Conjectural Variations Equilibrium Research Articles

Consistent Conjectural Variations Equilibrium for a Financial Model

Consistent Conjectural Variations Equilibrium for a Financial Model

Dynamic behaviors in a Cournot duopoly model with knowledge spillover effect based on constant conjectural variation

On the basis of constant conjectural variation, a static Cournot duopoly model is built first in this paper, where the effects of knowledge spillover and product differentiation have been parameterized. Through the first order conditions, we can obtain the static conjectural variation equilibrium. By using the gradient adjustment mechanism, a dynamic conjectural variation model, represented by a two-dimensional difference equation, is established, in which two firms have bounded rationality. Then, the local stability of the Nash equilibrium is analyzed. From further studies on the effects of conjectural variation to the dynamics of the established model, we conclude that the more intense the market competition, the bigger the size of the stability region. In general case, the two axes are invariant sets, while the diagonal line is also an invariant set in symmetric case. Through the method of numerical simulation, we can deeply understand the complex characteristics of dynamic behaviors and the means for economic activities. Finally, synchronized behaviors are also studied by the method of critical curves and basins of attraction.

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.

Inventory Control Over a Short Time Horizon Under Unknown Demand Distribution

We address inventory control by a manufacturer under stochastic customer demand over a finite time horizon when little is known about the demand. To handle the problem, we replace it with a deterministic differential game in which the manufacturer competes with the customer's demand. On the basis of the conjectural variation equilibrium of this game, we derive a heuristic for the original stochastic problem; conjectural variation is used as a tuning parameter for the heuristic.

Conjectural variations in aggregative games: An evolutionary perspective

Suppose that in symmetric aggregative games, in which payoffs depend only on a player’s strategy and on an aggregate of all players’ strategies, players have conjectures about the reaction of the aggregate to marginal changes in their strategy. The players play a conjectural variation equilibrium, which determines their fitness payoffs. The paper shows that only consistent conjectures can be evolutionarily stable in an infinite population, where a conjecture is consistent if it is equal to the marginal change in the aggregate determined by the actual best responses. In the finite population case, only zero conjectures representing aggregate-taking behavior can be evolutionarily stable.

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.

Analysis of Consistent Equilibria in a Mixed Duopoly

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.

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).

On Kantian Equilibrium and Conjectural Variation Equilibrium

In this paper, I make a connection between a Kantian equilibrium for a game as introduced in Roemer (2010) and a conjectural variation equilibrium as discussed in the literature on oligopolistic competition. I show that, for the class of games studied by Roemer (2010), any Kantian equilibrium is an appropriate conjectural variation equilibrium.

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.

Mixed oligopoly with consistent conjectures

In this paper, we consider a model of mixed oligopoly with conjectural variations equilibrium (CVE). The agents’ conjectures concern the price variations depending upon their production output’s increase or decrease. We establish existence and uniqueness results for the conjectural 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’s derivative with respect to the market price.

Strategic Delegation and Dynamic Competition

The separation of ownership and control in rms brings up the issue of how and what to delegate to managers. There exists a large body of literature that analyzes strategic delegation in which owners understand the incentives that managers face when they operate in imperfectly competitive product markets. In this paper we analyze strategic delegation under the assumption that rms operate in dynamic oligopolies. We derive the optimal strategic incentive in this setting and point out that the dynamic incentive can be replicated by a static one in which rms play a conjectural variations equilibrium in the output market.

Conjectural variations equilibrium in a mixed duopoly

We study a mixed duopoly model, in which a state-owned (public) firm maximizing domestic social surplus and a private (foreign) firm compete. Under general enough assumptions, we first justify the concept of conjectural variations equilibrium (CVE) applied to the model by demonstrating concavity of the expected profit function of each agent. Next we establish existence and uniqueness results for the conjectural variations equilibrium in the described duopoly. A particular case of a CVE with constant influence (conjecture) coefficients is also examined.

Numerical experimentation with a human migration model

In this paper, we develop a human migration model with a 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 1980–2000 dynamics of population growth in the three cities: Torreón (Coah.), Gómez 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 (i.e., migration) costs for each pair of the cities, we apply the above-mentioned human migration model to this example. Numerical experiments have been conducted with interesting results concerning the probable equilibrium states revealed.

Un modelo de migración humana: experimentos numéricos basados sobre los datos de las tres ciudades laguneras / A Model of Human Migration: Numerical Experiments Based on the Data of Three Lake Cities

Se aplica un modelo de migración humana al estudio de crecimiento de población en las tres ciudades aglomeradas en la región Lagunera de México. Se introducen tres tipos de funciones de utilidad para distintos grupos de población, y se investiga un equilibrio con variaciones conjeturales. Los experimentos numéricos basados en datos de las tres ciudades muestran la fuerte influencia de los coeficientes de variaciones conjeturales sobre la actividad migratoria esperada.AbstractWe extend a human migration model and apply it to study the growth of population in three agglomerated cities in the Laguna region in Mexico. Three different types of utility functions for various groups of population are proposed, and conjectural variations equilibrium is investigated. Numerical experiments demonstrate the strong influence of conjectural coefficients upon the expected migration activity.