Efficiency in Repeated Games Revisited: The Role of Private Strategies

Most theoretical or applied research on repeated games with imperfect monitoring has focused on public strategies: strategies that depend solely on the history of publicly observable signals. This paper sheds light on the role of private strategies: strategies that depend not only on public signals, but also on players' own actions in the past. Our main finding is that players can sometimes make better use of information by using private strategies and that efficiency in repeated games can be improved. Our equilibrium private strategy for repeated prisoners' dilemma games consists of two states and has the property that each player's optimal strategy is independent of the other player's state.     

Games With Discontinuous Payoffs: A Strengthening of Reny's Existence Theorem

We provide a pure Nash equilibrium existence theorem for games with discontinuous payoffs whose hypotheses are in a number of ways weaker than those of the theorem of Reny (1999). In comparison with Reny's argument, our proof is brief. Our result subsumes a prior existence result of Reny (1999) that is not covered by his theorem. We use the main result to prove the existence of pure Nash equilibrium in a class of finite games in which agents' pure strategies are subsets of a given set, and in turn use this to prove the existence of stable configurations for games, similar to those used by Schelling (1971, 1972) to study residential segregation, in which agents choose locations.     

产量-价格策略下的双寡头动态多维博弈

根据动态多维博弈理论,讨论了两个企业对具有一定替代性的两种产品的完全信息动态产量-价格二维博弈模型及其均衡,证明了两个企业关于无替代性的两种产品的产量-价格动态单独博弈模型是这种二维博弈模型的特例,并得到两个企业对每一种产品进行单独博弈的均衡策略劣于联合对两种产品进行二维博弈的均衡策略。结论表明,当两个企业对处于市场未饱和的一种产品产量策略和与其具有一定替代性的处于市场饱和的另一种产品价格策略同时进行二维博弈时,要充分考虑它们之间替代性,这样选择的产量和价格策略才是最优策略。     

团队生产动态博弈

本文建立了团队生产动态(微分 )博弈模型,用Pontryagin最大值原理和共轭点理论研究了该微分博弈的Nash均衡存在的充分必要条件。我们也讨论协调个人理性和集体理性的促进团队合作博弈的机制设置问题。     

有限理性下序贯价格竞争的动态演化

本文建立了两个企业的序贯价格竞争模型，基于有限理性预期调整，研究了企业博弈的动态演化特征，分析了模型的均衡解及其稳定性条件。研究发现，边界解和纳什均衡解是一定参数条件下的局部稳定均衡。基于有限理性的动态博弈能够实现基于完全信息的纳什均衡。单纯跟随策略是一定条件下的均衡策略，并能使跟随企业获得更高的销售价格。企业之间报价的相互跟随程度和企业预期的调整速度将会影响均衡点的稳定性。本文对模型进行了数值模拟分析，当参数不满足稳定性条件时会出现分岔、奇异吸引子等混沌现象。本文的主要研究结果对相关行业的企业竞争和稳定市场有启发意义。     

A Quantitative Theory of Unsecured Consumer Credit with Risk of Default

We study, theoretically and quantitatively, the general equilibrium of an economy in which households smooth consumption by means of both a riskless asset and unsecured loans with the option to default. The default option resembles a bankruptcy filing under Chapter 7 of the U.S. Bankruptcy Code. Competitive financial intermediaries offer a menu of loan sizes and interest rates wherein each loan makes zero profits. We prove the existence of a steady‐state equilibrium and characterize the circumstances under which a household defaults on its loans. We show that our model accounts for the main statistics regarding bankruptcy and unsecured credit while matching key macroeconomic aggregates, and the earnings and wealth distributions. We use this model to address the implications of a recent policy change that introduces a form of “means testing” for households contemplating a Chapter 7 bankruptcy filing. We find that this policy change yields large welfare gains.     

Estimating Dynamic Models of Imperfect Competition

We describe a two‐step algorithm for estimating dynamic games under the assumption that behavior is consistent with Markov perfect equilibrium. In the first step, the policy functions and the law of motion for the state variables are estimated. In the second step, the remaining structural parameters are estimated using the optimality conditions for equilibrium. The second step estimator is a simple simulated minimum distance estimator. The algorithm applies to a broad class of models, including industry competition models with both discrete and continuous controls such as the Ericson and Pakes (1995) model. We test the algorithm on a class of dynamic discrete choice models with normally distributed errors and a class of dynamic oligopoly models similar to that of Pakes and McGuire (1994).     

二次博弈下供应链的均衡订货批量分析

首先提出了二次博弈下供应商与零售商的四种博弈方式:静态-静态博弈、静态-动态博弈、动态-静态博弈和动态-动态博弈;并且分别对四种博弈方式下的均衡做了详细的分析和求解,同时通过一个实例求得了该博弈下的一个混合战略纳什均衡,对比一次博弈得到结论:在正常情况下,二次博弈较一次博弈而言,无论供应商、零售商还是整个供应链的成本都高。     

Optimal Dynamic Pricing of Perishable Items by a Monopolist Facing Strategic Consumers

We introduce a dynamic pricing model for a monopolistic company selling a perishable product to a finite population of strategic consumers (customers who are aware that pricing is dynamic and may time their purchases strategically). This problem is modeled as a stochastic dynamic game in which the company's objective is to maximize total expected revenues, and each customer maximizes the expected present value of utility. We prove the existence of a unique subgame‐perfect equilibrium pricing policy, provide equilibrium optimality conditions for both customer and seller, and prove monotonicity results for special cases. We demonstrate through numerical examples that a company that ignores strategic consumer behavior may receive much lower total revenues than one that uses the strategic equilibrium pricing policy. We also show that, when the initial capacity is a decision variable, it can be used together with the appropriate pricing policy to effectively reduce the impact of strategic consumer behavior. The proposed model is computationally tractable for problems of realistic size.     

基于合作性投资和价格策略的多式联运企业协作行为博弈分析

本文对联合运输中不同运输企业间的协作行为进行了研究。考虑了两家提供互补运输服务的寡头运输企业之间的合作和竞争的博弈决策问题,通过定义合作强度参数,并将其引入收益函数,构造了合作性投资和价格策略的两阶段动态博弈模型,讨论了该博弈子博弈完美Nash均衡解的存在条件,推出了一些重要的结论。研究发现:当双方投资效果系数组合在(0,1)区间时,随着市场潜量的增加,投资增长;随着价格弹性的增加,投资下降。而当双方投资效果系数组合在(1,2)区间时结论相反。最后通过算例和所设计的免疫遗传算法进行了不同参数环境下的数值模拟,验证了结论的正确性。     

基于共识程度的双体博弈纳什均衡拓展研究

首先对一般双体博弈的策略进行拓展,提出共识纳什均衡的概念,并证明其存在性;根据共识程度的降低提出其他3种拓展形式——近似共识纳什均衡、局部共识纳什均衡和局部近似共识纳什均衡,并举例进行说明;然后,对各种均衡形式下的合作效率进行分析和比较。研究表明,共识纳什均衡的利益分配是基于信息本身——竞争环境的特殊形式,它是具有效率的。其他3种形式均衡的效率低于共识纳什均衡,但仍高于双体博弈纳什均衡。共识纳什均衡和其他3种形式的均衡为参与人组织更具效率的合作提供了渠道和理论解释。     

Signaling to Partially Informed Investors in the Newsvendor Model

We analyze a signaling game between the manager of a firm and an investor in the firm. The manager has private information about the firm's demand and cares about the short‐term stock price assigned by the investor. Previous research has shown that under continuous decision choices and the Intuitive Criterion refinement, the least‐cost separating equilibrium will result, in which a low‐quality firm chooses its optimal capacity and a high‐quality firm over‐invests in order to signal its quality to investors. We build on this research by showing the existence of pooling outcomes in which low‐quality firms over‐invest and high‐quality firms under‐invest so as to provide identical signals to investors. The pooling equilibrium is practically appealing because it yields a Pareto improvement compared to the least‐cost separating equilibrium. Distinguishing features of our analysis are that: (i) we allow the capacity decision to have either discrete or continuous support, and (ii) we allow beliefs to be refined based on either the Undefeated refinement or the Intuitive Criterion refinement. We find that the newsvendor model parameters impact the likelihood of a pooling outcome, and this impact changes in both sign and magnitude depending on which refinement is used.     

基于不同预期报价决策的电力市场动态演化及其混沌控制

基于市场参与者不同预期的报价决策方式,提出了考虑输电网约束的电力市场动态模型,即内嵌市场清算优化问题的差分动态模型.该模型刻画出发电方和需求方同时报价的不用决策行为,并准确反映出独立系统调度员ISO的统一市场清算过程,考虑了输电网固有物理特性所赋予电力市场的复杂约束.借助非线性互补函数,对应不同的输电网运行状态:阻塞和不阻塞,分析比较了电力市场处于Nash均衡、周期和混沌的经济表现.针对经济表现差的市场混沌态,提出电力市场状态和参数时滞反馈控制方法,给出电力市场由混沌到Nash均衡的调控措施和手段,从而为有效提高电力市场的经济效益提供了理论依据.     

基于信号博弈模型的公立医院利益补偿机制

针对医疗服务市场的特点,讨论了医药分业后政府补贴公立医院的利益补偿机制,以优化资源配置为目标建立医院与政府的信号博弈模型并进行均衡分析,发现市场的均衡效率随作假的伪装成本和期望风险成本减少而降低;实现市场完全成功的分离均衡的关键条件为保持较高伪装成本和期望风险成本;相应的政策应集中于建立医疗服务行业规范和提升医疗监察效率.     

Approximate versus Exact Equilibria in Dynamic Economies

This paper develops theoretical foundations for an error analysis of approximate equilibria in dynamic stochastic general equilibrium models with heterogeneous agents and incomplete financial markets. While there are several algorithms that compute prices and allocations for which agents' first‐order conditions are approximately satisfied (“approximate equilibria”), there are few results on how to interpret the errors in these candidate solutions and how to relate the computed allocations and prices to exact equilibrium allocations and prices. We give a simple example to illustrate that approximate equilibria might be very far from exact equilibria. We then interpret approximate equilibria as equilibria for close‐by economies; that is, for economies with close‐by individual endowments and preferences. We present an error analysis for two models that are commonly used in applications, an overlapping generations (OLG) model with stochastic production and an asset pricing model with infinitely lived agents. We provide sufficient conditions that ensure that approximate equilibria are close to exact equilibria of close‐by economies. Numerical examples illustrate the analysis.     

Security Investment in Contagious Networks

Security of the systems is normally interdependent in such a way that security risks of one part affect other parts and threats spread through the vulnerable links in the network. So, the risks of the systems can be mitigated through investments in the security of interconnecting links. This article takes an innovative look at the problem of security investment of nodes on their vulnerable links in a given contagious network as a game‐theoretic model that can be applied to a variety of applications including information systems. In the proposed game model, each node computes its corresponding risk based on the value of its assets, vulnerabilities, and threats to determine the optimum level of security investments on its external links respecting its limited budget. Furthermore, direct and indirect nonlinear influences of a node's security investment on the risks of other nodes are considered. The existence and uniqueness of the game's Nash equilibrium in the proposed game are also proved. Further analysis of the model in a practical case revealed that taking advantage of the investment effects of other players, perfectly rational players (i.e., those who use the utility function of the proposed game model) make more cost‐effective decisions than selfish nonrational or semirational players.     

审计合谋的一个博弈均衡分析框架

当前审计环境中,审计合谋现象普遍存在,双重审计制度可以看作是阻止审计合谋的一种制度设计.在分析审计合谋成因的基础上,建立了一个包括引入第二个审计师的概率因子、融合外部监督惩罚与激励机制的博弈模型,对阻止审计合谋的条件进行了均衡分析.研究结果显示,当外部监督惩罚力度强化后与适当的激励机制存在时,双重审计制度有利于降低对审计师的监督成本,从而为其实施提供了理论依据;从多期博弈角度看,这一制度还有利于削弱审计师的"合谋偏好",最终使双重审计回归到单一审计路线上来,节约对审计师的社会监督成本.     

具有网络外部性的双寡头市场的动态定价策略

本文通过将消费者对网络大小的预期引入消费者的效用函数,刻画了消费者预期如何影响市场潜量。然后,通过微分对策,分析了在垄断竞争的市场结构中的厂商如何在考虑到消费者对今后的预期时,如何动态的决定自己的价格和相应的策略。结果表明,随着消费者对网络增长预期的增大,将导致更大的网络规模和更低的初始价格。寡头的利润受消费者对其产量的预期的影响。     

Markov Perfect Industry Dynamics With Many Firms

We propose an approximation method for analyzing Ericson and Pakes (1995)‐style dynamic models of imperfect competition. We define a new equilibrium concept that we call oblivious equilibrium, in which each firm is assumed to make decisions based only on its own state and knowledge of the long‐run average industry state, but where firms ignore current information about competitors' states. The great advantage of oblivious equilibria is that they are much easier to compute than are Markov perfect equilibria. Moreover, we show that, as the market becomes large, if the equilibrium distribution of firm states obeys a certain “light‐tail” condition, then oblivious equilibria closely approximate Markov perfect equilibria. This theorem justifies using oblivious equilibria to analyze Markov perfect industry dynamics in Ericson and Pakes (1995)‐style models with many firms.     

企业产品升级投资决策研究

本文应用期权博弈理论研究了在双寡头垄断的市场结构下,企业进行产品升级投资决策的问题,分析了在抢占均衡和同时投资均衡的情况下企业最优产品升级投资时机。研究表明,随着升级投资所导致的成本下降程度的增加,企业升级投资的临界值降低,这一结果与管理实践的直觉相一致,为企业的产品升级投资决策提供了理论指导。