Concept Of Equilibrium Research Articles

Economic Growth in a Cooperative Economy

Abstract We develop and formalise an equilibrium concept for a dynamic economy in which production takes place in worker cooperatives. The concept rules out allocations of workers to cooperatives in which a worker in one cooperative could move to a different cooperative and make both herself and the existing workers in the receiving cooperative better off. It also rules out allocations in which workers in a cooperative would be made better off by some of the other workers leaving. We also provide a minimum-information equilibrium-selection criterion which refines our equilibrium concept. We illustrate the application of our concept and refinement in the context of an overlapping-generation economy with specific preferences and technology. The cooperative economy follows a dynamic path qualitatively similar to the path followed by a capitalist economy, featuring gradual convergence to a steady state with constant output. However the cooperative economy features a static inefficiency, in that, for a given aggregate capital stock, firm size is smaller than what a social planner would choose. On the other hand, the cooperative economy cannot be dynamically inefficient, and could accumulate capital at a rate that is higher or lower than the capitalist economy. As a result, steady-state income per worker could be higher or lower in the cooperative economy. We also present an illustrative calibration which quantitatively compares steady-state incomes and welfare in a cooperative and in a capitalist economy.

Stabilization of the Shapley value for cooperative games through level‐induced structures

AbstractTaking into consideration that the Shapley value for cooperative games may not be resistant to potential blocking coalitions, this paper examines the integration of coalition formation and stability in cooperative games. Initially, we establish an endogenous procedure specifically designed for superadditive games. This procedure generates a levels structure and a payoff vector, consequently leading to a modified Shapley value that conforms to the stability notion defined as the levels core. Furthermore, we simulate the procedure in a noncooperative manner and employ the concept of strong Nash equilibrium to demonstrate the stability of the procedure's outcome. Lastly, we propose and delineate a value by applying the same procedural approach to scenarios where the levels structure is predetermined externally.

Cooperative coevolution for non-separable large-scale black-box optimization: Convergence analyses and distributed accelerations

Given the ubiquity of non-separable optimization problems in real worlds, in this paper we analyze and extend the large-scale version of the well-known cooperative coevolution (CC), a divide-and-conquer black-box optimization framework, on non-separable functions. First, we reveal empirical reasons of when decomposition-based methods are preferred or not in practice on some non-separable large-scale problems, which have not been clearly pointed out in many previous CC papers. Then, we formalize CC to a continuous-game model via simplification, but without losing its essential property. Different from previous evolutionary game theory for CC, our new model provides a much simpler but useful viewpoint to analyze its convergence, since only the pure Nash equilibrium concept is needed and more general fitness landscapes can be explicitly considered. Based on convergence analyses, we propose a hierarchical decomposition strategy for better generalization, as for any decomposition, there is a risk of getting trapped into a suboptimal Nash equilibrium. Finally, we use powerful distributed computing to accelerate it under the recent multi-level learning framework, which combines the fine-tuning ability from decomposition with the invariance property of CMA-ES. Experiments on a set of high-dimensional test functions validate both its search performance and scalability (w.r.t. CPU cores) on a clustering computing platform with 400 CPU cores.

Platform integration in ride-sourcing markets with heterogeneous passengers

This paper explores the impacts of a novel business model termed platform integration, which enables passengers to simultaneously request on-demand rides from multiple ride-sourcing platforms via a third-party integrator. In particular, we employ an equilibrium model where passenger demand and driver supply are endogenously dependent on the prices and wages that emerge from the competitive interaction between two platforms, with and without an integrator. A Hotelling model is adopted to characterize passengers’ heterogeneity in service preference for different platforms. We employ the concepts of a Nash equilibrium and a shared monopoly to analyze equilibrium outcomes that can arise in various settings of demand and supply characteristics with and without platform integration. We find that how the platform should adjust its price and wage at Nash equilibrium as potential demand increases is affected by the nature of supply. We also find that the profit at Nash equilibrium can increase or decrease in supply capacity depending on the competitive situation of the platforms. We build on these equilibrium results to analyze how platform integration affects the platform’s decision-making of price and wage, and market performance. We find that platform integration can increase platform profit but reduce driver income, and may hurt passengers who have a strong preference for one certain platform, especially in the case of a less heterogeneous supply.

Hierarchical null controllability of a semilinear degenerate parabolic equation with a gradient term

ABSTRACT In this paper, we apply a hierarchical strategy to a semilinear weakly degenerate parabolic equation with non-linearity that depends on the solution of the system and the spatial derivative of the solution. We use the Stackelberg–Nash strategy with one leader aiming to drive the solution to zero and two followers intended to solve a Nash equilibrium corresponding to a bi-objective optimal control problem. Since the system is semilinear, the functionals are not convex in general. To overcome this difficulty, we first prove the existence and uniqueness of the Nash quasi-equilibrium, which is a weaker formulation of the Nash equilibrium. Next, with additional conditions, we establish the equivalence between the concepts of Nash quasi-equilibrium and Nash equilibrium. We establish a suitable Carleman inequality for the adjoint system and then an observability inequality. Based on this observability inequality, we prove the null controllability of the linearized system. Then, using Kakutani's fixed point Theorem, we demonstrate the null controllability of the main system.

Game-Based Flexible Merging Decision Method for Mixed Traffic of Connected Autonomous Vehicles and Manual Driving Vehicles on Urban Freeways

Connected Autonomous Vehicles (CAVs) have the potential to revolutionize traffic systems by autonomously handling complex maneuvers such as freeway ramp merging. However, the unpredictability of manual-driven vehicles (MDVs) poses a significant challenge. This study introduces a novel decision-making approach that incorporates the uncertainty of MDVs’ driving styles, aiming to enhance merging efficiency and safety. By framing the CAV-MDV interaction as an incomplete information static game, we categorize MDVs’ behaviors using a Gaussian Mixture Model–Support Vector Machine (GMM-SVM) method. The identified driving styles are then integrated into the flexible merging decision process, leveraging the concept of pure-strategy Nash equilibrium to determine optimal merging points and timing. A deep reinforcement learning algorithm is employed to refine CAVs’ control decisions, ensuring efficient right-of-way acquisition. Simulations at both micro and macro levels validate the method’s effectiveness, demonstrating improved merging success rates and overall traffic efficiency without compromising safety. The research contributes to the field by offering a sophisticated merging strategy that respects real-world driving behavior complexity, with potential for practical applications in urban traffic scenarios.

East meets west: integrating Yin-Yang theory with immunology teaching.

This perspective article delves into a novel integration of Yin-Yang theory-an ancient Chinese philosophical cornerstone-with the sophisticated realm of immunology. Given the intricate concepts inherent in immunology, many students find it challenging to comprehend the delicate mechanisms governing immune equilibrium and regulation. Given the deep-rooted understanding of Yin-Yang theory among Chinese students, we advocate for an educational strategy that contextualizes the concept of immune equilibrium within the framework of Yin-Yang, thereby offering a more intuitive and engaging learning experience. This method not only capitalizes on the cultural significance of Yin-Yang, but also corresponds to its principles of equilibrium and harmony, thus mirroring the homeostatic essence of immune responses. This article critically assesses this technique's capacity to bolster immune comprehension amongst Chinese students, while also considering its limitations. Despite these limitations, the fusion of these seemingly divergent fields holds substantial promise for augmenting immunology education, promoting critical thinking, and advancing cross-cultural academic discourse. The amalgamation of age-old philosophical insights with modern scientific exploration prompts a reassessment of educational methodologies within immunology, underscoring a novel pedagogical approach that bridges traditional wisdom with contemporary scientific education.

Beckmann’s Bertrand–Edgeworth Duopoly Model: New Pure Strategy Equilibria

In this paper, the concept of weak active equilibrium, which was introduced in the eighties of the twentieth century by Smol’yakov, is used for the first time for a study of Bertrand– Edgeworth oligopoly (that is, competition among firms when firms’ strategies are prices and firms’ production capacities are limited). All symmetric weak active equilibria are found for the basic model of Bertrand–Edgeworth duopoly, which was analysed in the sixties of the twentieth century by Beckmann. However, this model is highly simplified. Also, the question of existence of nonsymmetric weak active equilibria is studied.

Analysis of Interview Results on The Remediation Process of The Dynamic Equilibrium Concept With The Representation-Metacognitive Reinforcement Conceptual Change Model (R-MR CCM)

Objective: This research aims to determine conceptions and changes in conceptions and analyze the results of interviews regarding the remediation process of the dynamic equilibrium concept. Theoretical Framework: Theories associated with student misconceptions, methods for identifying student misconceptions, and methods for resolving student misconceptions. Method: The method used in this study is a mixed method which is a combination of qualitative and quantitative methods, namely the Concurrent Embedded Strategy, which is a combination of qualitative methods and quantitative methods carried out at the same time. This method is very useful for students to find out the conceptions and misconceptions that occur in students. Results and Discussion: After conducting interviews and tests on respondents, the results of the analysis were obtained in the form of misconceptions among respondents that could be identified in the test and interview results at the stage of creating cognitive conflict and respondents could realize the misconceptions experienced after going through the stage of providing assistance for equilibration and using metacognition on an example of a concept so that respondents could dispelling misconceptions altogether. Research Implications: To reduce students' misconceptions about chemical equilibrium material, it is necessary to carry out research on this. With this gradual test instrument, students can get instant feedback and correct any misconceptions they have. Originality/Value: To provide insight into students' perceptions of the misconceptions they experience and how to reduce existing misconceptions. Apart from that, it is to provide insight to teachers regarding how to identify and reduce misconceptions that occur in students.

Recent advances on testability in economic equilibrium models

The revealed preference program started by Paul Samuelson brought a Popperian view of what constituted true scientific discovery to economic theory.11Samuelson (1938). In his Foundations, Samuelson states that “meaningful theorems” are hypotheses “about empirical data which could conceivably be refuted”.22See Samuelson (1947), p. 4. He worried that by appealing to unobservable fundamentals such as preferences, the body of economic theory built upon the premise of rational individual choice lacked a scientific foundation.While the program quickly succeeded in providing an empirical counterpart for the individual choice problem, its application to social outcomes, namely market interactions and games, proved more difficult, and only in the 1990s did the profession start to develop the testable implications of equilibrium concepts in these contexts. Carvajal et al. (2004) covered the early literature that followed the seminal contributions of Brown and Matzkin (1996) and Sprumont (2000). This survey is an update on the state of that literature covering the results of the last two decades. As the reader will see, the Journal of Mathematical Economics has played a key role in developing these ideas.

РАВНОВЕСНОЕ РАСПРЕДЕЛЕНИЕ ПОТОКА НА СЕТИ АВТОМАГИСТРАЛЕЙ ДЛЯ ЭСКИЗНОГО ПЛАНИРОВАНИЯ

The article provides an algorithm for equilibrium traffic alignment, which can be used for sketch plan-ning. The concept of equilibrium and network coding procedures are discussed in detail. It is con-cluded that the approaches need to be consistent with the goals of strategic planning

A Comprehensive Review of Distillation in the Pharmaceutical Industry

Distillation processes play a pivotal role in the pharmaceutical industry for the purification of active pharmaceutical ingredients (APIs), intermediates, and solvent recovery. This summary explores the fundamental principles governing distillation, including mass transfer and phase equilibrium concepts. It delves into various distillation methods employed in pharmaceutical engineering, encompassing fractional distillation, azeotropic/extractive distillation, steam distillation, vacuum distillation, membrane distillation, and molecular distillation. Recent advancements in distillation technology, such as process intensification, miniaturization, and integration with other separation processes, are highlighted. The current state of distillation in pharmaceutical engineering is discussed, addressing regulatory considerations, solvent selection, and recovery challenges. Future prospects emphasize the need for energy-efficient and sustainable processes, advanced distillation technologies, process modeling and optimization, continuous manufacturing integration, and interdisciplinary collaboration. These efforts aim to drive innovation and address the evolving needs of the pharmaceutical industry, ensuring the continued importance of distillation in the purification and separation of pharmaceutical compounds

Semi-empirical model for Henry’s law constant of noble gases in molten salts

Henry’s law constant, which describes the proportionality of dissolved gas to partial pressure of free gas in liquid–gas equilibrium systems, can also be applied to mass transport applications. In this work, we investigated an approach for determining the solubility of noble gases in a molten salt liquid utilizing the equilibrium concept of Henry’s gas constant. Henry’s gas constant is described as a mathematical function dependent on the van der Waals radius of the noble gas and the temperature of the molten salt. The alteration in Gibbs free energy encompasses contributions from both surface and volume energies. Enthalpy and entropy are deduced from these surface and volume energies in the Gibbs free energy formulation. A comparative analysis was conducted between the conventional method and our proposed model. Moreover, useful chemical properties can be determined from examination of surface and volume energies. Our findings provide an accurate and general theory of Gibbs free energy that can be validated experimentally based on the model proposed herein. This work unifies the prediction of Henry gas constant and subsequently the entropy and enthalpy calculation for noble gases in a molten salt solution to a single functional form using van der Waals radius of the gas and temperature of the system. This functional form is then used to perform a multiple regression method to find two parameters corresponding to the surface energy and volume energy. These two parameters are consistent between all combinations of noble gas and molten salt.

Feasibility of Four-Tier Multiple Choice Diagnostic Test for Identification Conception on Chemical Equilibrium Concept

The purpose of this study was to obtain the feasibility of a four-tier multiple choice (4TMC) diagnostic test instrument for the identification of conceptions on chemical equilibrium material in terms of validity, practicality, and effectiveness criteria. This type of research is ADDIE development research with the Analyze, Design, Development, and Evaluation stages. Validity is obtained from a validation sheet consisting of construct, content, and language validity which gets mode = 4, so that the four-tier multiple choice instrument is said to be valid. Practicality is obtained from a learner response questionnaire supported by a learner activity observation sheet. Practicality in terms of the student's response questionnaire is 84% with a very practical category, while the student activity observation sheet gets mode = 1, so the diagnostic test instrument is said to be practical. Effectiveness is obtained from the diagnostic test instrument reliability test. The Cronbach alpha value obtained in the reliability test was 0.798, so the diagnostic test instrument developed was declared reliable. Based on the results of validity, practicality, and effectiveness, the four-tier multiple choice diagnostic test instrument is declared suitable for use.

Monomer Equilibrium and Transport in Emulsion and Miniemulsion Polymerization.

The dual concepts of monomer equilibrium and monomer transport in emulsion and miniemulsion polymerization are discussed in depth. The concepts must be considered together since, first, dispersed-phase polymerizations (in this case emulsion and miniemulsion polymerizations) are by their nature multiphase systems that function only due to interphase mass transfer; and second, because phase equilibrium determines the driving force for monomer transport in these (and all heterophase reaction) systems. Concepts of polymer particle swelling are reviewed, and the question first addressed by Paul Flory in the 1950s: Are emulsion polymerizations transport or reaction limited? is revisited in detail.

A game theoretic decision forest for feature selection and classification

Abstract Classification and feature selection are two of the most intertwined problems in machine learning. Decision trees (DTs) are straightforward models that address these problems offering also the advantage of explainability. However, solutions that are based on them are either tailored for the problem they solve or their performance is dependent on the split criterion used. A game-theoretic decision forest model is proposed to approach both issues. DTs in the forest use a splitting mechanism based on the Nash equilibrium concept. A feature importance measure is computed after each tree is built. The selection of features for the next trees is based on the information provided by this measure. To make predictions, training data is aggregated from all leaves that contain the data tested, and logistic regression is further used. Numerical experiments illustrate the efficiency of the approach. A real data example that studies country income groups and world development indicators using the proposed approach is presented.

Game theoretical analysis in two-echelon sustainable supply chains to manage and coordinate strategic decisions

Business firms and consumers are increasingly and rapidly realizing the benefits of adopting environmental responsibility. The business firms stress including it in their supply chain strategy and/or operations. This paper explores the environmental consciousness and quality attentiveness of consumers in a supply chain. Demand for the product depends on its price, eco-friendly level, and quality of the product. Three decentralized models are developed under three different game theoretical settings. A comparative study of the three game-theoretical models reveals several characteristics. It determines conditions under which channel members can decide the policy for the best possible benefit. The present work explores the effect of customer environmental awareness on the optimal decision. Production of eco-friendly items is also the prime consideration of our paper. It reveals that the manufacturer gets the most profit in the manufacturer Stackelberg game model, but the retailer gets the maximum profit from the retailer Stackelberg game model. Although channel members prefer their leading position to make the game theoretical decision-making process, the most decentralized channel profit is obtained from the Nash game model. Thus, consumers will also benefit, and the best channel profit can be obtained if the channel members agree to make decentralized decisions using the Nash game model. The centralized channel profit outperforms all three decentralized channel profits. The paper applies the concepts of sub-game perfect equilibrium and alternating offer bargaining to coordinate the channel and distribute surplus profit. Finally, analytical results are verified using numerical examples.

An effective gradient jellyfish search algorithm for optimal reactive power dispatch in electrical networks

AbstractAn effective optimization technique, called gradient jellyfish search optimizer (GJSO), is introduced here to address the optimal reactive power dispatch (ORPD) issue in electric networks. The ORPD problem is a complex non‐linear optimization issue involving integrated variables, aimed at achieving safe and cost‐effective operation of the system by determining optimal values for generator voltage, tap changers of transformers, and reactive power compensation. The performance of the original JSO technique is enhanced by integrating the local escaping operator into the GJSO approach. The effectiveness of the GJSO methodology is evaluated via comparison with two existing methodologies: the original jellyfish search optimizer and the equilibrium optimizer. Jellyfish search optimizer is a meta‐heuristic optimization algorithm inspired by the movement of jellyfish in the water, while equilibrium optimizer draws inspiration from game theory and equilibrium concepts. Simulations were conducted using typical IEEE‐30 bus and IEEE‐57 bus systems to validate the performance of the GJSO methodology. Two versions of the objective function are examined: minimizing line power loss and minimizing total voltage deviations at the buses. The simulation results demonstrated that the GJSO algorithm exhibited superior performance in terms of accuracy and stability compared to the standard jellyfish search optimizer and equilibrium optimizer algorithms.

Testimonial justification under epistemic conflict of interest

Can a hearer be rationally justified to have beliefs based on testimony alone when the source of his information is known to have conflicting epistemic goals? When it comes to belief justification, existing theories either recommend avoiding epistemic conflicts of interest or ignoring them. This is an important epistemological limitation. A theory that comes in degrees, capable of explaining what beliefs we are justified to hold and why, despite epistemic conflict of interest, is still lacking. Building on a game-theoretical approach, I suggest such a theory and argue that the hearer can justify some beliefs on testimony alone. This justification relies on an equilibrium concept, which is only reached in the long run. In addition, the hearer’s justified beliefs will always be less accurate than those held by the original source. For instance, assume the speaker is a climate scientist who has good reasons to believe that a 2∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\circ }$$\\end{document}C increase in temperature will lower the current global GDP by 10 percentage points. Under epistemic conflict of interest, a hearer will typically be justified to a belief close to that value, but not equal to it. The smaller the epistemic conflict of interest, the closer, on average, the hearer’s and speaker’s belief. These results highlight the importance of scientific norms which, in practice, are the embodiment of these equilibrium mechanisms and thus of scientific credibility.

Pengembangan Instrumen Tes Diagnostik Five-Tier Multiple Choice untuk Mengidentifikasi Miskonsepsi Siswa pada Materi Kesetimbangan Kimia

This research aims to report the results of identifying the level of misconceptions and the sources causing the misconceptions experienced by class XI IPA students at SMAN 17 Medan regarding the concept of chemical equilibrium. This research is descriptive research using the ADDIE development model. Data collection in this research used tests, interviews and questionnaires. The results of the wide-scale trial showed that the level of misconception of class The largest percentage of misconceptions is the concept of chemical equilibrium in industry at 29%. The lowest percentage of misconceptions experienced by students was understanding the concept of chemical equilibrium at 2%. The highest percentage of categories that cause misconceptions experienced by students is in the MC-PT category or misconceptions caused by individuals at 73% and the lowest category percentage was shown in the MC-B category or misconceptions obtained from books at 34%.