Credibility of Incentive Equilibrium Strategies in Linear-State Differential Games

We characterize in this paper the credibility of incentive equilibrium strategies for the class of linear-state differential games. We derive a general condition for credibility and illustrate its use on two differential games taken from the literature of environmental economics and knowledge accumulation. We show that the proposed linear incentive strategies are not always credible. Further, we provide alternative nonlinear credible strategies which suggest that we should not stick only to linear incentive strategies, even in a simple class of differential games such as the linear-state one.This research was completed when the first author was visiting professor at GERAD, HEC, Montréal. The first author’s research was partially supported by MCYT under project BEC2002-02361 and by JCYL under project VA051/03, confinanced by FEDER funds. The second author’s research was supported by NSERC, Canada.     

Coalition-proof equilibria in a voluntary participation game

We examine the coalition-proof equilibria of a participation game in the provision of a (pure) public good. We study which Nash equilibria are achieved through cooperation, and we investigate coalition-proof equilibria under strict and weak domination. We show that under some incentive condition, (i) a profile of strategies is a coalition-proof equilibrium under strict domination if and only if it is a Nash equilibrium that is not strictly Pareto-dominated by any other Nash equilibrium and (ii) every strict Nash equilibrium for non-participants is a coalition-proof equilibrium under weak domination.     

中国高考招生匹配市场中的算法设计及公平激励机制

用匹配博弈的方法,研究中国高考招生市场的算法设计及公平激励机制.基于高考招生程序,构建高考招生匹配算法,证明该算法的可行性.证明一个稳定匹配,可以由一个纳什均衡策略经高考招生算法生成,但反之不一定成立.证明一个稳定匹配一定是公平的,反之不一定成立.构建拒绝-接受算法,证明该算法是一个稳定的、策略防御的匹配机制,因而是一个公平的激励机制.     

Pricing and equity in cross-regional green supply chains

This paper addresses the problem of the firms operating on cross-border or inter-regional platforms that are subject to the enforcement of each local government's carbon emissions regulatory policy, thus causing an imbalance in the sharing of the burden of the greening of the total supply chain. We introduce the concept of equity as the incentive mechanism to coordinate this green supply chain which is a function of the carbon emission permits and the revenue generated by the firms. Due to the complexity and imbalance in the original incentive mechanism to this problem, we provide a new equivalent supply chain network equilibrium model under elastic demand based on user equilibrium theory. We state the user equilibrium conditions and provide the equivalent formulation. We show the trade-offs under various carbon emissions regulatory policies. A product with higher price elasticity and carbon emission intensity not only hampers the firm from gaining a higher revenue, but it also reduces the equity of the system under an invariant emission regulatory policy.     

零售商主导型绿色供应链激励机制设计

以往有关绿色供应链激励机制的研究主要是围绕制造商为核心企业展开.而2014年12月颁布的《企业绿色采购指南(试行)》强调了采购商(或零售商)在绿色供应链当中所起的作用.以零售商(而不是供应商)作为核心企业,建立供应商-零售商绿色供应链博弈模型,用以研究零售商的激励制度设计以及绿色产品需求如何影响绿色供应链.分别求解供应商不进行绿色工艺研发、供应商单独进行绿色工艺研发的供应链均衡解,并且设计了转移支付激励机制.研究表明:1)供应商和零售商不一定都有激励提高产品绿色度,但在特定条件下,他们都有动力提高产品绿色度;2)如果供应商和零售商都有动力提高产品绿色度,那么供应商主导型的绿色供应链比零售商主导型的供应链在为整个供应链创造利润方面更佳;3)零售商主导型的绿色供应链可找到最优转移支付比例使得供应链整体利润最大化,且转移支付激励手段有效.     

混合策略纳什均衡的新教法

理解博弈论中的最优混合策略对本科生而言具有一定困难,而目前教材中对此内容的讲述又过于抽象.提出一个简单而有效地讲授混合策略纳什均衡的方法.首先利用猜硬币游戏引入并介绍混合策略的基本该念.再通过将混合策略加入到支付矩阵中构造拓展支付矩阵,使学生可以清晰地看到采用混合策略的结果,实现从纯策略到混合策略的自然过渡.然后引导学生思考博弈参与者采用混合策略的各种动机,并在拓展支付矩阵中检验其是否达成均衡.最后介绍最优混合策略计算的一般方法,并分析其与参与者行为动机之间的一致性.课堂实践证明,方法可以有效提高学生对混合策略纳什均衡的综合理解,学生不仅能够更好地掌握求解技术,而且能更深入地理解其经济学含义.     

Incentive strategies and equilibria for dynamic games with delayed information

The construction of time-lag incentive strategies for continuous time convex problems is considered. The strategies are affine in the data available and they are represented by means of Stieltjes measures. It is shown how incentive strategies can be used as equilibrium strategies in symmetric games where the decision makers are cooperative.This work was supported by the Research Council for Technology of the Academy of Finland and by the Emil Aaltonen Foundation.     

The impact of resale on entry in second price auctions

This paper investigates the effect of resale allowance on entry strategies in a second price auction with two bidders whose entries are sequential and costly. We first characterize the perfect Bayesian equilibrium in cutoff strategies. We then show that there exists a unique threshold such that if the reseller’s bargaining power is greater (less) than the threshold, resale allowance causes the leading bidder (the following bidder) to have a higher (lower) incentive on entry; i.e., the cutoff of entry becomes lower (higher). We also discuss asymmetric bidders and the original seller’s expected revenue.     

Equilibrium two-part cost structures

We consider an oligopolistic product market in which two competing firms instead of paying a competitive input price choose a two-part tariff. Costs for the input are divided up into upfront fixed costs independent of the output level and reductions in marginal costs. We explore under which competitive settings will such a two-part cost structure correspond to equilibrium behavior in a two stage game. We find that firms in a static model do have an incentive to choose a two-part cost structure when competition in the product market is not too strong and oligopoly rents can be shifted form the rival to the own firm. In a dynamic market when firms use Markov strategies competition is so intense that there are no rents to be shifted and firms do not benefit from two-part cost structures.     

需求信息不对称下供应链中流程与产品创新模式选择研究

在制造商进行流程创新和产品创新的供应链中,当需求预测信息不对称时,研究了零售商的需求信息分享策略以及制造商最优创新模式。利用精炼贝叶斯理论和Stackelberg博弈模型,首先求得了每一种创新模式下信息分享价值、促进需求信息分享的激励机制以及供应链均衡的信息分享策略,其次对两种创新模式下利润进行对比分析。研究发现,在两种创新供应链模型中,当创新效率较高和较低时,零售商自愿分享和不分享需求信息分别是均衡策略;当创新效率处于中间水平时,通过设计一个讨价还价机制可以使零售商分享需求信息成为一个均衡。此外,当消费者对质量(价格)更敏感时,制造商选择产品创新(流程创新)模式可以使供应链成员都获益。     

PPP项目中投资者协同行为发生机制及其演化规律研究

在公私合作项目(PPP)项目中,政府和私人投资者可能会采取协同行为来追求自身利益。这就需要对政府和私人投资者的协同行为进行研究,以了解提高项目绩效的基础机制。首先,基于演化博弈模型分析项目投资者策略选择的动态演化过程,据此政府和私人投资者通过交互选择来实现各自的最优策略。其次,通过演化博弈模型分析发现,政府和私人投资者协作管理具有多重复杂路径演化,其稳定策略很大程度上取决于组织的初始状态及相互激励关系。然后,探讨不同情境下投资者的最优策略和有效增强投资者协同行为的利益协调机制。     

Equilibrium payoffs of dynamic games

We give a characterization of the equilibrium payoffs of a dynamic game, which is a stochastic game where the transition function is either one or zero and players can only use pure actions in each stage. The characterization is in terms of convex combinations of connected stationary strategies; since stationary strategies are not always connected, the equilibrium set may not be convex. We show that subgame perfection may reduce the equilibrium set.     

Incentive mechanism to control customer buy-down behaviour

Airlines have successfully practiced revenue management over the past four decades and enhanced their revenue. Most of the traditional models that are applied assume that customers buying a high-fare class ticket will not purchase a low-fare class ticket even if it is available. This is not a very realistic assumption and has led to revenue leakage due to customers exhibiting buy-down behaviour. This paper aims at devising a suitable incentive mechanism that would incite the customer to reveal his nature. This helps in reducing revenue leakage. We show that the proposed incentive mechanism is profitable to both the buyer and seller and hence ensures the buyers participation in the mechanism.     

Game Options Analysis of the Information Role of Call Policies in Convertible Bonds

Abstract

In debt financing, existence of information asymmetry on the firm quality between the firm management and bond investors may lead to significant adverse selection costs. We develop the two-stage sequential dynamic two-person game option models to analyse the market signalling role of the callable feature in convertible bonds. We show that firms with positive private information on earning potential may signal their type to investors via the callable feature in a convertible bond. We present the variational inequalities formulation with respect to various equilibrium strategies in the two-person game option models via characterization of the optimal stopping rules adopted by the bond issuer and bondholders. The bondholders’ belief system on the firm quality may be revealed with the passage of time when the issuer follows his optimal strategy of declaring call or bankruptcy. Under separating equilibrium, the quality status of the firm is revealed so the information asymmetry game becomes a new game under complete information. To analyse pooling equilibrium, the corresponding incentive compatibility constraint is derived. We manage to deduce the sufficient conditions for the existence of signalling equilibrium of our game option model under information asymmetry. We analyse how the callable feature may lower the adverse selection costs in convertible bond financing. We show how a low-quality firm may benefit from information asymmetry and vice versa, underpricing of the value of debt issued by a high-quality firm.     

网络传媒业供应链质量控制策略与组织模式选择

网络传媒供应链由内容制作商提供有价值的信息产品(如娱乐、资讯等)并通过网站提供给消费者.产品质量控制对网络传媒供应链至关重要.首先利用博弈论的方法分析内容制作商和网站分别独立决策时的策略,纳什均衡揭示双方的"搭便车"动机使供应链整体利润无法达到最优.然后利用最优化的方法分析他们在垂直整合模式下的策略,发现协调决策可以提高整体利润.最后考虑垂直整合模式的新增成本,分析需求质量弹性、利润分配均匀性和质量控制成本等因素对供应链是否采取垂直整合模式的影响.帮助理解网络媒体产业的质量控制策略和供应链组织模式.     

The golden rule when preferences are time inconsistent

We investigate the classical Ramsey problem of economic growth when the planner uses non-constant discounting. It is well-known that this leads to time inconsistency, so that optimal strategies are no longer implementable. We then define equilibrium strategies to be such that unilateral deviations occurring during a small time interval are penalized. Non-equilibrium strategies are not implementable, so only equilibrium strategies should be considered by a rational planner. We show that there exists such strategies which are (a) smooth, and (b) lead to stationary growth, as in the classical Ramsey model. Finally, we prove an existence and multiplicity result: for logarithmic utility and quasi-exponential discount, there is an interval I such that, for every k in I, there is an equilibrium strategy converging to k. We conclude by giving an example where the planner is led to non-constant discount rates by considerations of intergenerational equity.     

项目管理中业主-承包商最优激励模型研究

为解决项目管理中承包商不努力工作的问题,运用信息经济学中的委托代理理论,建立了业主一承包商间的激励数学模型.构造了努力产出函数和努力成本函数,求出了业主的最优激励水平以及相应的承包商最优努力水平,给出了业主的最优激励合同安排.最后,通过一个简化算例求出了模型均衡解的解析式,结果表明模型的结论是符合工程项目实际的,从而本模型能够为业主的激励合同设计提供指导.     

考虑声誉效应的众包竞赛动态激励机制研究

将声誉效应引入众包竞赛的激励机制可以促使接包方为考虑未来绩效收益而提高当前努力。建立并求解了显性和隐性声誉效应下连续两个任务阶段的动态激励模型,探讨了显性声誉修正系数、隐性声誉系数以及参赛者数量对激励效果的影响,并与无声誉激励机制进行了对比。研究表明,声誉激励机制通过单位绩效激励强度和固定奖励水平两条途径起作用,增大隐性声誉系数有助于提高每个任务阶段的努力程度,显性声誉不确定性则会降低第2任务阶段的努力程度;各种条件下实施声誉激励对第1任务阶段中的努力程度和单位绩效奖励的影响存在不确定性;参赛者数量的增加有助于弱化第1任务阶段中棘轮效应,但也会降低声誉激励机制对努力程度的正向价值,扩大声誉激励机制对单位绩效奖励的负向价值。     

Some interesting properties of maximin strategies

Since the seminal paper of Nash (1950) game theoretic literature has focused mostly on equilibrium and not on maximin (minimax) strategies. We study the properties of these strategies in non-zero-sum strategic games that possess (completely) mixed Nash equilibria. We find that under certain conditions maximin strategies have several interesting properties, some of which extend beyond 2-person strategic games. In particular, for n-person games we specify necessary and sufficient conditions for maximin strategies to yield the same expected payoffs as Nash equilibrium strategies. We also show how maximin strategies may facilitate payoff comparison across Nash equilibria as well as refine some Nash equilibrium strategies.