Consistent Conjectural Variations Equilibrium Research Articles

Consistent Conjectural Variations Equilibrium for a Financial Model

Consistent Conjectural Variations Equilibrium for a Financial Model

Consistent Conjectural Variations Equilibrium in a Mixed Oligopoly Model With a Labor-Managed Company and a Discontinuous Demand Function

In this work, we examine a mixed oligopoly model within the framework of consistent conjectural variations, in which one of the producers is a labor-managed company competing with other private firms, and consumer demand is given by a discontinuous function. Private firms attempt to maximize their net profit while the labor-managed company attempts to maximize the convex combination of its net profit with an income-per-worker function, which describes the mixed nature of the model. Each producer conjectures the dependence of the market-clearing price on its own production volume and then selects its most suitable conjecture based on a verification procedure. We introduce the notions of exterior and interior equilibrium and prove the existence and uniqueness of the conjectural variation equilibrium, as well as the existence of the particular equilibrium states known as consistent. Finally, we analyze the behavior of the market’s consistent equilibrium state in response to changes in consumer demand.

Consistent Conjectural Variations Equilibrium in the Semi-Mixed Oligopoly

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.

Special Issue on Variational Inequalities: Consistent Conjectural Variations Coincide with the Nash Solution in the Meta-Model

We keep investigating the properties of consistent conjectural variations equilibrium (CCVE) developed for a single-commodity oligopoly. Although, in general, the consistent conjectures are distinct from those of Cournot-Nash, in our previous papers, we established the following remarkable fact. Define a meta-model as such where the players are the same agents as in the original oligopoly but now using the conjectures as their strategies. Then the Cournot-Nash equilibrium in the meta-model generated the consistent conjectural variations equilibrium in the original oligopoly. In this paper, we study the conditions under which the inverse is also true, that it, every consistent CVE provides for the Cournot-Nash optimal strategies for the meta-model. This equivalence allows one to extend the concept of CCVE to other kinds of economic and financial models lacking the oligopoly structure.

Consistent Conjectural Variations Equilibrium in a Semi-Mixed Duopoly

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).

Consistent conjectures are optimal Cournot-Nash strategies in the meta-game

In this paper, we investigate the properties of consistent conjectural variations equilibrium developed for a single-commodity oligopoly. Although, in general, the consistent conjectures are distinct from those of Cournot-Nash, we establish the following remarkable fact. Define a meta-game as such where the players are the same agents as in the original oligopoly but now using the conjectures as their strategies. Then the consistent conjectures of the original oligopoly game provide for the Cournot-Nash optimal strategies in the meta-game.

Finding Consistent Conjectural Variations Equilibrium in a Human Migration Model

Abstract In this paper, we develop a human migration model using the concept of conjectural variations equilibrium (CVE). In contrast to previous works we extend the model to the case where the conjectural variations coefficients may be not only constants, but also (continuously differentiable) functions of the total population at the destination and of the group's fraction in it. Moreover, we allow these functions to take distinct values at the abandoned location and at the destination. As an experimental verification of the proposed model, we develop a specific form of the model based upon relevant population data of a three-city agglomeration at the boundary of two Mexican states: Durango (Dgo.) and Coahuila (Coah.) Namely, we consider the 1980-2015 dynamics of population growth in the three cities: Torreon (Coah.), Gomez Palacio (Dgo.) and Lerdo (Dgo.), and propose utility functions of four various kinds for each of the three cities. After having collected necessary information about the average movement and transportation costs for each pair of the cities, we apply the above-mentioned human migration model to this example. Numerical experiments have been conducted revealing interesting results concerning the consistency of probable conjectural variations equilibrium states.

Structure of demand and consistent conjectural variations equilibrium (CCVE) in a mixed oligopoly model

We study conjectured variations equilibrium (CVE) in a model of mixed oligopoly with not necessarily continuous demand functions. The agents’ conjectures concern the price variations depending upon their production output increase or decrease. We establish the existence and uniqueness results for the CVE (called exterior equilibrium) for any set of feasible conjectures. To introduce the notion of 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 CVE with consistent conjectures, or CCVE). In addition, we also examine the behavior of the consistent conjectures as functions of a parameter representing the demand’s derivative with respect to the market price. The latter results allow one to predict the behavior of groups of consumers with different consumption abilities. The proposed techniques permit one to develop a qualitative description of the dependence of the market price on the active demand component, too. It should be noticed that due to the non-smoothness of the demand function, there is possibly a path dependency and indeterminacy of equilibria in certain cases. This is, on the one hand, a theoretically inconvenient result (multiple equilibria), but on the other hand, it may happen to be extremely useful for applications. Indeed, the latter multiplicity of equilibria might serve as a rationale for the regulatory intervention to induce a change of equilibrium whenever the total welfare could be improved (cf., for example, the Keynesian stimulus).

Consistent Conjectural Variations Equilibrium In A Bilevel Human Migration Model

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 Mixed Duopoly

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.

Consistency of conjectures and reactions?

This note discusses consistency in conjectural variations models for oligopoly theory. It is argued that consistency of conjectures and reactions is not an appropriate equilibrium concept, since reaction functions do not have a role in conjectural variations models. Furthermore, the reaction functions used in the concept of a consistent conjectural variations equilibrium are based on unobservable information sets. A weaker type of consistency, that is, consistency of conjectures and actions, is proposed as an alternative. This consistent conjectures equilibrium has for each set of conjectures one of a variety of competitive and collusive outcomes as a solution.

Optimal tariffs in consistent conjectural variations equilibrium

This paper analyzes the determination of the optimal tariff under the assumption of consistent conjectural variations (CCV). A general characterization of the CCV equilibrium is given. We show that (i) there are, in general, a multiplicity of each equilibria, and (ii) under certain restrictions, the Cournot equilibrium, which is based on the assumption of no retaliation, can also be a CCV equilibrium. By contrast, free trade is never a CCV equilibrium. Finally, the CCV equilibrium is solved explicitly in a simple example.