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.

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.

Modeling Financial Bubbles and Market Crashes

2017 ◽  
Author(s):  
Didier Sornette
Keyword(s):  
Stock Market ◽  
Hazard Rate ◽  
Market Price ◽  
Imitative Behavior ◽  
Rational Model ◽  
Basic Principles ◽  
Market Prices ◽  
Speculative Bubbles ◽  
Financial Bubbles ◽  
Market Crashes

This chapter considers two versions of a rational model of speculative bubbles and stock market crashes. According to the first version, stock market prices are driven by the crash hazard that may increase sometimes due to the collective behavior of “noise traders.” The second version assumes the opposite: the crash hazard is driven by prices that may soar sometimes, again due to investors' speculative or imitative behavior. The chapter first provides an overview of what a model is before discussing the basic principles of model construction in finance. It then describes the basic ingredients of the two models of speculative bubbles and market crashes, along with the main properties of the risk-driven model. It also examines how imitation and herding drive the crash hazard rate and concludes with an analysis of the price-driven model, how imitation and herding drive the market price, and how the price return drives the crash hazard rate.

scholarly journals Study of Inventory Model for Deteriorating Items With Exponential Demand Function

2016 ◽  
Vol 34 ◽  
pp. 89-100
Author(s):  
Manik Mondal ◽  
Mohammed Forhad Uddin ◽  
Kazi Anowar Hussain
Keyword(s):  
Opportunity Cost ◽  
Demand Function ◽  
Trade Credit ◽  
Unit Cost ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Bisection Method ◽  
Credit Policy ◽  
Deterioration Rate ◽  
Linear Demand

This paper develops an inventory model for deteriorating items consisting the ordering cost, unit cost, opportunity cost, deterioration cost and shortage cost. In this inventory model instead of linear demand function nonlinear exponential function of time for deteriorating items with deterioration rate has been considered. The formulated model has numerically solved by bisection method. The effects of inflation and cash flow are also taken into account under a trade-credit policy of discount with time. In order to validate the model, numerical examples have been solved by bisection method using Matlab. Further, the sensitivity of different parameters is considered in order to estimate the cash flow.GANIT J. Bangladesh Math. Soc.Vol. 34 (2014) 89-100

Scheduling jobs by stochastic processing requirements on parallel machines to minimize makespan or flowtime

1982 ◽  
Vol 19 (1) ◽  
pp. 167-182 ◽  
Author(s):  
Richard R. Weber
Keyword(s):  
Probability Distribution ◽  
Hazard Rate ◽  
Parallel Machines ◽  
Random Variables ◽  
Expected Value ◽  
Hazard Rates ◽  
Stochastic Processing ◽  
Identical Machines ◽  
Exponential Random Variables ◽  
Monotone Hazard Rate

A number of identical machines operating in parallel are to be used to complete the processing of a collection of jobs so as to minimize either the jobs' makespan or flowtime. The total processing required to complete each job has the same probability distribution, but some jobs may have received differing amounts of processing prior to the start. When the distribution has a monotone hazard rate the expected value of the makespan (flowtime) is minimized by a strategy which always processes those jobs with the least (greatest) hazard rates. When the distribution has a density whose logarithm is concave or convex these strategies minimize the makespan and flowtime in distribution. These results are also true when the processing requirements are distributed as exponential random variables with different parameters.

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