Linear Equilibrium Research Articles

Signaling games in multiple dimensions: Geometric properties of equilibrium solutions

Signaling game problems investigate communication scenarios where encoder(s) and decoder(s) have misaligned objectives due to the fact that they either employ different cost functions or have inconsistent priors. This problem has been studied in the literature for scalar sources under various setups. In this paper, we consider multi-dimensional sources under quadratic criteria in the presence of a bias leading to a mismatch in the criteria, where we show that the generalization from the scalar setup is more than technical. We show that the Nash equilibrium solutions lead to structural richness due to the subtle geometric analysis the problem entails, with consequences in both system design, the presence of linear Nash equilibria, and an information theoretic problem formulation. We first provide a set of geometric conditions that must be satisfied in equilibrium considering any multi-dimensional source. Then, we consider independent and identically distributed sources and characterize necessary and sufficient conditions under which an informative linear Nash equilibrium exists. These conditions involve the bias vector that leads to misaligned costs. Depending on certain conditions related to the bias vector, the existence of linear Nash equilibria requires sources with a Gaussian or a symmetric density. Moreover, in the case of Gaussian sources, our results have a rate–distortion theoretic implication that achievable rates and distortions in the considered game theoretic setup can be obtained from its team theoretic counterpart.

Existence of linear equilibria in the Kyle model with partial correlation and two risk neutral traders

We study a generalization of the static model of [11] with two risk neutral insiders to the case where each insider is partially informed about the value of the stock. First, we provide a necessary and sufficient condition for the uniqueness of the linear Bayesian equilibrium. Specifically, we show that, when the covariance matrix of the errors terms of the insiders' signals, is not singular, the linear Bayesian equilibrium is not unique. Then, we carry out a comparative statics analysis.

Dynamic demand and noncompetitive intertemporal output adjustments: correction and extension

While hundreds of papers study the strategic interactions of oligopolists facing sticky prices only very few treat the in my opinion more important and opposite case of sticky or sluggish demand and supply, e.g., for energy. This point was taken up in Wirl (Int J Ind Organ 28:220–229, 2010) but unfortunately, the computation of the linear Markov perfect equilibrium is wrong. The situation in energy markets following Russia’s invasion of Ukraine adds a topical element to the theoretical analysis. Application to the oil market suggests that the difference between collusion and oligopolistic competition among few (symmetric) players is small for Markov perfect linear eqilibria. This is in stark contrast to the outcome in open loop strategies.

Climate Change: Linear and Nonlinear Causality Analysis

The goal of this study is to detect linear and nonlinear causal pathways toward climate change as measured by changes in global mean surface temperature and global mean sea level over time using a data-based approach in contrast to the traditional physics-based models. Monthly data on potential climate change causal factors, including greenhouse gas concentrations, sunspot numbers, humidity, ice sheets mass, and sea ice coverage, from January 2003 to December 2021, have been utilized in the analysis. We first applied the vector autoregressive model (VAR) and Granger causality test to gauge the linear Granger causal relationships among climate factors. We then adopted the vector error correction model (VECM) as well as the autoregressive distributed lag model (ARDL) to quantify the linear long-run equilibrium and the linear short-term dynamics. Cointegration analysis has also been adopted to examine the dual directional Granger causalities. Furthermore, in this work, we have presented a novel pipeline based on the artificial neural network (ANN) and the VAR and ARDL models to detect nonlinear causal relationships embedded in the data. The results in this study indicate that the global sea level rise is affected by changes in ice sheet mass (both linearly and nonlinearly), global mean temperature (nonlinearly), and the extent of sea ice coverage (nonlinearly and weakly); whereas the global mean temperature is affected by the global surface mean specific humidity (both linearly and nonlinearly), greenhouse gas concentration as measured by the global warming potential (both linearly and nonlinearly) and the sunspot number (only nonlinearly and weakly). Furthermore, the nonlinear neural network models tend to fit the data closer than the linear models as expected due to the increased parameter dimension of the neural network models. Given that the information criteria are not generally applicable to the comparison of neural network models and statistical time series models, our next step is to examine the robustness and compare the forecast accuracy of these two models using the soon-available 2022 monthly data.

A Modal Derivatives Enhanced Kron’s Substructuring Method to Calculate Structural Responses and Response Sensitivities of Geometrically Nonlinear Systems

This paper develops a modal derivative enhanced Kron’s substructuring method to calculate the structural responses and response sensitivities of geometrically nonlinear systems. The proposed method divides the global structure into substructures, which are then assembled in a dual form. The substructural displacements are approximated around the initial linear equilibrium position by using a quadratic modal manifold governed by a few master modes only. A time-variant reduction basis augmented by the master modal derivatives is derived from the quadratic modal manifold, enabling the geometric nonlinearities to be accurately captured. With the reduction basis, the global system is transformed into a reduced one containing the master modes only. Subsequently, the master modal responses and response sensitivities are solved efficiently from the reduced system. The global structural responses and response sensitivities are finally recovered from the master modal solutions based on the quadratic modal manifold. The effectiveness of the proposed method is demonstrated through its application to a thin plate structure. The reduced system enjoys the merit of Kron’s substructuring method that does not contain the interface degrees of freedom. Besides, the proposed reduced system is formed from the quadratic modal manifold directly. Its size is equal to the number of master modes of the substructures and smaller than that of the conventional method, where its size grows quadratically with the number of master modes.

Pure-displacement formulation and bulk modulus propagation for topology optimization with pressure loads

This work proposes a pure-displacement formulation for topology optimization with pressure loads and the use of a continuous boundary propagation technique. This technique allows controlling the non-solid (fluid or void) constitutive behavior by disseminating the desired bulk modulus to holes in the solid domain. The novelty of the proposed approach is to enable the distribution of solid, fluid, and void simultaneously with one design variable field. A density-based topology optimization approach is considered, and a gradient-based interior point algorithm is used. The linear elasticity equilibrium equations are discretized by the finite element method and solved with a sparse direct solver. The sensitivities are calculated by the discrete adjoint method with automatic differentiation. The optimization problems encompass compliance minimization (in 2D and 3D) and a compliant mechanism design to maximize the output displacement. Three examples evaluate the proposed formulation: the internally-pressurized lid, the piston head, and the inverter-compliant mechanism. The results show that different designs are obtained by considering different constitutive behavior for the non-solid phase.

Information linkages in a financial market with imperfect competition

This study proposes a tractable imperfectly competitive economy where traders are socially connected with each other via an information network. We investigate the impact of information linkages on market equilibrium outcomes. In the linear-quadratic-normal framework, we first establish the existence and uniqueness of symmetric linear Bayesian Nash equilibrium. We then show that an increase of the level of information linkages decreases price impact, belief disagreement, return volatility and trading volume. Additionally, unlike the non-monotonicity results in large economies, we also show that increasing the level of information linkages always improves liquidity, increases price volatility, and decreases trading profits in our imperfectly competitive economy.

Mudflat surface sediment type mapping by remote sensing considering the effect of the chlorophyll-a content

Mudflats are critical interfaces between the marine and terrestrial environment of muddy coasts. Mapping mudflat surface sediment types and analyzing their dynamic changes are helpful to understand the variations of sedimentary environments and their responses to tidal current movements. To obtain the surface sediment types of the mudflats, this study first took the chlorophyll-a content as an environmental variable and combined it with satellite spectral reflectance data processed by fractional-order derivative (FOD) to establish a machine learning model for retrieving sediment component content (SCC) of the sand, silt, and clay. Then, the three SCCs were linear equilibrium corrected and inputted into Folk's ternary classification model, and the spatial distribution map of the sediment types was accurately obtained. The results showed that the use of the FODs for satellite image enhancement could provide richer spectral information and improve the accuracy of the chlorophyll-a content and SCCs inversed by the grid search-support vector machine (GS-SVM) model. When compared to direct spectral modeling, considering the effect of the chlorophyll-a content as the key input factor, the coefficients of determination (R2) for the sand, silt, and clay contents inversion were increased by 15.1, 9.2, and 38.2%, and the root mean square error (RMSE) were reduced by 9.7, 5.5, and 2.5%, respectively. Surface sediment type maps obtained from the three SCCs showed that the main sediments in the mudflats on the central coast of Jiangsu Province, China were silty sand and sandy silt. Between 2019 and 2021, the sediment types in 84.46% of the total area were unchanged. For the changing area, the sediment transitioned toward finer-grained types near the seawall of the coastal region. Whereas in the offshore area, especially along the edge of the huge tidal channels, the sediments tended to be coarser because of strong hydrodynamic screening. The findings will be helpful for improving the ability of mudflat sedimentation environmental monitoring and spatial resource management via remote sensing.

Numerical investigation of large‐scale seasonal rock‐pit energy storage system

AbstractA twodimensional axisymmetric model, which is computationally inexpensive, has been proposed to predict the property changes that occur in a seasonal rock‐pit energy storage (RPES) system. The geometry of the rock‐pit has been simplified into a shape that can be extended for any seasonal storage system with a three‐dimensional conical geometry. The computational domain has been solved using both linear thermal equilibrium (LTE) and linear thermal non‐equilibrium (LTNE) models, and the former has been found to be computationally quick and accurate. The model has predicted a 95% energy saving at the highest flow conditions required in the mine. Further analysis has suggested that the increase in storage capacity by decreasing the porosity of rocks in the rock‐pit is insignificant compared to the corresponding increase in fan power. Furthermore, the investigation done on natural rocks has indicated an increased ability to store heat in the rock‐pit when rocks with higher thermal mass have been used. The use of RPES has shown a significant potential to reduce the carbon footprint. Finally, an economic analysis done on the system has shown a return on investment of just under 12 years.

Insider trading with dynamic asset under market makers' partial observations

<abstract><p>This paper studies an extended continuous-time insider trading model of Calentey and Stacchetti (2010, Econometrica), which allows market makers to observe some partial information about a dynamic risky asset. For each of the two cases with trading until either a fixed time or a random time, we establish the existence and uniqueness of linear Bayesian equilibrium, consisting of insider trading intensity, price pressure on market orders and price pressure on asset observations. It shows that at each of the two equilibria, all information on the risky asset is incorporated in the market price and when the volatility of observation noise keeps constant, the more information observed by market makers, the smaller price pressure on market orders but the greater price pressure on asset observations such that the insider earns less profit and vice versa. It suggests that the partial observation of market makers weakens the information advantage of the insider, which prevents the insider from monopolizing the market to make excessive profit, then reduces the losses of noise traders, thus improving the fairness and effectiveness in the insider trading market.</p></abstract>

Risk-seeking insider trading with partial observation in continuous time

<abstract><p>In this paper, a continuous-time insider trading model is investigated in which an insider is risk-seeking and market makers may receive partial information on the value of a risky asset. With the help of filtering theory and dynamic programming principle, the uniqueness and existence of linear equilibrium is established. It shows that (ⅰ) as time goes by, the residual information decreases, but both the trading intensity and the market liquidity increases, and (ⅱ) with the partial observation accuracy decreasing, both the market liquidity and the residual information will increase while the trading intensity decreases. On the whole, the risk-seeking insider is eager to trade all the trading period, and for market development, it is necessary to increase the insider's risk-preference behavior appropriately.</p></abstract>

Information Entropy Theory and Asset Valuation: A Literature Survey

The purpose of this study is to review the empirical work applied to market efficiency, portfolio selection and asset valuation, focusing on the presentation of the comprehensive theoretical framework of Information Entropy Theory (IET). In addition, we examine how entropy addresses the shortcomings of traditional models for valuing financial assets, including the market efficiency hypothesis, the capital asset pricing model (CAPM), and the Black and Scholes option pricing model. We thoroughly reviewed the literature from 1948 to 2022 to achieve our objectives, including well-known asset pricing models and prominent research on information entropy theory. Our results show that portfolio managers are particularly attracted to valuations and strive to achieve maximum returns with minimal risk. The entropy-based portfolio selection model outperforms the standard model when return distributions are non-Gaussian, providing more comprehensive information about asset and distribution probabilities while emphasising the diversification principle. This distribution is then linked to the entropic interpretation of the no-arbitrage principle, especially when extreme fluctuations are considered, making it preferable to the Gaussian distribution for asset valuation. This study draws important conclusions from its extensive analysis. First, entropy better captures diversification effects than variance, as entropy measures diversification effects more generically than variance. Second, mutual information and conditional entropy provide reasonable estimates of systematic and specific risk in the linear equilibrium model. Third, entropy can be used to model non-linear dependencies in stock return time series, outperforming beta in predictability. Finally, information entropy theory is strengthened by empirical validation and alignment with financial views. Our findings enhance the understanding of market efficiency, portfolio selection and asset pricing for investors and decision-makers. Using Information Entropy Theory as a theoretical framework, this study sheds new light on its effectiveness in resolving some of the limitations in traditional asset valuation models, generating valuable insights into the theoretical framework of the theory.

On enhancing interfacial mass transport through microextraction in dispersed droplet systems

The physio-chemical hydrodynamics and the solute transport around a translating dispersed drop are often multicomponent and multiphase systems. When such a dispersed droplet system is out of the thermodynamic equilibrium, steep momentum and concentration gradients are developed around the interface leading to rapid flow and solute transport. In broader perspectives, the dispersed droplet system has direct/indirect relevance to addressing the technological challenges in the 21st century, namely, energy storage, hydrogen production, CO2 capture, biofuel production, chemical analysis, diagnosis extraction, and drug delivery. Environmental engineering challenges include flotation and separation technology, inkjet printing, coatings, and paints. The most challenging issue in such applications is enhancing the transport rate from the droplet to the bulk of the fluid. In this work, we have proposed a novel method to foster the transport of solute from the drop to the bulk fluid by altering the viscosity of the bulk fluid. We have exploited the shear-thinning behavior of the fluid in bulk to reduce the viscous losses and resistances to the mass transfer. A linear thermodynamic equilibrium relation at the fluid-fluid interface is considered. The scant prior experimental results were observed to agree with the present findings. Therefore, the extensive numerical findings are presented for the ranges of pertinent parameters such as Reynolds number, (1≤Re≤75) Peclet number, (10≤Pe≤103), internal to external fluid diffusivity ratio, (0.5≤dratio≤4), dispersed to continuous fluid viscosity ratio, (0.25≤μratio≤4) and power-law index, (0.4≤n≤1). The drag coefficient exhibits an increase of 180% with the increase in the μratio as well as with the n at the maximum convective regime. The Sherwood number exhibits a positive dependence on the Reynolds number, Peclet number, and the diffusivity ratio. On the contrary, the viscosity ratio lowers the transport of species from the droplet to the fluid due to the reduced internal circulations inside the droplet. Shear-thinning fluid behavior offers a higher extraction efficiency than the Newtonian fluid (upto 30% increase in at low Pe). Finally, simple predictive correlative equations have been proposed for the drag coefficient and the average Sherwood number over the conditions considered here.

Learning equilibrium in bilateral bargaining games

Bilateral bargaining of a single good among one buyer and one seller describes the simplest form of trade, yet Bayes–Nash equilibrium strategies are largely unknown. Only for the average mechanism in the standard independent private values model with independent and uniform priors, we know that there is a continuum of equilibria. However, a non-uniform prior distribution already leads to a system of non-linear differential equations for which closed-form bidding strategies cannot be derived. Recent advances in equilibrium learning provide a numerical approach to equilibrium analysis, which can push the boundaries of existing results and allow for the analysis of environments that have been considered intractable so far. We study Neural Pseudogradient Ascent (NPGA) and Simultaneous Online Dual Averaging (SODA), two new equilibrium learning algorithms for Bayesian auction games with continuous type and action spaces. Although the environment is simple to describe, the continuum of equilibria makes it challenging for equilibrium learning algorithms. Empirically, NPGA finds the payoff-maximizing linear equilibrium, while SODA also finds non-differentiable step-function equilibria. Interestingly, the algorithms also find equilibrium with non-uniform priors and risk-averse traders for which we do not know an analytical solution. We show that the game is not globally monotone, but we can prove local convergence for a model with uniform priors and linear bid functions.

Coverage hole aware optimal cluster based routing for wireless sensor network assisted IoT using hybrid deep recurrent neural network

SummaryNowadays, the wireless sensor network (WSN) with IoT is intended to monitor real‐world physical or environmental phenomena in a number of applications, including foreign areas such as health and habitat monitoring. The WSN‐IoT network generates huge volume of data, which has to be processed and accessed by the remote users. Due to this large volume of data generation and resource constraint ability make achieving optimal cluster based routing in WSN‐IoT. The location of the sensor nodes significantly affects the accuracy of the information collected, which determines the quality of service provided by the application system. WSN can have multiple conflicts, which can create different coverage holes. These holes will break the existing overlap or connection and affect the required operation of the networks. Therefore, it is essential to find and repair the coverage holes to ensure the full functioning of the WSN as a motivation of this study. In this paper, we suggest a novel Coverage Hole aware Optimal Cluster based Routing (CHOCR) scheme for WSN‐IoT. First, we propose Modified Lichtenberg optimization (MLO) algorithm for balanced clustering which improve the performance of coverage hole. Second, we develop a linear equilibrium optimization based decision making (LEO‐DM) technique to subtract trust value of each IoT node using multiple restraints in cluster and consider the highest trusted node is act as cluster head (CH). After that, a hybrid deep recurrent neural network (HD‐RNN) is developed for intermediate node selection to frame the routing between two nodes. Finally, we simulate our proposed CHOCR scheme on the NS3.26 simulator. According to energy consumption, network longevity, number of nodes that are still alive and packet delivery ratio, packet loss ratio and throughput, end‐to‐end latency and delay of our proposed CHOCR routing system, we compare it to other current routing schemes.

Thermal lattice Boltzmann model for liquid-vapor phase change.

The lattice Boltzmann method is adopted to solve the liquid-vapor phase change problems in this article. By modifying the collision term for the temperature evolution equation, a thermal lattice Boltzmann model is constructed. As compared with previous studies, the most striking feature of the present approach is that it could avoid the calculations of both the Laplacian term of temperature [∇·(κ∇T)] and the gradient term of heat capacitance [∇(ρc_{v})]. In addition, since the present approach adopts a simple linear equilibrium distribution function, it is possible to use the D2Q5 lattice for the two-dimensional cases considered here. Thus, the present model is more efficient than previous models in which the lattice is usually limited to the D2Q9. The proposed model is first validated by the problems of droplet evaporation in open space and droplet evaporation on a heated surface, and the numerical results show good agreement with the analytical results and the finite difference method. Then it is used to model the nucleate boiling problem, and the relationship between detachment bubble diameter and gravitational acceleration obtained with the present approach fits well with previous works.

Asymptotic Behavior of Constrained Local Minimizers in Finite Elasticity

We provide an approximation result for the pure traction problem of linearized elasticity in terms of local minimizers of finite elasticity, under the constraint of vanishing average curl for admissible deformation maps. When suitable rotations are included in the constraint, the limit is shown to be the linear elastic equilibrium associated to rotated loads.

Static analysis and boundary effect of FG-CNTRC cylindrical shells with various boundary conditions using quasi-3D shear and normal deformations theory

In this paper, static analysis and the stress concentration phenomenon of functionally graded carbon nanotubes reinforced composite cylindrical shells with various boundary conditions are explored by using higher-order shear-normal deformation theory and an analytical approach. Five types of distributions of reinforced carbon nanotubes are considered, that is, uniform and four kinds of functionally gradient distribution of carbon nanotubes along with the thickness of the shell. Effective material properties of carbon nanotubes reinforced composite are estimated to the rule of mixture. The governing equations for FG-CNTRC cylindrical shells with various boundary conditions are solved analytically using simple trigonometric series and the Laplace transform. Moreover, the transverse shear and normal stress are reconstructed using 3D linear elasticity equilibrium equations. The present model is validated by comparing its numerical results with those of published works, including the 3D exact model. Using higher-order shear-normal deformation theory, this article has focused on investigating the stress concentration phenomenon, the distribution of stress components in the near-boundary region, and also assessing the effects of various parameters on the stress state of the FG-CNTRC cylindrical shells.

A new analytical model for transport of multiple contaminants considering remediation of both NAPL source and downgradient contaminant plume in groundwater

The contamination of groundwater aquifers by chlorinated solvents is a water-resource issue of great importance worldwide. Such contaminants are difficult to treat because they are often released as dense non-aqueous phase liquids (DNAPLs). Research shows that the application of remediation technologies to both the NAPL source and dissolved plume can lead to more efficient remediation, rather than to either alone. In these remediation efforts, analytical models that evaluate behavior and fate of contaminants do provide a better understanding of the performance of these remedial technologies. To the best of our knowledge, there exist no analytical model of simulating the plume migration of multiple contaminants with capabilities of accounting for both NAPL source and plume remediation simultaneously and different retardation for original chlorinated solvent contaminant and its degradation byproducts. In this study, we present a new analytical model for remediating both NAPL source and downgradient contaminant plume in groundwater at sites contaminated with chlorinated solvents and their degradation products with different retardation factors as well as considering both NAPL source and plume remediation simultaneously. A source model that accounts for the depletion of mass by the processes of dissolution or first-order decay reactions, corresponding with the removal or destruction of the source mass, is coupled to a plume reactive transport model. The source model is accounted for by relating source mass to the flux-averaged source discharge concentration through a power function. The developed analytical model considers 1-D advection, 3-D dispersion, first-order decay reactions and ingrowth as well as linear isothermal equilibrium sorption. The proposed analytical solution was derived through successive application of the Laplace transform in time and the double finite Fourier cosine transform regarding y and z. The correctness of the analytical model and its auxiliary FORTRAN computer program code are proved by showing excellent agreements between the simulated plume concentrations of all contaminants obtained from the derived analytical model and from a semi-analytical model available in the literature. Application of the proposed analytical solutions illustrates that the use of identical retardation factors for all contaminants may lead to underestimation or overestimation of the mobility of the contaminants, in cases when the retardation factors of the individual contaminants are greatly different from the identical retardation factor value adopted in all contaminants. From the experiments on six scenarios corresponding six remedial treatments, we found out that both the enhanced source decay and partial removal of source mass are main controlling factors at reducing the concentrations of all the contaminants, whereas plume decay leads to effective reduction in the concentrations of PCE, however, rather it causes unfavorable increases of the concentrations of the degradation byproducts.Ultimately, the developed model is used to better understand the impacts of various possible combinations of remedial efforts and management decisions on remediation of the subsurface contamination and quantify the benefit of a certain remediation decision.

Adsorptive separation of dissolved cadmium from aqueous solution using (Ziziphus Spina-Christi) leaves as an adsorbent

Sidr (Ziziphus spina-christi) leaves powder was tested extensively to find out its ability as cadmium ions adsorbent. Parametric studies were carried out in a batch system and the results showed that removal efficiency increased to 98% when using an adsorbent dosage of 2 g L−1 and stayed high when the initial concentration was less than 100 ppm. Adsorption temperature might be maintained at less than 40 °C and the recommended pH was found to be in the range of 4.5–5.5. The main and effective functional groups detected on the surface of the adsorbent by using Fourier transform infrared spectroscopy were carboxylic acid, alcohol, nitro and alkyl halides groups. Isotherm equilibrium results depicted that the sequence of model fitness to experimental data (based on R2) was: Langmuir > Freundlich > Harkin-Jura > Jovanovic > Temkin > Dubinin –Radushkevich. Linear and non-linear equilibrium, and kinetics models were experienced. Maximum metal uptake, 95.2 mg/g was evaluated using a linearized form of the Langmuir model having higher R2 than a non-linear model. Kinetic and thermodynamics predictions revealed that mass transfer across the aqueous boundary layer, intra-particle diffusion, and exothermic pseudo-first-order reaction on the adsorbent surface were the main mechanisms of Cd(II) adsorption on the present adsorbent. Ten adsorption-desorption cycles were performed to evaluate the adsorbent reusability. In conclusion, the novelty of this work represents the successively chosen of sidr leaves as a new, abundant, low-cost, and favorable adsorbent for the removal of cadmium cations from aqueous solutions.