Stability of the Cournot equilibrium for a Cournot oligopoly model with n competitors

In this paper a Cournot-like model is constructed with an iso-elastic demand function for n competitors. The Cournot equilibrium is constructed for general constant unit costs. Finally, it is proved that for identical unit costs the Cournot point is a sink for two or three competitors and a saddle for more than four players.     

Rivalry and uncertainty in complementary investments with dynamic market sharing

We study the effects of revenue and investment cost uncertainty, as well non-preemption duopoly competition, on the timing of investments in two complementary inputs, where either spillover-knowledge is allowed or proprietary-knowledge holds. We find that the ex-ante and ex-post revenue market shares play a very important role in firms’ behavior. When competition is considered, the leader’s behavior departs from that of the monopolist firm of Smith (Ind Corp Change 14:639–650, 2005). The leader is justified in following the conventional wisdom (i.e., synchronous investments are more likely), whereas, the follower’s behavior departs from that of the conventional wisdom (i.e., asynchronous investments are more likely).     

On Nash–Cournot oligopolistic market equilibrium models with concave cost functions

We consider Nash–Cournot oligopolistic market equilibrium models with concave cost functions. Concavity implies, in general, that a local equilibrium point is not necessarily a global one. We give conditions for existence of global equilibrium points. We then propose an algorithm for finding a global equilibrium point or for detecting that the problem is unsolvable. Numerical experiments on some randomly generated data show efficiency of the proposed algorithm.     

On the assortment optimization with endogenized market size

In this paper, we consider the joint effects of product substitution and market size endogenization. Under the substitution effects, a product’s demand may be cannibalized by other substitutable products; while the market size, measured by the number of customers who are interested in the products from the same category, may be largely influenced by the product offer set. We establish the computational complexity for the assortment problem under the joint effects, and develop a fully polynomial-time approximation scheme (FPTAS).     

Ruin probability in the Cramér-Lundberg model with risky investments

We consider the Cramér-Lundberg model with investments in an asset with large volatility, where the premium rate is a bounded nonnegative random function c_t and the price of the invested risk asset follows a geometric Brownian motion with drift a and volatility σ>0. It is proved by Pergamenshchikov and Zeitouny that the probability of ruin, ψ(u), is equal to 1, for any initial endowment u≥0, if ρ?2a/σ²≤1 and the distribution of claim size has an unbounded support. In this paper, we prove that ψ(u)=1 if ρ≤1 without any assumption on the positive claim size.     

A mathematical model for weighing investments

This model assumes three separate investors each with a set amount of money. The full amount is to be invested in six investments, namely: long‐term bonds, short‐term bonds, treasury bonds, common stock, treasury bills, and commercial paper. The investment is made according to weights assigned to safety of principal, growth, current income, taxable income and volatility. The weights are derived by obtaining pairwise comparison matrices and then using an averaging process.     

一类带投资和副索赔的二维时依风险模型破产概率的渐近估计

考虑一类二维风险模型,其中两个保险公司共同承担所有的索赔,且每个(主)索赔都会引起一个副索赔.假定两个保险公司均将其资产投资到金融市场中,其投资回报服从几何Levy过程.在索赔分布属于C族以及索赔额与索赔到达时间间隔具有某种相依结构的条件下,对该二维风险模型盈余过程的有限时破产概率进行渐近估计.     

Bargaining outcomes in patent licensing: Asymptotic results in a general Cournot market

We study asymptotic bargaining outcomes in licensing a patented technology of an external patent holder to firms in a general Cournot market. Our results are as follows: when the number of firms is large, the bargaining set for each permissible coalition structure suggests that the patent holder should extract the entire profits of all licensees. The outcome that the bargaining finally reaches exactly coincides with the non-cooperative outcome, and it cannot be improved upon even by any objections with almost zero cost. Thus, it is strongly stable. The fair allocation represented by the Aumann-Drèze value is, however, not realized as such a stable bargaining outcome.     

Multicriteria energy policy investments and energy market clearance via integer programming

The deregulation of energy markets has created a framework for policy making, still under evolution, which is much more complex than the previous one. As a consequence, new requirements need to be met, concerning both technical design and financial management. This framework renders the use of multicriteria techniques attractive. Here, the investments in suppliers, depending on the policy implemented, are formulated as an integer programming problem, which consists of different sub-problems according to the assumptions made and the market’s regulations. The equivalent relaxed problem is a mixed integer programming problem that can represent the clearance of the energy market by considering several criteria besides price and quantity. Nonlinearities are reformulated by inserting additional binary variables so that the solution algorithms are more effective and efficient in most realistic cases. The feasible solutions and the optimal solution that maximizes every time the market regulator’s gain are obtained, after imposing some thresholds on the criteria used to evaluate the different energy technologies, thus creating a decision support system for the regulator.     

Stable cycles in a Cournot duopoly model of Kopel

We consider a discrete map proposed by M. Kopel that models a nonlinear Cournot duopoly consisting of a market structure between the two opposite cases of monopoly and competition. The stability of the fixed points of the discrete dynamical system is analyzed. Synchronization of two dynamics parameters of the Cournot duopoly is considered in the computation of stability boundaries formed by parts of codim-1 bifurcation curves. We discover more on the dynamics of the map by computing numerically the critical normal form coefficients of all codim-1 and codim-2 bifurcation points and computing the associated two-parameter codim-1 curves rooted in some codim-2 points. It enables us to compute the stability domains of the low-order iterates of the map. We concentrate in particular on the second, third and fourth iterates and their relation to the period doubling, 1:3 and 1:4 resonant Neimark–Sacker points.     

Existence and uniqueness of an optimum in the infinite-horizon portfolio-cum-saving model with semimartingale investments

The model considered here is essentially that formulated in the author's previous paper Conditions for Optimality in the Infinite-Horizon Portfolio-cum-Saving Problem with Semimartingale Investments, Stochastics and Stochastics Reports 29 (1990), 133-171. In this model, the vector process representing returns to investments is a general semimartingale. Processes defining portfolio plans arc here required only to be predictable and non-negative. Existence of an optimal portfolio-cum-saving plan is proved under slight conditions of integrability imposed on the welfare functional; the proofs rely on properties of weak precompactness of portfolio and utility sequences in suitable L _p spaces together with dominated and monotone convergence arguments. Conditions are also obtained for the uniqueness of the portfolio plan generating a given returns process (i.e. for the uniqueness of the integrands generating a given sum of semimartingale integrals) and for the uniqueness of an optimal plan; here use is made of random measures associated with the jumps of a semimartingale     

A nonlinear Cournot duopoly with advertising

This paper aims at studying local and global dynamics in a nonlinear duopoly with quantity-setting firms and non-cooperative advertising investments that affect the degree of (horizontally) differentiated products. It concentrates on persuasive advertising in a model where each firm has limited information and uses a behavioural rule to set the quantity for the subsequent period. By using some mathematical techniques and numerical simulations, our results show the existence of weak (à la Milnor) attractors, multistability and chaotic dynamics. In the long term, firms may continuously shift from states in which they invest in advertising to states in which advertising investment is absent.     

A dynamic analysis of corporate investments and emission tax policy in an oligopoly market with network externality

We investigate the product innovation, green R&D investments and the emission tax policy in an oligopoly market with network externality. It is shown that an appropriate tax policy should be deployed to effectively control pollution and motivate innovation. At the early stage of the market, the emission tax should gradually reduce to motivate firms to achieve optimal investments. Later at the mature stage, the emission tax policy should carefully consider both the market competition and green technology levels.     

Optimizing venture capital investments in a jump diffusion model

We study two practical optimization problems in relation to venture capital investments and/or Research and Development (R&D) investments. In the first problem, given the amount of the initial investment and the cash flow structure at the initial public offering (IPO), the venture capitalist wants to maximize overall discounted cash flows after subtracting subsequent investments, which keep the invested company solvent. We describe this problem as a mixture of singular stochastic control and optimal stopping problems. The second problem is concerned with optimal dividend policy. Rather than selling the company at an IPO, the investor may want to harvest technological achievements in the form of dividend when it is appropriate. The optimal control policy in this problem is a mixture of singular and impulse controls. E. Bayraktar was supported in part by the National Science Foundation, under grant DMS-0604491.     

养老保险基金投资的目标规划模型

本文根据养老保险基金的性质和投资运营的基本原则,利用单指数模型衡量投资组合的收益和风险,建立了养老保险基金投资的目标规划模型。     

Analysis of the dynamics of Cournot team-game with heterogeneous players

In this paper, we study a dynamical system of a two-team Cournot game played by a team consisting of two firms with bounded rationality and a team consisting of one firm with naive expectation. The equilibrium solutions and the conditions of their locally asymptotic stability are studied. It is demonstrated that, as some parameters in the model are varied, the stability of the equilibrium will get lost and many such complex behaviors as the period bifurcation, chaotic phenomenon, periodic windows, strange attractor and unpredictable trajectories will occur. The great influence of the model parameters on the speed of convergence to the equilibrium is also shown with numerical analysis.     

Local stability of the Cournot solution with increasing heterogeneous competitors

In this paper we try to solve a paradox related to the results of Theocharis (1960). When the number of competitors increases the Cournot–Nash equilibrium loses stability. We relax the assumption about homogeneity in the decision mechanism and show that if we admit heterogeneity than by increasing the number of competitors the stability region on the parameters’ space may enlarge instead of shrinking.     

Complex nonlinear dynamics and controlling chaos in a Cournot duopoly economic model

Complex nonlinear economic dynamics in a Cournot duopoly model proposed by M. Kopel is studied in detail in this work. By utilizing the topological horseshoe theory proposed by Yang XS, the authors detect the topological horseshoe chaotic dynamics in the Cournot duopoly model for the first time, and also give the rigorous computer-assisted verification for the existence of horseshoe. In the process of the proof, the topological entropy of the Cournot duopoly model is estimated to be bigger than zero, which implies that this economic system definitely exhibits chaos. In particular, the authors observe two different types of economic intermittencies, including the Pomeau–Manneville Type-I intermittency arising near a saddle-node bifurcation, and the crisis-induced attractor widening intermittency caused by the interior crisis, which lead to the appearance of intermittency chaos. The authors also observe the transient chaos phenomenon which leads to the destruction of chaotic attractors. All these intermittency phenomena will help us to understand the similar dynamics observed in the practical stock market and the foreign exchange market. Besides, the Nash-equilibrium profits and the chaotic long-run average profits are analyzed. It is numerically demonstrated that both firms can have higher profits than the Nash-equilibrium profits, that is to say, both of the duopolists could be beneficial from a chaotic market. The controlled Cournot duopoly model can make one firm get more profit and reduce the profit of the other firm, and control the system to converge to an equilibrious state, where the two duopolists share the market equally.