战略联盟竞合行为的随机突变分析与仿真

针对多成员战略联盟在不确定环境下策略的演化过程,借助演化博弈论建立了含有白噪声的随机动力学。利用随机突变理论来分析在不确定性条件下,联盟成员行为(竞争或合作)随着参数的连续变化在整体上发生突变的问题,给出了联盟发生突变的临界集,以此来解释和预测在不确定性环境下,战略联盟发生非计划性解体或者合作失败的突发性问题。对不同场景下的模型进行了数值仿真,结果表明,在临界集附近,联盟集体的行为发生了突变。     

Deterministic Approximation of Stochastic Evolution in Games

This paper provides deterministic approximation results for stochastic processes that arise when finite populations recurrently play finite games. The processes are Markov chains, and the approximation is defined in continuous time as a system of ordinary differential equations of the type studied in evolutionary game theory. We establish precise connections between the long‐run behavior of the discrete stochastic process, for large populations, and its deterministic flow approximation. In particular, we provide probabilistic bounds on exit times from and visitation rates to neighborhoods of attractors to the deterministic flow. We sharpen these results in the special case of ergodic processes.     

基于投资理论的保险定价公式

在保险公司是风险中性的假设下,运用倒向随机微分方程的理论,研究了保险公司在风险投资框架下的保险定价问题。首先,建立了保险定价问题的线性正倒向随机微分方程数学模型;然后,根据一类特殊线性倒向随机微分方程的显式解,推出了由风险投资确定的保险定价公式;最后,进行了算例分析。     

Market Structure and Multiple Equilibria in Airline Markets

We provide a practical method to estimate the payoff functions of players in complete information, static, discrete games. With respect to the empirical literature on entry games originated by Bresnahan and Reiss (1990) and Berry (1992), the main novelty of our framework is to allow for general forms of heterogeneity across players without making equilibrium selection assumptions. We allow the effects that the entry of each individual airline has on the profits of its competitors, its “competitive effects,” to differ across airlines. The identified features of the model are sets of parameters (partial identification) such that the choice probabilities predicted by the econometric model are consistent with the empirical choice probabilities estimated from the data. We apply this methodology to investigate the empirical importance of firm heterogeneity as a determinant of market structure in the U.S. airline industry. We find evidence of heterogeneity across airlines in their profit functions. The competitive effects of large airlines (American, Delta, United) are different from those of low cost carriers and Southwest. Also, the competitive effect of an airline is increasing in its airport presence, which is an important measure of observable heterogeneity in the airline industry. Then we develop a policy experiment to estimate the effect of repealing the Wright Amendment on competition in markets out of the Dallas airports. We find that repealing the Wright Amendment would increase the number of markets served out of Dallas Love.     

Genericity and Markovian Behavior in Stochastic Games

This paper examines Markov perfect equilibria of general, finite state stochastic games. Our main result is that the number of such equilibria is finite for a set of stochastic game payoffs with full Lebesgue measure. We further discuss extensions to lower dimensional stochastic games like the alternating move game.     

Single‐Crossing Random Utility Models

We propose a novel model of stochastic choice: the single‐crossing random utility model (SCRUM). This is a random utility model in which the collection of preferences satisfies the single‐crossing property. We offer a characterization of SCRUMs based on two easy‐to‐check properties: the classic Monotonicity property and a novel condition, Centrality. The identified collection of preferences and associated probabilities is unique. We show that SCRUMs nest both single‐peaked and single‐dipped random utility models and establish a stochastic monotone comparative result for the case of SCRUMs.     

随机最高限价拍卖的报价策略

借助非合作博弈理论构造模型分析了随机限价拍卖的竞买者报价策略.通过对模型的求解得到了以微分方程形式表示的竞买者Nash均衡报价策略.通过与普通的英式拍卖相比较,发现两类拍卖的Nash均衡报价策略具有相同的微分方程结构.根据所得到的微分方程形式的Nash均衡报价策略,计算了一个经过简化的案例,以说明文中结果具有一定的实用性,可以为这类拍卖的报价决策提供一定的支持.     

Sequential Estimation of Dynamic Discrete Games

This paper studies the estimation of dynamic discrete games of incomplete information. Two main econometric issues appear in the estimation of these models: the indeterminacy problem associated with the existence of multiple equilibria and the computational burden in the solution of the game. We propose a class of pseudo maximum likelihood (PML) estimators that deals with these problems, and we study the asymptotic and finite sample properties of several estimators in this class. We first focus on two‐step PML estimators, which, although they are attractive for their computational simplicity, have some important limitations: they are seriously biased in small samples; they require consistent nonparametric estimators of players' choice probabilities in the first step, which are not always available; and they are asymptotically inefficient. Second, we show that a recursive extension of the two‐step PML, which we call nested pseudo likelihood (NPL), addresses those drawbacks at a relatively small additional computational cost. The NPL estimator is particularly useful in applications where consistent nonparametric estimates of choice probabilities either are not available or are very imprecise, e.g., models with permanent unobserved heterogeneity. Finally, we illustrate these methods in Monte Carlo experiments and in an empirical application to a model of firm entry and exit in oligopoly markets using Chilean data from several retail industries.     

具公平行为的零售商回收闭环供应链动态均衡策略研究

本文研究了一主导制造商（再制造商）和一"嫉妒/自豪"公平关切行为的零售商（回收商）组成的闭环供应链系统的成员动态均衡策略。利用伊藤过程，刻画了闭环供应链系统的废旧品回收率的随机演化过程。基于利润结构，给出了制造商的期望利润目标泛函。基于零售商的"嫉妒/自豪"型模式，构建了零售商的期望效用目标泛函，进而建立了闭环供应链系统的随机微分博弈模型。利用随机微分博弈理论，给出了制造商和零售商最优值函数应满足的偏微分方程组。通过求解该偏微分方程组，获得了制造商和零售商最优值函数，据此得到了制造商的动态均衡批发价格策略以及零售商的动态均衡销售价格与回收投入努力策略。为了掌握废旧品回收率的统计特征，揭示了废旧品回收率的随机演进性质。结合算例，研究了零售商公平关切程度对成员均衡策略以及绩效的影响。结果表明：零售商公平关切程度越高，制造商的均衡批发价格越低，进而导致其最优值函数将减少。与制造商不同，零售商公平关切程度将增加其最优值函数。另外，零售商公平关切程度越高，系统回收率越低。     

待遇预定制养老基金资产组合与缴费计划最优决策——基于随机波动率Heston模型及Legendre对偶变换法

待遇预定制养老金制度在中国应用非常广泛,缴费制定和资产配置是此类养老金管理的两大核心问题。由此,面对随机波动的现实市场,文章针对待遇预定制养老基金的资产组合管理问题,应用最优控制理论,选用对数效用函数,建立Heston随机波动率模型;在难以求解随机微分Bellman方程的情况下,应用Legendre变换,将原来问题转化为对偶问题,从而求得原问题的解析解。在理论上,进一步丰富了资产组合问题的随机最优控制模型的构建和随机微分方程的求解理论。在实践上,确定了养老金管理风险资产配置比例和缴费水平,给出了最优决策与总资产、发放待遇、净资产与风险溢价之间的数量关系,从而实现养老基金管理的最优资产配置和最低缴费水平的效用目标。     

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.     

一类高新技术企业专利权价值的实物期权评估方法——基于跳扩散过程和随机波动率的美式期权的建模与模拟

由于经典的Black-Scholes期权定价模型的假设忽略了突发事件对资产价格的影响和"波动率微笑"对期权价值的影响而与实际情形往往存在偏差,因此学者们对Black-Scholes模型的改进则主要分别集中在带跳扩散过程的期权定价模型与具随机波动率的期权定价模型等两个方面,然而却少见将这两种模型结合起来的研究。本文首先在带跳扩散过程的期权定价模型与具随机波动率的期权定价模型的研究工作的基础上,建立了一种同时带跳扩散过程和具随机波动率的美式期权定价模型,并通过伊藤引理推导出了资产价格、随机波动率和期权满足的偏微分方程;然后,利用特征函数法和傅里叶变换导出了资产价格的随机分布,进而通过马尔科夫链方法给出了基于跳扩散过程和随机波动率的美式期权的数值解;最后,运用已建立的带跳扩散过程和随机波动率的美式期权定价模型对高新技术企业项目投资的专利权价值进行实物期权定价评估的案例研究,并对跳扩散强度参数和随机波动率参数进行敏感性分析,研究结果表明:将项目收益跳扩散过程和市场环境随机波动率加入到专利权实物期权定价模型中,可以有效避免专利权的期权价值被高估。     

Clocks and Trees: Isomorphic Dutch Auctions and Centipede Games

We report an experiment on effects of varying institutional format and dynamic structure of centipede games and Dutch auctions. Centipede games with a clock format unravel, as predicted by theory but not reported in previous literature on two‐player tree‐format centipede games. Dutch auctions with a tree format produce bids close to risk neutral Nash equilibrium bids, unlike previous literature on clock‐format Dutch auctions. Our data provide a new, expanded set of stylized facts which may provide a foundation for unified modeling of play in a class of games that includes centipede games and Dutch auctions.     

参数互补性目标函数构造方法研究

在业务流程重组中,通过对业务流程价值模型的分析发现,价值模型的决策参数间往往 存在互补性. 文章探讨表征参数互补相关性函数的性质及方法,对于构造业务流程的价值模型 具有重要价值. 根据互补理论和超模函数特性,分析超模函数表征参数互补相关性的特性,讨 论复合超模函数存在的条件,给出参数互补性目标函数的构造方法和步骤,为决策者分析价值 模型提供了一种定量化的工具.     

基于机制转换与随机波动的我国短期利率研究

本文针对我国短期利率具有非线性,易受政策影响,波动较大并存在结构变化等特点,在Smith(2002)机制转换随机波动模型基础上,引入了非线性漂移项,并同时考虑了随机波动方程中常数项、滞后一阶项及方差的机制转换。该模型应用于我国银行间7天同业拆月度利率的研究发现,银行7天同业拆借利率存在明显的非线性、机制转换和波动的水平效应,而且引入机制转换后波动的持久性显著下降。另外,研究还发现高位概率对应着高的波动率和高的通货膨胀率,而低位概率对应着低的波动率和低的通货膨胀率。     

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).     

Recursive Methods in Discounted Stochastic Games: An Algorithm for δ→ 1 and a Folk Theorem

We present an algorithm to compute the set of perfect public equilibrium payoffs as the discount factor tends to 1 for stochastic games with observable states and public (but not necessarily perfect) monitoring when the limiting set of (long‐run players') equilibrium payoffs is independent of the initial state. This is the case, for instance, if the Markov chain induced by any Markov strategy profile is irreducible. We then provide conditions under which a folk theorem obtains: if in each state the joint distribution over the public signal and next period's state satisfies some rank condition, every feasible payoff vector above the minmax payoff is sustained by a perfect public equilibrium with low discounting.     

Time Horizon and Cooperation in Continuous Time

We study social dilemmas in (quasi‐) continuous‐time experiments, comparing games with different durations and termination rules. We discover a stark qualitative contrast in behavior in continuous time as compared to previously studied behavior in discrete‐time games: cooperation is easier to achieve and sustain with deterministic horizons than with stochastic ones, and end‐game effects emerge, but subjects postpone them with experience. Analysis of individual strategies provides a basis for a simple reinforcement learning model that proves to be consistent with this evidence. An additional treatment lends further support to this explanation.     

Risk and Rationality: Uncovering Heterogeneity in Probability Distortion

It has long been recognized that there is considerable heterogeneity in individual risk taking behavior, but little is known about the distribution of risk taking types. We present a parsimonious characterization of risk taking behavior by estimating a finite mixture model for three different experimental data sets, two Swiss and one Chinese, over a large number of real gains and losses. We find two major types of individuals: In all three data sets, the choices of roughly 80% of the subjects exhibit significant deviations from linear probability weighting of varying strength, consistent with prospect theory. Twenty percent of the subjects weight probabilities near linearly and behave essentially as expected value maximizers. Moreover, individuals are cleanly assigned to one type with probabilities close to unity. The reliability and robustness of our classification suggest using a mix of preference theories in applied economic modeling.     

Identification and Estimation of a Discrete Game of Complete Information

We discuss the identification and estimation of discrete games of complete information. Following Bresnahan and Reiss (1990, 1991), a discrete game is a generalization of a standard discrete choice model where utility depends on the actions of other players. Using recent algorithms to compute all of the Nash equilibria to a game, we propose simulation‐based estimators for static, discrete games. We demonstrate that the model is identified under weak functional form assumptions using exclusion restrictions and an identification at infinity approach. Monte Carlo evidence demonstrates that the estimator can perform well in moderately sized samples. As an application, we study entry decisions by construction contractors to bid on highway projects in California. We find that an equilibrium is more likely to be observed if it maximizes joint profits, has a higher Nash product, uses mixed strategies, and is not Pareto dominated by another equilibrium.