On the Equilibrium Uniqueness in Cournot Competition with Demand Uncertainty

2020 ◽  
Vol 20 (2) ◽  
Author(s):  
Stefanos Leonardos ◽  
Costis Melolidakis
Keyword(s):  
Failure Rate ◽  
Demand Uncertainty ◽  
Sufficient Conditions ◽  
Cournot Competition ◽  
Uncertain Demand ◽  
Cournot Model ◽  
Equilibrium Uniqueness ◽  
Residual Demand ◽  
Uniqueness Of Equilibrium ◽  
Additional Assumptions

AbstractWe revisit the linear Cournot model with uncertain demand that is studied in Lagerlöf (2006. “Equilibrium Uniqueness in a Cournot Model with Demand Uncertainty.” The B.E. Journal of Theoretical Economics 6, no. 1. (Topics), Article 19: 1–6.) and provide sufficient conditions for equilibrium uniqueness that complement the existing results. We show that if the distribution of the demand intercept has the decreasing mean residual demand (DMRD) or the increasing generalized failure rate (IGFR) property, then uniqueness of equilibrium is guaranteed. The DMRD condition implies log-concavity of the expected profits per unit of output without additional assumptions on the existence or the shape of the density of the demand intercept and, hence, answers in the affirmative the conjecture of Lagerlöf (2006. “Equilibrium Uniqueness in a Cournot Model with Demand Uncertainty.” The B.E. Journal of Theoretical Economics 6, no. 1. (Topics), Article 19: 1–6.) that such conditions may not be necessary.

Equilibrium Uniqueness in a Cournot Model with Demand Uncertainty

2006 ◽  
Vol 6 (1) ◽  
Author(s):  
Johan N.M. Lagerlöf
Keyword(s):  
Hazard Rate ◽  
Demand Uncertainty ◽  
Demand Function ◽  
Market Price ◽  
Cournot Model ◽  
Weak Assumption ◽  
Equilibrium Uniqueness ◽  
Linear Demand ◽  
Uniqueness Of Equilibrium ◽  
Monotone Hazard Rate

If Cournot oligopolists face uncertainty about the intercept of a linear demand function and if the realized market price must be non-negative, then expected demand becomes convex, which can create a multiplicity of equilibria. This note shows that if the distribution of the demand intercept has a monotone hazard rate and if another, rather weak, assumption is satisfied, then uniqueness of equilibrium is guaranteed.

scholarly journals Inference for the Exponential Distribution under Generalized Progressively Hybrid Censored Data from Partially Accelerated Life Tests with a Time Transformation Function

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1510
Author(s):  
Alaa H. Abdel-Hamid ◽  
Atef F. Hashem
Keyword(s):  
Exponential Distribution ◽  
Failure Rate ◽  
Censored Data ◽  
Sufficient Conditions ◽  
Transformation Function ◽  
Point Estimation ◽  
Estimation Methods ◽  
Time Transformation ◽  
Monte Carlo Simulation Study ◽  
Accelerated Life

In this article, the tampered failure rate model is used in partially accelerated life testing. A non-decreasing time function, often called a ‘‘time transformation function", is proposed to tamper the failure rate under design conditions. Different types of the proposed function, which have sufficient conditions in order to be accelerating functions, are investigated. A baseline failure rate of the exponential distribution is considered. Some point estimation methods, as well as approximate confidence intervals, for the parameters involved are discussed based on generalized progressively hybrid censored data. The determination of the optimal stress change time is discussed under two different criteria of optimality. A real dataset is employed to explain the theoretical outcomes discussed in this article. Finally, a Monte Carlo simulation study is carried out to examine the performance of the estimation methods and the optimality criteria.

ON COURNOT COMPETITION UNDER RANDOM YIELD

2013 ◽  
Vol 30 (04) ◽  
pp. 1350007 ◽  
Author(s):  
XIAOMING YAN ◽  
YONG WANG
Keyword(s):  
Nash Equilibrium ◽  
Production Cost ◽  
Pure Strategy ◽  
Cournot Competition ◽  
Random Yield ◽  
Cournot Model ◽  
Random Capacity ◽  
Strategy Nash Equilibrium

We look at a Cournot model in which each firm may be unreliable with random capacity, so the total quantity brought into market is uncertain. The Cournot model has a unique pure strategy Nash equilibrium (NE), in which the number of active firms is determined by each firm's production cost and reliability. Our results indicate the following effects of unreliability: the number of active firms in the NE is more than that each firm is completely reliable and the expected total quantity brought into market is less than that each firm is completely reliable. Whether a given firm joins in the game is independent of its reliability, but any given firm always hopes that the less-expensive firms' capacities are random and stochastically smaller.

Failure distributions of shock models

1980 ◽  
Vol 17 (03) ◽  
pp. 745-752 ◽  
Author(s):  
Gary Gottlieb
Keyword(s):  
Failure Rate ◽  
Sufficient Conditions ◽  
Cumulative Damage ◽  
Shock Model ◽  
Life Distribution ◽  
Increasing Failure Rate ◽  
Shock Models ◽  
Damage Process

A single device shock model is studied. The device is subject to some damage process. Under the assumption that as the cumulative damage increases, the probability that any additional damage will cause failure increases, we find sufficient conditions on the shocking process so that the life distribution will be increasing failure rate.

scholarly journals Equilibrium states for a class of skew products

2019 ◽  
Vol 40 (11) ◽  
pp. 3030-3050
Author(s):  
MARIA CARVALHO ◽  
SEBASTIÁN A. PÉREZ
Keyword(s):  
Existence And Uniqueness ◽  
Global Analysis ◽  
American Mathematical Society ◽  
Sufficient Conditions ◽  
Equilibrium States ◽  
Axiom A ◽  
Skew Products ◽  
Pure Mathematics ◽  
Partially Hyperbolic ◽  
Uniqueness Of Equilibrium

We consider skew products on $M\times \mathbb{T}^{2}$, where $M$ is the two-sphere or the two-torus, which are partially hyperbolic and semi-conjugate to an Axiom A diffeomorphism. This class of dynamics includes the open sets of $\unicode[STIX]{x1D6FA}$-non-stable systems introduced by Abraham and Smale [Non-genericity of Ł-stability. Global Analysis (Proceedings of Symposia in Pure Mathematics, XIV (Berkeley 1968)). American Mathematical Society, Providence, RI, 1970, pp. 5–8.] and Shub [Topological Transitive Diffeomorphisms in$T^{4}$ (Lecture Notes in Mathematics, 206). Springer, Berlin, 1971, pp. 39–40]. We present sufficient conditions, both on the skew products and the potentials, for the existence and uniqueness of equilibrium states, and discuss their statistical stability.

Robust Pricing of Transportation Networks under Uncertain Demand

2008 ◽  
Vol 2085 (1) ◽  
pp. 21-30 ◽  
Author(s):  
Lauren M. Gardner ◽  
Avinash Unnikrishnan ◽  
S. Travis Waller
Keyword(s):  
Demand Uncertainty ◽  
Travel Demand ◽  
Transportation Networks ◽  
Random Variable ◽  
User Equilibrium ◽  
Uncertain Demand ◽  
Optimal Pricing ◽  
Elastic Demand ◽  
Marginal Costs ◽  
Pricing Scheme

Traditionally, tolls on transportation networks are determined on the basis of a single value of travel demand, deterministic elastic demand relationships, or informal scenario analysis. However, since the demand on the network cannot be forecast perfectly, pricing may prove to be suboptimal when the realized value of demand deviates significantly from the planned value. Therefore, there is a need for a robust pricing scheme that accounts for demand uncertainty. Optimal pricing is examined through marginal costs in which origin-destination travel demand is a random variable to understand better the direct impact and sensitivity of the uncertainty. Three methods are evaluated for determining robust prices: inflation or deflation of the planning demand, averaging tolls from various planning demands, and genetic algorithms. The performance of these three methods is evaluated by analyzing user equilibrium for various future travel demand scenarios. From the results of the analysis, a more robust pricing scheme that accounts for variations in demand is developed.

APPLICATION OF POSSIBILITY THEORY TO ROBUST COURNOT EQUILIBRIUM IN THE ELECTRICITY MARKET

2005 ◽  
Vol 19 (4) ◽  
pp. 519-531 ◽  
Author(s):  
F. A. Campos ◽  
J. Villar ◽  
J. Barquín
Keyword(s):  
Electricity Market ◽  
Imperfect Information ◽  
Demand Uncertainty ◽  
Programming Model ◽  
Possibility Theory ◽  
Cournot Equilibrium ◽  
Theoretical Approaches ◽  
Cournot Game ◽  
Residual Demand ◽  
Possibility Distributions

It is known that Cournot game theory has been one of the theoretical approaches used more often to model electricity market behavior. Nevertheless, this approach is highly influenced by the residual demand curves of the market agents, which are usually not precisely known. This imperfect information has normally been studied with probability theory, but possibility theory might sometimes be more helpful in modeling not only uncertainty but also imprecision and vagueness. In this paper, two dual approaches are proposed to compute a robust Cournot equilibrium, when the residual demand uncertainty is modeled with possibility distributions. Additionally, it is shown that these two approaches can be combined into a bicriteria programming model, which can be solved with an iterative algorithm. Some interesting results for a real-size electricity system show the robustness of the proposed methodology.

Asymptotic failure rate of a Markov deteriorating system with preventive maintenance

2003 ◽  
Vol 40 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Sophie Mercier ◽  
Michel Roussignol
Keyword(s):  
Failure Rate ◽  
Preventive Maintenance ◽  
Sufficient Conditions ◽  
Maintenance Policy ◽  
System A ◽  
Up States ◽  
Finite State ◽  
Degradation Degree ◽  
Preventive Maintenance Policy ◽  
Finite State Space

We consider a system with a finite state space subject to continuous-time Markovian deterioration while running that leads to failure. Failures are instantaneously detected. This system is submitted to sequential checking and preventive maintenance: up states are divided into ‘good’ and ‘degraded’ ones and the system is sequentially checked through perfect and instantaneous inspections until it is found in a degraded up state and stopped to allow maintenance (or until it fails). Time between inspections is random and is chosen at each inspection according to the current degradation degree of the system. Markov renewal equations fulfilled by the reliability of the maintained system are given and an exponential equivalent is derived for the reliability. We prove the existence of an asymptotic failure rate for the maintained system, which we are able to compute. Sufficient conditions are given for the preventive maintenance policy to improve the reliability and the asymptotic failure rate of the system. A numerical example illustrates our study.

The risk assessment of manufacturing supply chains based on Bayesian networks with uncertainty of demand

2021 ◽  
pp. 1-19
Author(s):  
Mengjun Meng ◽  
Qiuyun Lin ◽  
Yingming Wang
Keyword(s):  
Risk Assessment ◽  
Supply Chain ◽  
Information Sharing ◽  
Evaluation System ◽  
Demand Uncertainty ◽  
Risk Identification ◽  
Assessment Model ◽  
Risk Indicators ◽  
Uncertain Demand ◽  
Manufacturing Supply Chain

The great changes in the external environment of the manufacturing supply chain make its demand more complex and difficult to control. This paper takes China as an example. According to questionnaire survey and principal component analysis, the risk indicators caused by uncertain demand are screened and classified to construct evaluation system and complete risk identification. The Bayesian network integrating fuzzy set theory and left and right fuzzy ranking is used to explore the relationship between risk indicators and supply chain to achieve risk evaluation. In view of the highest risk factors, an incentive mechanism model based on information sharing is put forward to prove theoretically that information sharing is an important strategy to reduce risk. The results are as follows: The uncertain demand will lead to a high level of risk in China’s manufacturing supply chain, in which the level of information technology is the biggest cause. Only when manufacturing enterprises are willing to share information and other node enterprises join the information sharing team, can demand uncertainty be fundamentally reduced. The proposed risk assessment model realizes the method innovation and theoretical innovation. It can practical and effectively help relevant enterprises to determine and control risks.

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