination, the so-called price of anarchy, is determined by the maximum ratio of the central objective function value of an equilibrium schedule divided by the optimal value. In the first part of the paper, we consider a mixed local policy with some machines using the SPT rule and other machines using the LPT rule. We obtain the exact price of anarchy for the problem of minimizing the makespan and some bounds for the problem of minimizing the total completion time. In the second part of the paper, we consider parallel machine scheduling subject to eligibility constraints. We devise new local policies based on the flexibilities and the processing times of the jobs. We show that the newly devised local policies outperform both the SPT and the LPT rules.     

Two-period dynamic versus fixed-ratio pricing in a capacity constrained duopoly

This paper analyzes the impact of dynamic and fixed-ratio pricing policies on firm profits and equilibrium prices under competition. Firms that have equal inventories of perfectly substitutable and perishable products compete for customer segments that demand the product at different times. In each period, customers first purchase from the low price firm and then from the high price firm up to their inventories, provided the prices are lower than the maximum they are willing to pay. The main conclusions of this paper are as follows: although dynamic pricing is a more sophisticated policy than fixed-ratio pricing, it may lead to decreased equilibrium profits; under both pricing policies, one firm assumes the role of a low-cost high-output firm while the other assumes the role of a high-cost low-output firm; and, the supply demand ratio has more impact on the outcome of the competition than the heterogeneity in consumer reservation prices.     

Congestion games with failures

We introduce a new class of games, congestion games with failures (CGFs), which allows for resource failures in congestion games. In a CGF, players share a common set of resources (service providers), where each service provider (SP) may fail with some known probability (that may be constant or depend on the congestion on the resource). For reliability reasons, a player may choose a subset of the SPs in order to try and perform his task. The cost of a player for utilizing any SP is a function of the total number of players using this SP. A main feature of this setting is that the cost for a player for successful completion of his task is the minimum of the costs of his successful attempts. We show that although CGFs do not, in general, admit a (generalized ordinal) potential function and the finite improvement property (and thus are not isomorphic to congestion games), they always possess a pure strategy Nash equilibrium. Moreover, every best reply dynamics converges to an equilibrium in any given CGF, and the SPs’ congestion experienced in different equilibria is (almost) unique. Furthermore, we provide an efficient procedure for computing a pure strategy equilibrium in CGFs and show that every best equilibrium (one minimizing the sum of the players’ disutilities) is semi-strong. Finally, for the subclass of symmetric CGFs we give a constructive characterization of best and worst equilibria.     

New product advertising in dynamic oligopolies

The success of the introduction of a new product in a market is very sensitive to the marketing decision variables adopted by the firm. In the present paper we are concerned with the question of new product advertising in a heterogeneous oligopoly market consisting of N firms. A dynamic game is formulated to model strategic as well as sales interactions in such a market. Optimal advertising strategies are identified as open-loop Nash solutions.The comments of two anonymous referees are appreciated. The first author wishes to acknowledge support from NSERC (Grant No. OGP0037342).     

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.     

Strategic delegation in a differentiated duopoly with asymmetric costs

This paper examines the impact of product differentiation on strategic delegation in a Cournot duopoly with asymmetric costs. We show that compared with the no-delegation case, when both firms delegate, although the cost-inefficient firm always gets worse, the efficient firm gets better when the degree of product differentiation is sufficiently low and/or the cost asymmetry is sufficiently large. Moreover, as products become closer substitutes, the efficient firm always makes its manager more aggressive, however, the inefficient firm may make its manager less aggressive.     

A differential oligopoly game with differentiated goods and sticky prices

We investigate a dynamic oligopoly game where goods are differentiated and prices are sticky. We study the open-loop and the closed-loop memoryless Nash equilibrium, and show that the latter equilibrium entails a larger level of steady state production as compared to the former; both equilibria entail a larger level of production in steady state than the static game. We also study the effects of price stickiness and product differentiation upon the steady state equilibrium allocation and profits. The per-firm equilibrium output is increasing in both product differentiation and price stickiness, while profits are increasing in both product differentiation and the speed of price adjustment. The steady state social welfare monotonically increases in the speed of price adjustment, and the overproduction entailed by dynamic competition has beneficial effect from a social standpoint.     

带参量的非合作装箱博弈

带参量的非合作装箱博弈是指:每个物品的尺寸都介于0和参量x(0相似文献   

广告盈利模式下网购平台间的竞争对其质量管控力度的影响

当前网购市场中的假冒伪劣现象备受社会关注,作为网购供应链的核心主体,网购平台企业应承担相应质量管控义务。既有文献对平台企业的质量管控进行了有益的探索,文章在此基础之上,探讨广告收入为网购平台主要营收来源时,两个不同规模平台企业间的竞争对其质量管控力度的影响。在双边市场理论框架下,通过构建博弈模型得到如下结果：随着网购平台之间竞争程度的增加,或随着网购平台之间广告宣传替代性的增强,或随着进驻网购平台在线商家数量的增多,每个平台企业均会提高质量管控力度;两个平台企业的质量管控力度随着在线消费者对广告厌恶度的增加均呈倒U型变化趋势。