Mixed Oligopoly: Analysis of Consistent Equilibria

2014 ◽  
Vol 18 (6) ◽  
pp. 971-984
Author(s):  
Vyacheslav V. Kalashnikov ◽  
◽  
Vladimir A. Bulavsky ◽  
Nataliya I. Kalashnykova ◽  
Junzo Watada ◽  
...  
Keyword(s):  
Existence And Uniqueness ◽  
Convex Combination ◽  
Mixed Oligopoly ◽  
Private Companies ◽  
Interior Equilibrium ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Net Profit ◽  
Fixed Set ◽  
Social Surplus

In this paper, a model of mixed oligopoly with conjectured variations equilibrium (CVE) is examined, in which one of the agents maximizes a convex combination of its net profit with the domestic social surplus. The agents’ conjectures concern the price variations, which depend on the variations in their production outputs. Using the established existence and uniqueness results for the CVE (theexterior equilibrium) for any fixed set of feasible conjectures, the notion of the interior equilibrium is introduced by developing a conjecture consistency criterion. Then, the existence theoremfor the interior equilibrium (defined as a CVE state withconsistent conjectures) is proven. When the convex combination coefficient tends to 1 (thus transforming the model into the mixed oligopoly in its extreme form), two trends are apparent. First, for private companies, the equilibrium with consistent conjectures becomes more proficient than the Cournot-Nash equilibrium. Second, there exists a (unique) value of the convex combination coefficient such that the private agent’s aggregate profit is the same in both the above-mentioned equilibria, which makes subsidies to producers or consumers unnecessary.

Analysis of Consistent Equilibria in a Mixed Duopoly

2014 ◽  
Vol 18 (6) ◽  
pp. 962-970 ◽  
Author(s):  
Vyacheslav V. Kalashnikov ◽  
◽  
Vladimir A. Bulavsky ◽  
Nataliya I. Kalashnykova ◽  
Junzo Watada ◽  
...  
Keyword(s):  
Convex Combination ◽  
Mixed Duopoly ◽  
Private Company ◽  
Interior Equilibrium ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Influence Coefficients ◽  
Social Surplus ◽  
Production Output ◽  
Conjectural Variations Equilibrium

This paper examines a model of a mixed duopoly with conjectural variations equilibrium (CVE), in which one of the agents maximizes a convex combination of his/her net profit and domestic social surplus. The agents’ conjectures concern the price variations, which depend on their production output variations. Based on the already established existence and uniqueness results for the CVE (called theexterior equilibrium) for any set of feasible conjectures, the notion of interior equilibrium is introduced by developing a consistency criterion for the conjectures (referred to as influence coefficients), and the existence theorem for the interior equilibrium (understood as a CVE state withconsistent conjectures) is proven. When the convex combination coefficient tends to 1, thus transforming the model into the mixed duopoly in its extreme form, two trends are apparent. First, for the private company, the equilibrium with consistent conjectures becomes more proficient than the Cournot-Nash equilibrium. Second, there exists a (unique) value of the combination coefficient such that the private agent’s profit is the same in both of the above-mentioned equilibria, which makes subsidies to the producer or to consumers unnecessary.

scholarly journals Consistent Conjectural Variations Equilibrium in the Semi-Mixed Oligopoly

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Gabriela Renata Huarachi-Benavídez ◽  
José Guadalupe Flores-Muñiz ◽  
Nataliya Kalashnykova ◽  
Viacheslav Kalashnikov
Keyword(s):  
Convex Combination ◽  
Mixed Oligopoly ◽  
Perfect Competition ◽  
Oligopoly Model ◽  
Interior Equilibrium ◽  
Public Company ◽  
Conjectural Variations ◽  
Social Surplus ◽  
Production Output ◽  
Conjectural Variations Equilibrium

We study a variant of the mixed oligopoly model with conjectural variations equilibrium, in which one of the producers maximizes not his net profit but the convex combination of the latter with the domestic social surplus. The coefficient of this convex combination is named socialization level. The producers’ conjectures concern the price variations depending upon their production output variations. In this work, we extend the models studied before, considering the case of the producers’ cost functions being convex but not necessarily quadratic. The notion of exterior and interior equilibrium is introduced (similarly to previous works), developing a consistency criterion for the conjectures. Existence and uniqueness theorems are formulated and proven. Results concerning the comparison between conjectural variations, perfect competition, and Cournot equilibriums are provided. Based on these results, we formulate an optimality criterion for the election of the socialization level. The existence of the optimal socialization level is proven under the condition that the public company cannot be too weak as compared to the private firms.

scholarly journals Multi-term fractional differential equations with nonlocal boundary conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 1519-1536
Author(s):  
Bashir Ahmad ◽  
Najla Alghamdi ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
The Given

AbstractWe introduce and study a new kind of nonlocal boundary value problems of multi-term fractional differential equations. The existence and uniqueness results for the given problem are obtained by applying standard fixed point theorems. We also construct some examples for demonstrating the application of the main results.

scholarly journals BSDEs with polynomial growth generators

2000 ◽  
Vol 13 (3) ◽  
pp. 207-238 ◽  
Author(s):  
Philippe Briand ◽  
René Carmona
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Polynomial Growth ◽  
Probabilistic Representation ◽  
Existence And Uniqueness Results ◽  
State Variable ◽  
Cahn Equation ◽  
Uniqueness Results ◽  
Terminal Time

In this paper, we give existence and uniqueness results for backward stochastic differential equations when the generator has a polynomial growth in the state variable. We deal with the case of a fixed terminal time, as well as the case of random terminal time. The need for this type of extension of the classical existence and uniqueness results comes from the desire to provide a probabilistic representation of the solutions of semilinear partial differential equations in the spirit of a nonlinear Feynman-Kac formula. Indeed, in many applications of interest, the nonlinearity is polynomial, e.g, the Allen-Cahn equation or the standard nonlinear heat and Schrödinger equations.

Nontrivial solutions of non-autonomous dirichlet fractional discrete problems

2020 ◽  
Vol 23 (4) ◽  
pp. 980-995
Author(s):  
Alberto Cabada ◽  
Nikolay Dimitrov
Keyword(s):  
Existence And Uniqueness ◽  
Point Boundary ◽  
Nontrivial Solutions ◽  
Fractional Difference ◽  
Nonlinear Part ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Difference Equation ◽  
Discrete Problems ◽  
Series Of Functions

AbstractIn this paper, we introduce a two-point boundary value problem for a finite fractional difference equation with a perturbation term. By applying spectral theory, an associated Green’s function is constructed as a series of functions and some of its properties are obtained. Under suitable conditions on the nonlinear part of the equation, some existence and uniqueness results are deduced.

Modeling the dynamics of hepatitis E via the Caputo–Fabrizio derivative

2019 ◽  
Vol 14 (3) ◽  
pp. 311 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Zakia Hammouch ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Numerical Scheme ◽  
Arbitrary Order ◽  
Fixed Point Theory ◽  
Hepatitis E ◽  
Point Theory ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Essential Properties

A virus that causes hepatitis E is known as (HEV) and regarded on of the reason for lever inflammation. In mathematical aspects a very low attention has been paid to HEV dynamics. Therefore, the present work explores the HEV dynamics in fractional derivative. The Caputo–Fabriizo derivative is used to study the dynamics of HEV. First, the essential properties of the model will be presented and then describe the HEV model with CF derivative. Application of fixed point theory is used to obtain the existence and uniqueness results associated to the model. By using Adams–Bashfirth numerical scheme the solution is obtained. Some numerical results and tables for arbitrary order derivative are presented.

scholarly journals On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 476
Author(s):  
Jiraporn Reunsumrit ◽  
Thanin Sitthiwirattham
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper, we propose sequential fractional delta-nabla sum-difference equations with nonlocal fractional delta-nabla sum boundary conditions. The Banach contraction principle and the Schauder’s fixed point theorem are used to prove the existence and uniqueness results of the problem. The different orders in one fractional delta differences, one fractional nabla differences, two fractional delta sum, and two fractional nabla sum are considered. Finally, we present an illustrative example.

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