scholarly journals Consistent Conjectural Variations Equilibrium in a Mixed Duopoly

2011 ◽  
Vol 15 (4) ◽  
pp. 425-432 ◽  
Author(s):  
Nataliya I. Kalashnykova ◽  
◽  
Vladimir A. Bulavsky ◽  
Vyacheslav V. Kalashnikov ◽  
Felipe J. Castillo Pérez ◽  
...  
Keyword(s):  
Demand Function ◽  
Market Price ◽  
Mixed Duopoly ◽  
Demand Functions ◽  
Interior Equilibrium ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Influence Coefficients ◽  
Conjectural Variations ◽  
Conjectural Variations Equilibrium

In this paper, we consider a model of mixed duopoly with Conjectured Variations Equilibrium (CVE). The agents’ conjectures concern the price variations depending on the increase or decrease in their production outputs. We establish existence and uniqueness results for the conjectured variations equilibrium (called an exterior equilibrium) for any set of feasible conjectures. To introduce the notion of an interior equilibrium, we develop a consistency criterion for the conjectures (referred to as influence coefficients) and prove the existence theorem for the interior equilibrium (understood as a CVE with consistent conjectures). To prepare the base for the extension of our results to the case of non-differentiable demand functions, we also investigate the behavior of the consistent conjectures in dependence upon a parameter representing the demand function derivative with respect to the market price.

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 A Bilevel Human Migration Model

2012 ◽  
Vol 11 (2) ◽  
pp. 195 ◽  
Author(s):  
Vyacheslav V. Kalashnikov ◽  
Nataliya I. Kalashnykova ◽  
M. Aracelia Alcorta Garcia ◽  
Yazmin G. Acosta Sanchez ◽  
Vitaly V. Kalashnikov
Keyword(s):  
Programming Model ◽  
Human Migration ◽  
Special Technique ◽  
Migration Model ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Influence Coefficients ◽  
Conjectural Variations ◽  
Upper Level ◽  
Conjectural Variations Equilibrium

In this paper, we develop a bi-level human migration model using the concept of conjectural variations equilibrium (CVE). In contrast to previous works, here we construct a bi-level programming model. The upper level agents are municipalities of competing locations, whose strategies are investments into infrastructures of the locations (cities, towns, etc.). These investments aim at making the locations more attractive for both the residents and potential migrants from other locations. At the lower level of the model, the present residents (grouped into professional communities) are also considered as potential migrants to other locations. They make their decision where to migrate (if at all) comparing the expected values of the utility functions of the destinations and original locations, which are estimated by taking into account their group's conjectures concerning equilibrium migration flows between the involved locations. Applying a special technique to verify the consistency of the conjectures (influence coefficients), the existence and uniqueness results for the consistent conjectural variations equilibrium (CCVE) are established.

Consistent Conjectural Variations Equilibrium in a Semi-Mixed Duopoly

2017 ◽  
Vol 21 (7) ◽  
pp. 1125-A-17
Author(s):  
Vitaliy V. Kalashnikov ◽  
José G. Flores-Muñiz ◽  
Vyacheslav V. Kalashnikov ◽  
Nataliya I. Kalashnykova ◽  
◽  
...  
Keyword(s):  
Convex Combination ◽  
Mixed Duopoly ◽  
Private Company ◽  
Interior Equilibrium ◽  
Public Company ◽  
Optimal Value ◽  
Conjectural Variations ◽  
Social Surplus ◽  
The One ◽  
Conjectural Variations Equilibrium

This paper considers conjectural variations equilibrium (CVE) in the one item market with a mixed duopoly of competitors. The duopoly is calledsemi-mixedbecause one (semi-public) company’s objective is to maximize a convex combination of her net profit and domestic social surplus (DSS). The two agents make conjectures about fluctuations of the equilibrium price occurring after their supplies having been varied. Based on the concepts of theexteriorandinterior equilibrium, as well as the existence theorem for the interior equilibrium (a.k.a. the consistent CVE, or the exterior equilibrium withconsistent conjectures) demonstrated in the authors’ previous papers, we analyze the behavior of the interior equilibrium as a function of the semi-public firm’s level of socialization. When this parameter reflected by the convex combination coefficient tends to 1, thus transforming the semi-public company into a completely public one, and the considered model into the classical mixed duopoly, two trends are apparent. First, for the private company, the equilibrium with consistent conjectures (CCVE) becomes more attractive (lucrative) than the Cournot-Nash equilibrium. Second, there exists a (unique in the case of an affine demand function) value of the convex combination coefficient such that the private agent’s profit is the same in both of the above-mentioned equilibrium types, thus making no subsidy to the producer or to the consumers necessary. Numerical experiments with various mixed duopoly models confirm the robustness of the proposed algorithm for finding the optimal value of the above-mentioned combination coefficient (a.k.a. the semi-public company’s socialization level).

Conjectural variations equilibrium in a mixed duopoly

2009 ◽  
Vol 192 (3) ◽  
pp. 717-729 ◽  
Author(s):  
Vyacheslav Kalashnikov ◽  
Claudia Kemfert ◽  
Vitaly Kalashnikov
Keyword(s):  
Mixed Duopoly ◽  
Conjectural Variations ◽  
Conjectural Variations Equilibrium

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.

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.

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