The cournot duopoly model reconsidered in the presence of costly communication and enforcement agreements

Recently I proposed a general notion of equilibrium for n-person games which is based on mutual threats and promises (responses), and which leads, in general, to a determinate solution with respect to the order of choice moves. The nature of the solution set in our model is a function of the action sets, the payoff functions, and the cost of ‘communication and enforcement of agreements’ (C&E). The main concern of this paper is to show that the Cournot duopoly solution, for the case of a linear demand function facing two identical firms, can be regenerated by our solution concept under a certain assumption about a high cost C&E. On the other hand, it is shown that under a relatively low cost of C&E the Cournot/Nash solution does not belong to our solution set, because it is Pareto inferior for both duopolists relative to some solutions in our set, among them, the standard monopoly solution.     

Collective choice with endogenous reference outcome

A collective choice problem—essentially a bargaining problem without disagreement outcome—is studied. An extended solution, which determines a solution and a reference point simultaneously, is characterized. The unique extended solution that meets the extended versions of Pareto-optimality, independence of irrelevant alternatives, symmetry, and scale invariance maximizes the Nash product with respect to both the solution and the reference point.     

The Nash bargaining solution in general n-person cooperative games

We present a noncooperative foundation for the Nash bargaining solution for an n-person cooperative game in strategic form. The Nash bargaining solution should be immune to any coalitional deviations. Our noncooperative approach yields a new core concept, called the Nash core, for a cooperative game based on a consistency principle. We prove that the Nash bargaining solution can be supported (in every subgame) by a stationary subgame perfect equilibrium of the bargaining game if and only if the Nash bargaining solution belongs to the Nash core.     

Strategic games beyond expected utility

This paper argues that Nash equilibrium is a solution where all strategic uncertainty has been resolved and, therefore, inappropriate to model situations that involve ??ambiguity.?? Instead, to capture what players will do in the presence of some strategic uncertainty, takes a solution concept that is closed under best replies. It is shown that such a solution concept, fixed sets under the best reply correspondence, exists for a class of games significantly wider than those games for which generalizations of Nash equilibrium exist. In particular, this solution can do without the expected utility hypothesis.     

Risk sensitivity in bargaining with more than two participants

In two-person bargaining over riskless outcomes where the outcome is chosen according to the Nash solution or the Kalai-Smorodinsky solution, an increase in a player's risk aversion is to the advantage of the opponent. It is shown in this note that for the n-person Nash solution, an increase in risk aversion is to the player's own disadvantage but needs not be advantageous to all the opponents. For the n-person Kalai-Smorodinsky solution, the increase is to the player's own disadvantage and to the advantage of all the opponents.     

论两主体情形下合作剩余的分配——以悬赏广告为例

本文讨论在两经济主体的合作能够产生剩余的情况下 ,这些剩余如何在他们之间进行分配。以往研究提出了分配问题的几个可能的解 ,并对解的存在性和唯一性进行了讨论。但他们的分析或是直接对解用不可验证的公理进行描述 ;或是对个体偏好强加一些不可验证的假设 ,然后得到存在性或唯一性的结论。作者发现 ,运用类似于博弈论中多个策略均衡点存在时“聚点”决定解的唯一性的分析方法 ,可以得到这样的结论 :实际中多个解都可能存在 ,不同问题的不同解是由社会习俗决定的 ;即便是同一个问题 ,由于社会习俗的不同 ,也可能有不同形式的解 ;并且解的大小及其变化与社会习俗互有影响。接下来 ,作者以悬赏广告为例 ,对悬赏广告中悬赏金的大小进行求解。我们发现用前面的结论可以比较好地解释所得到的结果。另一方面 ,得到的结果在一定程度上也可以验证前面的结论。     

物业管理企业顾客满意度测评研究——基于改进的TOPSIS法

在分析TOPSIS法的基本计算原理的基础上,指出传统TOPSIS模型在计算相对贴近度方面存在的缺陷,提出用"垂直距离"代替"欧氏距离"的方法来避免方案点同时贴近正理想解和负理想解的问题。针对物业管理企业的特点,应用顾客满意度理论对物业管理企业样本的顾客满意度进行了测评。     

Signaling and mediation in games with common interests

Players who have a common interest are engaged in a game with incomplete information. Before playing they get differential stochastic signals that depend on the actual state of nature. These signals provide the players with partial information about the state of nature and may also serve as a means of correlation.Different information structures induce different outcomes. An information structure is better than another, with respect to a certain solution concept, if the highest solution payoff it induces is at least that induced by the other structure. This paper characterizes the situation where one information structure is better than another with respect to various solution concepts: Nash equilibrium, strategic-normal-form correlated equilibrium, agent-normal-form correlated equilibrium and belief-invariant Bayesian solution. These solution concepts differ from one another in the scope of communication allowed between the players. The characterizations use maps that stochastically translate signals of one structure to signals of another.     

On the Interpretation of Nonsymmetric Bargaining Solutions and Their Extension to Nonexpected Utility Preferences

In a recent paper, Rubinstein, Safra, and Thomson reexamine the foundations of the axiomatic bargaining theory as formulated by Nash. In it they reinterpret the Nash bargaining solution and extend it to a family of nonexpected utility preferences, providing an interpretation of this solution concept and an axiomatization by means of a suitable translation of Nash axioms. This paper extends the work of these authors to the family, characterized by Kalai, of nonsymmetric solutions that appear from the Nash bargaining solution when the symmetry axiom is dropped. This extension requires an axiom relating the solution outcomes of isomorphic games. Journal of Economic Literature Classification Number: C78.     

Rational expectations models with partial information

This paper provides a general solution to the problem of partial information in linear discrete time stochastic rational expectations models. The full information case is first reviewed and the solution of Blanchard and Kahn [4] extended. Then we consider the problem of partial information for the special case where only the current values of some variables are unobserved. The solution can be treated as a straightforward extension to the full information case. In the general problem where in addition to some current variables being unobserved, certain variables are unobserved for all lags, we provide a solution which requires the use of Kalman filters. The paper concludes by examining the covariance properties of the rational expectations system under different informational assumptions.     

Comparative Research Productivity Measures for Economics Departments

The typical profit-maximization solution for the joint-production problem found in intermediate texts, managerial texts, and other texts concerned with optimal pricing is oversimplified and inconsistent with profit maximization, unless there is either no excess of any of the joint products or no costs associated with dumping. However, it is an inappropriate method of solution where excess does exist and the costs of dumping are explicitly recognized and, with respect to such cases, is at least nongeneral. The authors present a more realistic alternative method of solution, although more complex, as a substitute for the textbook method of solution typically offered.     

Towards a Characterization of Second-Best Pure Strategy Solutions to a Smooth and Symmetric Partnership Problem

This article makes a start in characterizing the second-best solution to a smooth, symmetric partnership problem. It derives a more tractable formulation of the problem using a modified version of the condition in Legros and Matthews (1993). Then it uses this formulation to show that the second-best solution will depend crucially on the curvature (third derivatives) of the production and disutility schedules. Moreover, it shows that the residual claimant solution will be second-best for sufficiently large partnerships.     

Continuous time one-dimensional asset-pricing models with analytic price–dividend functions

A continuous time one-dimensional asset-pricing model can be described by a second-order linear ordinary differential equation which represents equilibrium or a no-arbitrage condition within the economy. If the stochastic discount factor and dividend process are analytic, then the resulting differential equation has analytic coefficients. Under these circumstances, the one-dimensional Cauchy–Kovalevsky Theorem can be used to prove that the solution to such an asset-pricing model is analytic. Also, this theorem allows for the development of a recursive rule, which speeds up the computation of an approximate solution. In addition, this theorem yields a uniform bound on the error in the numerical solution. Thus, the Cauchy–Kovalevsky Theorem yields a quick and accurate solution of many known asset-pricing models.     

Bubble-free policy feedback rules

We consider a broad class of linear dynamic stochastic rational-expectations models made of a finite number N of structural equations for N+1 endogenous variables and to be closed by one policy feedback rule. We design, for any model of this class and any stationary VARMA solution of that model, a “bubble-free” policy feedback rule ensuring that this solution is not only the unique stationary solution of the closed model, but also its unique solution. We apply these results to locally linearisable models of the monetary transmission mechanism and obtain interest-rate rules that not only ensure the local determinacy of the targeted equilibrium in the neighbourhood of the steady state considered, but also prevent the economy from gradually leaving this neighbourhood.     

Decomposable solutions for N — person bargaining games

Two solutions for n-person bargaining games are defined and axiomatized, which exhibit the so called “decomposability property”. One of the solutions extends the two-person Kalai-Smorodinsky solution to n-person games. The other is the Raiffa solution.     

On the asymptotic uniqueness of bargaining equilibria

This note reexamines the connection between the asymmetric Nash bargaining solution and the equilibria of strategic bargaining games. A first example shows non-convergence to the asymmetric Nash bargaining solution. A second example demonstrates the possibility of multiple limits.     

On the faustmann solution to the forest management problem

This paper is concerned with optimal solutions to the forest management problem when future utilities are undiscounted. By examining asymptotic properties of such solutions, we find that (i) if the utility function is linear, then the Faustmann periodic solution is optimal; (ii) if the utility function is increasing and strictly concave, an optimal solution converges to the maximum sustained yield solution, which we characterize as a golden rule. These results may be viewed as a possible resolution to the debate in forestry economics about what constitutes an optimal policy in forest management.     

Implementations of the Nash solution based on its Walrasian characterization

Summary. The present paper provides three different support results for the Nash bargaining solution of -person bargaining games. First, for any bargaining game there is defined a non-cooperative game in strategic form, whose unique Nash equilibrium induces a payoff vector that coincides with the Nash solution of the bargaining game. Next this game is modified in such a way that the unique Nash equilibrium that supports the Nash solution is even in dominant strategies. After that an -stage game in extensive form is presented whose unique subgame perfect equilibrium supports the Nash solution of the bargaining game. Finally, the support results are shown to induce implementation results in the sense of mechanism theory. Received: October 3, 1999; revised version: October 26, 1999     

TAYLOR PROJECTION: A NEW SOLUTION METHOD FOR DYNAMIC GENERAL EQUILIBRIUM MODELS

This article presents a new solution method for dynamic equilibrium models. The solution is approximated by polynomials that zero the residual function and its derivatives at a given point x₀. The algorithm is essentially a type of projection but is significantly faster, since the problem is highly sparse and can be easily solved by a Newton solver. The obtained solution is accurate locally in the neighborhood of x₀. Importantly, a local solution can be obtained at any point of the state space. This makes it possible to solve models at points that are further away from the steady state.     

The Chamberlin and Stackelberg Duopoly Relation*

The paper investigates and identifies an important relationship between the Chamberlin and Stackelberg duopoly models. Under conditions of symmetry, linear demand and constant costs, the two iso-profit curves identifying the Stackelberg leadership points are shown to be tangent at the Chamberlin point. Under these conditions profit-maximising duopolists are indifferent to being Stackelberg output leaders and coalescing in an equal-shares-joint-monopoly solution. This result is shown to be sensitive to the constant cost and linear assumptions. Under increasing linear marginal costs, the joint monopoly solution is preferred by both sellers to a leader-follower solution.