Stability and Generalized Competitive Equilibria in a Many-to-Many Gale-Shapley Market Model

2016 ◽  
Vol 63 (3) ◽  
pp. 237-254
Author(s):  
Zbigniew Świtalski
Keyword(s):  
Competitive Equilibrium ◽  
College Admissions ◽  
Supply And Demand ◽  
Type A ◽  
Market Model ◽  
Stable Matchings ◽  
Competitive Equilibria

We define, for some variant of a many-to-many market model of Gale-Shapley type, a concept of generalized competitive equilibrium and show that, under suitable conditions, stable matchings in such a model can be represented as competitive equilibria allocations (and vice versa). Our results are far-reaching generalizations of the “discrete supply and demand lemma” of Azevedo, Leshno (2011) for the college admissions market.Using the results of Alkan, Gale (2003), we also prove a theorem on existence of generalized equilibria in our model.

Competing Teams

2019 ◽  
Vol 87 (3) ◽  
pp. 1134-1173 ◽  
Author(s):  
Hector Chade ◽  
Jan Eeckhout
Keyword(s):  
Market Power ◽  
Competitive Equilibrium ◽  
Knowledge Spillovers ◽  
Market Model ◽  
Strategic Interactions ◽  
Market Structures ◽  
Economic Applications ◽  
The Standard Model ◽  
Competitive Equilibria ◽  
Shed Light

Abstract In many economic applications of matching, the teams that form compete later in market structures with strategic interactions or with knowledge spillovers. Such post-match competition introduces externalities at the matching stage: a team’s payoff depends not only on their members’ attributes but also on those of other matched teams. This article develops a large market model of matching with externalities, in which first teams form, and then they compete. We analyse the sorting patterns that ensue under competitive equilibrium as well as their efficiency properties. Our main results show that insights substantially differ from those of the standard model without externalities: there can be multiple competitive equilibria with different sorting patterns; both optimal and competitive equilibrium matching can involve randomization; and competitive equilibrium can be inefficient with a matching that can drastically deviate from the optimal one. We also shed light on the economic relevance of our matching model with externalities. We analyse two economic applications that illustrate how our model can rationalize the trend in within- and between-firm inequality, and also the evolution of markups of sectors where firms have market power.

Stability and Price Equilibria in a Many-to-Many Gale-Shapley Market Model

2017 ◽  
Vol 64 (3) ◽  
pp. 229-248
Author(s):  
Zbigniew Świtalski
Keyword(s):  
Market Model ◽  
Stable Matchings ◽  
Competitive Equilibria ◽  
The Many

In the paper we study relationships between generalized competitive equilibria defined in the paper of Świtalski (2016) and price equilibria for some variant of many-to-many market model of Gale- Shapley type and between price equilibria and stable matchings for such a model. Obtained results are used for proving theorems on existence of price equilibria in the many-to-many GS-model and in the many-to-many model generalizing the model of Chen, Deng and Ghosh (Chen et al., 2014).

scholarly journals Non-smooth analysis in a national electricity market model: a complex approach

Memorias ◽  
2018 ◽  
pp. 58-66
Author(s):  
Johnny Valencia ◽  
Gerard Olivar ◽  
Johan Manuel Redondo ◽  
Danny Ibarra Vega ◽  
Carlos Peña Rincón
Keyword(s):  
System Dynamics ◽  
Electricity Market ◽  
Equilibrium Points ◽  
Supply And Demand ◽  
Market Model ◽  
National Network ◽  
Demand Growth ◽  
Zero Rate ◽  
National Electricity Market ◽  
Business Approach

In this paper, we show the preliminary results in a proposed a model for the supply and demand of electricity in a domestic market based on system dynamics. Additionally, the model indicates piecewise smooth differential equations arising from the diagram of flows and levels, using dynamical systems theory for the study of the stability of the equilibrium points that have such a system. A bifurcation analysis approach is proposed to define and understand the complex behavior. Until now, no work has been reported related to this topic using bifurcations criteria. The growing interest in personal ways of self-generation using renewable sources can lead the national grid to a standstill and low investment in the system. However, it is essential to preserve the national network as a power supply support to domestic and enterprise demand. To understand this scenario, we include an analysis of zero-rate demand growth. Under this hypothesis, a none smooth bifurcation appears related to a policy which involves the variation of the capacity charge. As a first significant result, we found that it is possible to preserve the investments in the market since, through the capacity charge parameter, the system dynamics can be controlled. Then, from a business approach, it is necessary to know the effects of the capacity charge as the strategic policy in the system generation price scheme.

scholarly journals Existence of General Competitive Equilibria: A Variational Approach

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
G. Anello ◽  
F. Rania
Keyword(s):  
Variational Inequalities ◽  
Finite Number ◽  
Variational Methods ◽  
Variational Approach ◽  
Existence Result ◽  
Competitive Equilibrium ◽  
Utility Functions ◽  
Locally Lipschitz ◽  
Competitive Equilibria

We study the existence of general competitive equilibria in economies with agents and goods in a finite number. We show that there exists a Walras competitive equilibrium in all ownership private economies such that, for all consumers, initial endowments do not contain free goods and utility functions are locally Lipschitz quasiconcave. The proof of the existence of competitive equilibria is based on variational methods by applying a theoretical existence result for Generalized Quasi Variational Inequalities.

scholarly journals Market Model with Positive Demand Curve Overthrows Marxist and Keynesian Model

2020 ◽  
Vol 9 (3) ◽  
pp. 59
Author(s):  
Alqi Naqellari
Keyword(s):  
Demand Curve ◽  
Supply And Demand ◽  
Market Price ◽  
Marxist Theory ◽  
Market Model ◽  
Supply Curve ◽  
Demand And Supply ◽  
Keynesian Model ◽  
Analysis And Synthesis ◽  
Macroeconomic Indicators

In this paper is analyzed the demand and supply side from the perspective of Marxist theory. The supply and demand side is both analyzed with their respective characteristics in capitalism, socialism and in a mixed economy. The possibilities of a macroeconomic equilibrium by considering the following concepts such as commodity, value, price, profit are analyzed. The aim of this paper is: to develop through a non-exhaustive analysis, the common features and differences between macroeconomic models of the aggregate market in the two systems, to build the aggregate market of a macroeconomic model by taking into account these characteristics and to emphasize its importance for the economy. In conclusion, differences between concepts related to macroeconomic equilibrium were identified. A new equilibrium model for the socialist and capitalist model was built. In centralized economies, demand and supply curve lies in a parallel curve with the X-axis, were domestic product is placed. In the market economy model, the demand and supply curve has a positive slope and stretch simultaneously over the market price line. They do not intersect with each other as in the Classical and Keynesian model. This market model applies to the economy. It allows governments, central banks, research institutions, universities, various researchers, etc. to analyze macroeconomic indicators. In this paper, the model is applied to the Albanian economy. In this paper, we used the methods of analysis and synthesis, comparison and description, the method of creating virtual market models, etc.

scholarly journals Competitive Equilibrium and Trading Networks: A Network Flow Approach

2020 ◽  
Author(s):  
Ozan Candogan ◽  
Markos Epitropou ◽  
Rakesh V. Vohra
Keyword(s):  
Network Flow ◽  
Competitive Equilibrium ◽  
Flow Problem ◽  
Comparative Statics ◽  
Bilateral Contracts ◽  
Submodular Flow ◽  
Competitive Equilibria ◽  
Trading Networks ◽  
The Impact ◽  
Shed Light

This paper considers a network of agents who trade indivisible goods or services via bilateral contracts. Under a substitutability assumption on preferences, it is known that a competitive equilibrium exists. In “Competitive Equilibrium and Trading Networks: A Network Flow Approach,” Candogan, Epitropou, and Vohra show how to determine equilibrium outcomes as a generalized submodular flow problem. Existence of a competitive equilibrium and its equivalence to seemingly weaker notions of stability follow directly from the optimality conditions of the flow problem. The formulation enables the authors to perform comparative statics with respect to the number of buyers, sellers, and trades. In particular, they are able to shed light on the impact of new trading opportunities on the equilibrium trades, prices, and surpluses. In addition, they present algorithms for finding competitive equilibria in trading networks and testing stability.

Statistical Representations

2013 ◽  
Author(s):  
Lars Peter Hansen ◽  
Thomas J. Sargent
Keyword(s):  
Competitive Equilibrium ◽  
Likelihood Function ◽  
Linear Functions ◽  
State Variables ◽  
Vector Autoregressive ◽  
Competitive Equilibria ◽  
History Of ◽  
Complete History ◽  
Recursive Representation ◽  
Over Time

This chapter describes links between competitive equilibria and autoregressive representations. It shows how to obtain an autoregressive representation for observable variables that are error-ridden linear functions of state variables. In describing how to deduce an autoregressive representation from a competitive equilibrium and parameters of measurement error processes, it completes a key step that facilitates econometric estimation of free parameters. An autoregressive representation is naturally affiliated with a recursive representation of a likelihood function for the observable variables. More precisely, a vector autoregressive representation implements a convenient factorization of the joint density of a complete history of observables (i.e., the likelihood function) into a product of densities of time t observables conditioned on histories of those observables up to time t−1. The chapter also treats two other topics intimately related to econometric implementation: aggregation over time and the theory of approximation of one model by another.

scholarly journals A Sparsity-Based Model of Bounded Rationality *

2014 ◽  
Vol 129 (4) ◽  
pp. 1661-1710 ◽  
Author(s):  
Xavier Gabaix
Keyword(s):  
Phillips Curve ◽  
Competitive Equilibrium ◽  
Limited Attention ◽  
One Dimensional ◽  
First Order ◽  
The World ◽  
Welfare Theorems ◽  
Competitive Equilibria ◽  
Rational Version ◽  
Offer Curve

AbstractThis article defines and analyzes a “sparse max” operator, which is a less than fully attentive and rational version of the traditional max operator. The agent builds (as economists do) a simplified model of the world which is sparse, considering only the variables of first-order importance. His stylized model and his resulting choices both derive from constrained optimization. Still, the sparse max remains tractable to compute. Moreover, the induced outcomes reflect basic psychological forces governing limited attention. The sparse max yields a behavioral version of basic chapters of the microeconomics textbook: consumer demand and competitive equilibrium. I obtain a behavioral version of Marshallian and Hicksian demand, Arrow-Debreu competitive equilibrium, the Slutsky matrix, the Edgeworth box, Roy’s identity, and so on. The Slutsky matrix is no longer symmetric: nonsalient prices are associated with anomalously small demand elasticities. Because the consumer exhibits nominal illusion, in the Edgeworth box, the offer curve is a two-dimensional surface rather than a one-dimensional curve. As a result, different aggregate price levels correspond to materially distinct competitive equilibria, in a similar spirit to a Phillips curve. The Arrow-Debreu welfare theorems typically do not hold. This framework provides a way to assess which parts of basic microeconomics are robust, and which are not, to the assumption of perfect maximization.

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