On the convergence to the Cournot equilibrium in a productive asset oligopoly

We derive a feedback equilibrium of a dynamic Cournot game where production requires exploitation of a renewable asset. As in the classical Cournot model, quantity-setting firms compete in the same market for a given homogeneous good. We show that, when the asset stock grows sufficiently fast, the unique globally asymptotically stable steady state of the dynamic Cournot game corresponds to the static Cournot solution. Initial differences between firms’ production rates due to asymmetric allocations of asset stocks tend to disappear over time. When instead the asset stock grows slowly, the system does not converge to any stationary point. We also show that, within the class of linear feedback equilibrium strategies, besides the couple of strategies that stabilizes the states for every possible initial conditions, there exists another couple which is more efficient, in that it leads to higher stationary equilibrium profits for both firms, closer to the collusive outcome. Finally, we show that, as the discount rate approaches zero, there exist multiple linear feedback equilibrium strategies that induce a price trajectory that converges asymptotically to a price which is above the static Cournot equilibrium price.     

基于博弈分析的废旧家电逆向物流研究

废旧家电回收利用的有效实施,离不开良好的经济条件和社会环境。文中在循环经济理念指导下,从政府、企业和市民三个利益主体出发,运用博弈论的理论和方法,对三方在废旧家电回收过程中的利益博弈关系进行分析,建立相应的博弈模型,并对模型的均衡求解进行比较,提出了政府补贴下的专业企业有偿回收废旧家电的新机制。文中通过博弈分析,为我国构建良好的废旧家电回收利用体系和营造良好的废旧家电回收环境,实现资源的循环利用,提出建设性的意见和建议。     

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.     

The determination of stability and similarity of Markovian land use change processes: A theoretical and empirical analysis

This paper examines the process of land use change as a Markov process. The model as developed in this paper ateempts to specify criteria to determine the stability and similarity of the process of land use change before it reaches the equilibrium state which may take an infinite number of time periods. It is shown that the model is capable of identifying the time horizon during which the system shows sufficient stability since prediction with respect to future pattern is more likely to conform to the actual pattern if the system in question is stable.     

Inference in a synchronization game with social interactions

This paper studies inference in a continuous time game where an agent’s decision to quit an activity depends on the participation of other players. In equilibrium, similar actions can be explained not only by direct influences but also by correlated factors. Our model can be seen as a simultaneous duration model with multiple decision makers and interdependent durations. We study the problem of determining the existence and uniqueness of equilibrium stopping strategies in this setting. This paper provides results and conditions for the detection of these endogenous effects. First, we show that the presence of such effects is a necessary and sufficient condition for simultaneous exits. This allows us to set up a nonparametric test for the presence of such influences, which is robust to multiple equilibria. Second, we provide conditions under which parameters in the game are identified. Finally, we apply the model to data on desertion in the Union Army during the American Civil War, and find evidence of endogenous influences.     

Stability of Climate Coalitions in a Cartel Formation Game

This paper analyses the formation and stability of coalitions to form international environmental agreements. We present and apply the Stability of coalitions model to assess the internal and external stability of all possible coalition structures in a cartel formation game; first under the assumption that no transfers take place and second for a transfer scheme. One important novelty of this paper is the analysis of the incentive structure of twelve regions for all possible combinations of (cartel) coalitions in an empirical setting with asymmetric regions. We show that stable coalitions can emerge only if benefits from global abatement are sufficiently high or if an appropriate transfer scheme is introduced.The authors acknowledge the support of Juan-Carlos Altamirano-Cabrera, Eligius Hendrix, Niels Olieman, Pepijn van Oort, Arjan Ruijs and Hans-Peter Weikard in the analysis. Furthermore, the comments by two anonymous referees are gratefully acknowledged. The usual disclaimer applies.     

Trade through endogenous intermediaries

We propose an intermediation core for an economy that explicitly specifies how traders organize themselves into trade cooperatives (intermediaries) and how trade between them gets carried out. The intermediation core allocations are closely related to the equilibrium allocations of a non-cooperative intermediation game in Townsend (1983). We show that the intermediation core contains all subgame perfect equilibrium allocations of the intermediation game, similar to the inclusion of competitive equilibrium allocations in the core usually studied. We identify intermediation core allocations that are also subgame perfect equilibrium allocations of the intermediation game in terms of the supporting intermediary structures. These results help to characterize subgame perfect equilibrium allocations of the intermediation game and to analyze their welfare and stability properties.     

基于信息不对称房价博弈模型的优化均衡研究

目前我国住宅市场存在严重的信息不对称,如何进行规制引起多方关注。首先利用房价博弈模型研究我国住宅市场信息不对称下的非理性均衡和精炼优化的序贯均衡,进而探求政府对市场房价经济优化规制后的理性序贯均衡,以此提出政府对住宅产业的规制方式和对策建议。     

Strategic behavior in non-atomic games

In order to remedy the possible loss of strategic interaction in non-atomic games with a societal choice, this study proposes a refinement of Nash equilibrium, strategic equilibrium. Given a non-atomic game, its perturbed game is one in which every player believes that he alone has a small, but positive, impact on the societal choice; and a distribution is a strategic equilibrium if it is a limit point of a sequence of Nash equilibrium distributions of games in which each player’s belief about his impact on the societal choice goes to zero. After proving the existence of strategic equilibria, we show that all of them must be Nash. We also show that all regular equilibria of smooth non-atomic games are strategic. Moreover, it is displayed that in many economic applications, the set of strategic equilibria coincides with that of Nash equilibria of large finite games.     

Migrant wages,remittances and recipient labour supply in a moral hazard model

This paper analyzes the interaction between migrants’ income and remittances and between remittances and the labour supply of residents. The model is cast as a two-period game with imperfect information about the residents’ real economic situation. Residents subject to a good economic situation may behave as if they were in a poor economic situation only in order to manipulate remitters’ expectations. The latter, being aware of this risk, reduce the remitted amount accordingly. Therefore, in the equilibrium, residents who really are victims of the bad economic outlook are penalized as compared to the perfect information set-up. In some circumstances, they can signal their type by drastically cutting working hours, thus further enhancing their precarity right when their economic situation is the worst.     

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.     

Piecewise closed-loop equilibria in differential games with regime switching strategies

We propose a new methodology exploring piecewise closed-loop equilibrium strategies in differential games with regime switching actions. We develop a general game with two players. Players choose an action that influences the evolution of a state variable, and decide on the switching time from one regime to another. Compared to the optimal control problem with regime switching, necessary optimality conditions are modified for the first player to switch. When choosing her optimal switching strategy, this player considers the impact of her choice on the other player’s actions and consequently on her own payoffs. In order to determine the equilibrium timing of regime changes, we derive conditions that help eliminate candidate equilibrium strategies that do not survive deviations in switching strategies. We then apply this new methodology to an exhaustible resource extraction game.     

Invader strategies in the war of attrition with private information

Second price all-pay auctions (wars of attritions) have an evolutionarily stable equilibrium in pure strategies if valuations are private information. I show that for any level of uncertainty there exists a pure deviation strategy arbitrarily close to the equilibrium strategy such that for some valuations the equilibrium strategy has a selective disadvantage against the deviation if the population mainly plays the deviation strategy. I show that agents with those valuations would prefer to deviate even farther from the equilibrium strategy, if the population collectively uses the deviation strategy. I argue that in the Bayesian game studied here, a mass deviation can be caused by the entry of a small group of agents. The results provided in this paper imply that the equilibrium strategy is indeed unstable if one considers rare and independent mutations on the space of valuations. Numeric calculations indicate that the closer the deviation strategy to the equilibrium strategy, the more valuations are destabilizing.     

Discrete-space agglomeration model with social interactions: Multiplicity,stability, and continuous limit of equilibria

This study examines the properties of equilibrium, including the stability, of discrete-space agglomeration models with social interactions. The findings reveal that while the corresponding continuous-space model has a unique equilibrium, the equilibrium in discrete space can be non-unique for any finite degree of discretization by characterizing the discrete-space model as a potential game. Furthermore, it indicates that despite the above result, any sequence of discrete-space models’ equilibria converges to the continuous-space model’s unique equilibrium as the discretization of space is refined.     

国际环境合作的经济学分析

本文利用现代经济学理论与方法，构筑了一个分析国际环境合作问题的经济学框架。分析的中心是建立一个静态模型来寻求作为一个联盟形态的国际环境合作的内部和外部稳定性条件，主要结论是稳定的国际环境合作是由模型给定的参数内生地决定的。与当前大多数研究的一个重要不同是，我们的模型没有采用通常的减少污染排放这一分析参数，而是选用了更为直接的污染排放量这一指标。在运用联盟理论对两类情形即不合作和完全合作进行模型化处理的基础上，本文导出了联盟成员国与非成员国福利水平和污染排放量的若干命题，并建立起国际环境合作稳定性的条件。     

Can money matter for interest rate policy?

In this paper it is shown that money can matter for macroeconomic stability under interest rate policy when transactions frictions are non-negligible. We develop a sticky price model with a shopping time function, which induces the marginal utility of consumption to depend on the (predetermined) stock of money held at the beginning of the period. Equilibrium stability and uniqueness are then ensured by a passive interest rate policy, whereas activeness is associated with an explosive equilibrium. By reacting to changes in beginning-of-period real balances, the central bank can restore stability. Interest rates further depend on lagged real balances even if the central bank acts in an entirely forward-looking way, as under discretionary optimization. If the model is revised such that end-of-period money provides transaction services, money can in principle be neglected for a stabilizing interest rate policy. Discretionary monetary policy is, however, likely to be associated with equilibrium indeterminacy, which can be avoided if interest rates are set contingent on beginning-of-period real balances.     

A characterization of equilibria in the Groves–Ledyard mechanism

In this paper, we characterize all interior and boundary equilibria of the Groves–Ledyard mechanism for a large class of economies and determine their stability properties. We show that the mechanism admits three types of equilibria: a symmetric, efficient, stable interior equilibrium, a large set of asymmetric, efficient, unstable, interior equilibria, and a large set of asymmetric, inefficient, stable boundary equilibria. We further show that asymmetric equilibria fail to exist for large values of the punishment parameter or if the message space is bounded sufficiently. The boundary equilibria previously had not been located nor had the instability of the asymmetric equilibria been known. Interestingly, the stability of the symmetric equilibrium rests on two dynamics that individually produce instability.     

Negotiation games with unobservable mixed disagreement actions

A negotiation model combines an alternating offers bargaining game with a normal form stage game that determines players’ (interim) disagreement payoffs. Busch and Wen [Econometrica 63 (1995) 545] investigated this negotiation model under the assumption that players’ past mixed disagreement actions are observable. The question arises if this assumption is a substantial restriction. In this paper, we adopt the more plausible assumption that only the realizations of past mixed actions are observable, and find that the set of equilibrium payoffs shrinks, compared to that when mixed disagreement actions are observable. We precisely identify the effects of the unobservability and characterize the limiting set of equilibrium payoffs as the two players become sufficiently patient.     

Cournot outcomes under Bertrand–Edgeworth competition with demand uncertainty

We provide new results for two-stage games in which firms make capacity investments when demand is uncertain, then, when demand is realized, compete in prices. We consider games with demand rationing schemes ranging from efficient to proportional rationing. In all cases, there is a subgame perfect equilibrium outcome coinciding with the outcome of the Cournot game with demand uncertainty if and only if (i) the fluctuation in absolute market size is small relative to the cost of capacity, or (ii) uncertainty is such that with high probability the market demand is very large and with the remaining probability the market demand is extremely small. Otherwise, equilibria involve mixed strategies. Further, we show under efficient rationing that condition (i) is sufficient for the unique equilibrium outcome to be an equilibrium outcome of the Cournot game with demand uncertainty.     

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.