Convergence to Walrasian equilibrium with minimal information

We consider convergence to Walrasian equilibrium in a situation where firms know only market price and their own cost function. We term this a situation of minimal information. We model the problem as a large population game of Cournot competition. The Nash equilibrium of this model is identical to the Walrasian equilibrium. We apply the best response (BR) dynamic as our main evolutionary model. This dynamic can be applied under minimal information as firms need to know only the market price and the their own cost to compute payoffs. We show that the BR dynamic converges globally to Nash equilibrium in an aggregative game like the Cournot model. Hence, it converges globally to the Walrasian equilibrium under minimal information. We extend the result to some other evolutionary dynamics using the method of potential games.

     

Theoretical and Empirical Analysis of the Multiperiod Pricing Pattern in the Real Estate Market

We examine empirically and theoretically the multiperiod pricing pattern in the real estate market. First, in a game theoretic framework, we identify conditions for determining whether potential closing prices increase or decrease and marginally increase with time on market. Then, by observing rental housing transactions, we empirically find evidence that the difference between the list price and the settlement price rises and marginally decreases with time on market. This empirical result is consistent with a perfect Nash equilibrium previously proposed in the model.     

On pure-strategy Nash equilibria in price–quantity games

This paper examines the existence and characteristics of pure-strategy Nash equilibria in oligopoly models in which firms simultaneously set prices and quantities. Existence of a pure-strategy equilibrium is proved for a class of price–quantity games. If the demand function is continuous, then the equilibrium outcome is similar to that of a price-only model. With discontinuous demand and limited spillover, there are rationing equilibria in which combined production falls short of market demand. Moreover, there might again be an equilibrium reflecting the outcome of a price game. Competition in price and quantity thus yields Bertrand outcomes under a variety of market conditions.     

Endogenous mechanisms and Nash equilibrium in competitive contracting games

We model strategic competition in a market with asymmetric information as a noncooperative game in which each firm competes for the business of a buyer of unknown type by offering the buyer a catalog of products and prices. The timing in our model is Stackelberg: in the first stage, given the distribution of buyer types known to all firms and the deducible, type-dependent best responses of the agent, firms simultaneously and noncooperatively choose their catalog offers. In the second stage the buyer, knowing his type, chooses a single firm and product-price pair from that firm’s catalog. By backward induction, this Stackelberg game with asymmetric information reduces to a game over catalogs with payoff indeterminacies. In particular, due to ties within catalogs and/or across catalogs, corresponding to any catalog profile offered by firms there may be multiple possible expected firm payoffs, all consistent with the rational optimizing behavior of the agent for each of his types. The resolution of these indeterminacies depends on the tie-breaking mechanism which emerges in the market. Because each tie-breaking mechanism induces a particular game over catalogs, a reasonable candidate would be a tie-breaking mechanism which supports a Nash equilibrium in the corresponding catalog game. We call such a mechanism an endogenous Nash mechanism. The fundamental question we address in this paper is, does there exist an endogenous Nash mechanism—and therefore, does there exist a Nash equilibrium for the catalog game? We show under fairly mild conditions on primitives that catalog games naturally possess tie-breaking mechanisms which support Nash equilibria.     

基于博弈视角的证券市场监管方式改进研究

监管行为和违规行为是证券市场中的一对矛盾体,两者互相博弈。本文通过建立证券市场中监管行为与违规行为的博弈模型,分别得出纯策略纳什均衡和混合策略纳什均衡。结果表明:均衡点与监管成本、违规行为处罚力度和违规收益等因素有关。最后提出了规范我国证券市场发展的若干政策建议。     

基于道德的企业产品定价博弈模型及其分析

企业产品定价道德是指导产品定价活动中企业行为善恶的规范。利用博弈方法对产品定价过程中企业的道德问题进行了理论分析,在建立基于道德的企业产品定价静态博弈模型和基于企业长期收益的重复动态博弈模型的基础上,对其纳什均衡结果进行分析,找出了影响企业道德水平的主要因素,并确定了具体的控制水平,为管理实践中的定价道德控制提供了理论依据。     

Technology choice in an evolutionary oligopoly game

In this paper, we propose and analyze a two-stage oligopoly game in which firms first simultaneously choose production technologies and in the second stage simultaneously choose production quantities. After characterizing the Nash equilibrium of the game, we cast our static model in a dynamic setting exploring the stability properties of the market equilibrium in two different cases: (i) exogenously distributed technologies and Cournot adjustments and (ii) endogenously distributed technologies in an infinite population game with Cournot–Nash equilibrium outputs. The main aim of the paper is that of extending the results about Cournot oligopoly stability in an evolutionary setting of heterogeneous decreasing returns-to-scale technologies. We show how the interplay between production decisions and R&D decisions can generate endogenous market fluctuations leading to complex dynamic phenomena.     

Rational expectations equilibrium and the strategic choice of costly information

This paper studies costly information acquisition in one-good production economies when agents acquire private information and prices transmit information. Before asset markets open, agents choose the quality of their private information. After this information stage, agents trade assets in sequentially complete markets taking into account their private information and the information revealed by equilibrium prices (rational expectations equilibrium, (Radner, R., 1979. Rational expectations equilibrium: generic existence and the information revealed by prices, Econometrica 47, 655–678.)). An overall equilibrium in asset and information market is defined as a Nash equilibrium of the information game in which agents’ actions are information choices and their utility payoffs are the ex-ante expected utilities of the corresponding rationale expectations equilibrium. This paper shows that for a generic set of economies parameterized by endowments and productivity shocks, an overall equilibrium in information and asset market (a Nash equilibrium of the induced information game) with costly information acquisition and fully-revealing prices exists. In other words, informational efficiency is in general consistent with costly information acquisition.     

The local stability of an open-loop Nash equilibrium in a finite horizon differential game

We propose a finite time differential game as a model for some economic processes and derive conditions for the Nash equilibrium solution to be locally asymptotically stable. We adopt the traditional ‘Cournot-reaction function’ notion of stability, which in our (continuous time) model becomes a function-to-function, or trajectory-to-trajectory, mapping. The conditions for stability seem to make economic sense. The equilibrium is less stable if the interaction terms in each period are large, if the game has a long duration, and if the discount rate is small.     

Two-period supply chain coordination strategies with ambidextrous sustainable innovations

This study considers a manufacturer with ambidextrous sustainable innovation capability selling products in environmentally conscious market through an independent retailer in a two-period game setting. We design a two-period game theoretic and dyadic supply chain (SC) model considering exploitative and exploratory nature of environmental innovations. We study five different contract types, namely, wholesale price contract, vertical Nash game structure, cost sharing contract, revenue sharing contract and two-part tariff contract. We demonstrate the impact of market sensitivity towards sustainable innovation and cost parameters on optimal level of decision parameters. The equilibrium results reveal that a suitably designed two-part tariff contract can be used to achieve coordination in a fragmented SC. The equilibrium results assist managers to optimise the SC based on the two-period contract model. The results obtained in this study can help the decision-makers to take decisions on investment in the ambidextrous sustainable innovation under different types of contract structures.     

Bounds for best response functions in binary games

This paper studies the identification of best response functions in binary games without making strong parametric assumptions about the payoffs. The best response function gives the utility maximizing response to a decision of the other players. This is analogous to the response function in the treatment-response literature, taking the decision of the other players as the treatment, except that the best response function has additional structure implied by the associated utility maximization problem. Further, the relationship between the data and the best response function is not the same as the relationship between the data and the response function in the treatment-response literature. We focus especially on the case of a complete information entry game with two firms. We also discuss the case of an entry game with many firms, non-entry games, and incomplete information. Our analysis of the entry game is based on the observation of realized entry decisions, which we then link to the best response functions under various assumptions including those concerning the level of rationality of the firms, including the assumption of Nash equilibrium play, the symmetry of the payoffs between firms, and whether mixed strategies are admitted.     

中国债券市场开放度的博弈分析

本文从信息是否完全的角度出发,运用博弈论和信息经济学的相关理论,对债券市场信息不对称、境外机构发行人民币债券和境外机构市场准入问题进行了静态和动态博弈分析。求解了不同情况下的纳什均衡,对债券融资中现实问题给予了理论阐述和证明,并分析了境外机构在境内发行人民币债券的各种影响。     

产品成本内生化的企业定价选址博弈分析

运用三阶段博弈模型研究了双寡头厂商面对需求非对称、产品成本内生时的定价选址决策问题,并分别分析了供应商Nash谈判参数的变化对生产商均衡位置以及均衡利润的影响.研究发现,与产品成本外生的情形相比,供应商的存在改变了生产商的均衡位置.当某一供应商的相对谈判能力增强时,与之形成双边垄断关系的生产商就会远离其垄断市场,均衡利润将会减少,而竞争对手则会靠近其对应的垄断市场,均衡利润将会增加.两个生产商之间的均衡距离会随供应商谈判能力的增强而缩小.     

An Econometric Analysis of Brand-Level Strategic Pricing Between Coca-Cola Company and PepsiCo.

We investigate market structure and strategic pricing for leading brands sold by Coca-Cola Company and PepsiCo. in the context of a flexible demand specification (i.e., nonlinear AIDS) and structural price equations. Our flexible and generalized approach does not rely upon the often used ad hoc linear approximations to demand and profit-maximizing first-order conditions, and the assumption of Nash-Bertrand competition. We estimate a conjectural variation model and test for different brand-level pure strategy games. This approach of modeling market competition using the nonlinear Full Information Maximum Likelihood (FIML) estimation method provides insights into the nature of imperfect competition and the extent of market power. We find no support for a Nash-Bertrand or Stackelberg Leadership equilibrium in the brand-level pricing game. Results also provide insights into the unique positioning of PepsiCo.'s Mountain Dew brand.     

Observable implications of Nash and subgame-perfect behavior in extensive games

We provide necessary and sufficient conditions for observed outcomes in extensive game forms, in which preferences are unobserved, to be rationalized first, weakly, as a Nash equilibrium and then as the unique subgame-perfect equilibrium. Thus, one could use these conditions to find that play is (a) consistent with subgame-perfect equilibrium, or (b) not consistent with subgame-perfect behavior but is consistent with Nash equilibrium, or (c) consistent with neither.     

Bayesian Nash equilibrium and variational inequalities

This paper provides a sufficient condition for the existence and uniqueness of a Bayesian Nash equilibrium by regarding it as a solution of a variational inequality. The payoff gradient of a game is defined as a vector whose component is a partial derivative of each player’s payoff function with respect to the player’s own action. If the Jacobian matrix of the payoff gradient is negative definite for each state, then a Bayesian Nash equilibrium is unique. This result unifies and generalizes the uniqueness of an equilibrium in a complete information game by Rosen (1965) and that in a team by Radner (1962). In a Bayesian game played on a network, the Jacobian matrix of the payoff gradient coincides with the weighted adjacency matrix of the underlying graph.     

Constitutional implementation

We consider the problem of implementing a social choice correspondence H in Nash equilibrium when the constitution of the society is given by an effectivity function E. It is assumed that the effectivity function of , is a sub-correspondence of E. We found necessary and efficient conditions for a game form to implement H (in Nash equilibria), and to satisfy, at the same time, that , the effectivity function of , is a sub-correspondence of (which guarantees that is compatible with E). We also find sufficient conditions for the coincidence of the set of winning coalitions of and , and for . All our results are sharp as is shown by suitable examples. Received: 15 December 2000 / Accepted: 3 September 2001     

供应商激励机制下信息共享模型

在供应链管理中,供应链上各个节点之间的信息共享是影响供应链整体效益的关键。通过博弈理论,首先分析了供应链中供应商激励机制下的信息共享问题,建立了供应链中信息共享博弈模型,其次根据模型分析了不同情况下供应商的信息共享情况,最后根据模型分析结果,提出了加强供应链管理中加强供应商信息共享的相关策略。