Prediction Of Equilibria Research Articles

An Equilibrium Prediction Method for Control and Fault Detection of Energy Systems

Abstract Many fault detection, optimization, and control logic methods rely on sensor feedback that assumes the system is operating at steady-state conditions, despite persistent transient disturbances. While filtering and signal processing techniques can eliminate some transient effects, this paper proposes an equilibrium prediction method for first-order dynamic systems using an exponential regression. This method is particularly valuable for many commercial and industrial energy system, whose dynamics are dominated by first-order thermo-fluid effects. To illustrate the basic advantages of the proposed approach, Monte Carlo simulations are used. This is followed by three distinct experimental case studies to demonstrate the practical efficacy of the proposed method. First, the ability to predict the carbon dioxide level in classrooms allows for energy efficient control of the ventilation system and ensures occupant comfort. Second, predicting the optimal time to end the cool-down of an industrial sintering furnace allows for maximum part throughput and worker safety. Finally, fault detection and diagnosis (FDD) methods for air conditioning systems typically use static system models; however, the transient response of many air conditioning signals may be approximated as first-order, and therefore, the prediction model enables the use of static fault detection methods with transient data (a need that has not been addressed in over 20 years of air conditioning FDD research). In this paper, the equilibrium prediction method's performance will be quantified using both Monte Carlo simulations and case studies.

Dynamical Coulomb blockade under a temperature bias

We observe and comprehend the dynamical Coulomb blockade suppression of the electrical conductance across an electronic quantum channel submitted to a temperature difference. A broadly tunable, spin-polarized Ga(Al)As quantum channel is connected on-chip, through a micron-scale metallic node, to a linear $RC$ circuit. The latter is made up of the node's geometrical capacitance $C$ in parallel with an adjustable resistance $R\in \{1/2,1/3,1/4\}\times h/e^2$ formed by 2--4 quantum Hall channels. The system is characterized by three temperatures: a temperature of the electrons in the large electrodes ($T$) and in the node ($T_\mathrm{node}$), and a temperature of the electromagnetic modes of the $RC$ circuit ($T_\mathrm{env}$). The temperature in the node is selectively increased by local Joule dissipation, and characterized from current fluctuations. For a quantum channel in the tunnel regime, a close match is found between conductance measurements and tunnel dynamical Coulomb blockade theory. In the opposite near ballistic regime, we develop a theory that accounts for different electronic and electromagnetic bath temperatures, again in very good agreement with experimental data. Beyond these regimes, for an arbitrary quantum channel set in the far out-of-equilibrium situation where the temperature in the node significantly exceeds the one in the large electrodes, the equilibrium (uniform temperature) prediction for the conductance is recovered, albeit at a rescaled temperature $\alpha T_\mathrm{node}$.

Bargains, price signaling, and efficiency in markets with asymmetric information

We experimentally investigate bargains, price signaling, and efficiency in markets with asymmetric information where some buyers are informed and some sellers are informed. We show that all perfect Bayesian equilibria where transactions occur under known gains from trade fall into one of two categories. In some cases, uninformed sellers charge high prices but uninformed buyers are only willing to pay low prices. Otherwise, uninformed sellers charge low prices and uninformed buyers are willing to pay high prices. This latter case is shown to exhibit more bargains and greater efficiency. Consistent with equilibrium predictions, we observe significantly fewer transactions and bargains in our first treatment. In contrast to equilibrium predictions, uninformed buyers selected far lower reservation prices than informed high quality buyers in the second treatment as predicted by adaptive models.

Do traders learn to select efficient market institutions?

When alternative market institutions are available, traders have to decide both where and how much to trade. We conducted an experiment where traders decided first whether to trade in an (efficient) double-auction institution or in a posted-offers one (favoring sellers), and second how much to trade. When sellers face decreasing returns to scale (increasing production costs), fast coordination on the double-auction occurs, with the posted-offers institution becoming inactive. In contrast, under constant returns to scale, both institutions remain active and coordination is slower. The reason is that sellers trade off higher efficiency in a market with dwindling profits for biased-up profits in a market with vanishing customers. Hence, efficiency alone might not be sufficient to guarantee coordination on a single market institution if the surplus distribution is asymmetric. Trading behavior approaches equilibrium predictions (market clearing) within each institution, but switching behavior across institutions is explained by simple rules of thumb, with buyers chasing low prices and sellers considering both prices and trader ratios.

Random Actions in Experimental Zero-Sum Games

A mixed strategy, a strategy of unpredictable actions, is applicable to business, politics, and sports. Playing mixed strategies, however, poses a challenge, as the game theory involves calculating probabilities and executing random actions. I test i.i.d. hypotheses of the mixed strategy Nash equilibrium with the simplest experiments in which student participants play zero-sum games in multiple iterations and possibly figure out the optimal mixed strategy (equilibrium) through the games. My results confirm that most players behave differently from the Nash equilibrium prediction for the simplest 2x2 zero-sum game (matching-pennies) and 3x3 zero-sum game (e.g., the rock-paper-scissors game). The results indicate the need to further develop theoretical models that explain a non-Nash equilibrium behavior.

Autothermal hybridization and controlled production of hydrogen-rich syngas in a molten salt solar gasifier

High efficiency solar steam gasification of biomass is carried out in a prototype molten salt reactor for solar-only and solar-autothermal hybrid operation. Previous demonstration of the prototype 3-kW solar gasifier for steam gasification of cellulose at stoichiometric conditions demonstrated thermal efficiency of 44% during continuous operation at 1200 K. The present work expands the range of operating conditions to consider two challenges. Hybridization between solar and autothermal modes of operation is accomplished by adding oxygen directly to the reactor. Control of the H2:CO ratio of the product gas is accomplished through in-situ steam shifting. Hybridization stabilized temperatures for variations in radiative input as large as a 30% reduction in power, corresponding to conditions where both sensible and chemical heat demands for the process were fully met by exothermic heat release with no significant challenges. Peak efficiencies and carbon conversion values observed are 45% and 99.5% respectively. The resulting product gas stream composition was shifted from a hydrogen and carbon monoxide ratio of 1:1 with stoichiometric steam delivery to a ratio of 1.7:1 with steam at nine times the stoichiometric amount, only slightly lower than equilibrium predictions. The results demonstrate very favorable attributes for the molten salt reactor in a continuous fuel production process.

Competitive insurance markets with unbounded cost

Azevedo and Gottlieb (2017) (AG) define a notion of equilibrium that always exists in the Rothschild and Stiglitz (1976) (RS) model of competitive insurance markets, provided costs are bounded. However, equilibrium predictions are fragile: introducing an infinitesimal mass of high-cost individuals discretely increases all prices and reduces coverage for all individuals. We study sensitivity w.r.t. cost bounds by considering sequences of economies with increasing upper bounds of cost, and determining whether their equilibria converge. We present sufficient conditions under which AG equilibrium exists when cost is unbounded. For simple insurance markets, we derive a necessary and sufficient condition for existence: surplus from insurance increases faster than linearly with expected cost. This condition is empirically common. If the condition fails, a higher bound on cost results in market unraveling: all prices diverge and, in the limit, an AG equilibrium does not exist. We use these results to show that the equilibrium for an insurance market with an unbounded continuum of types is characterized by a simple differential equation. We also provide examples of non-existence for a (single-product) market for lemons with unbounded cost.

NATURALLY OCCURRING PREFERENCES AND GENERAL EQUILIBRIUM: A LABORATORY STUDY

AbstractWe examine whether economies constructed using experimentally measured preferences (for risk) tend to suffer from aggregation pathologies (like nonexistence and multiplicity of equilibrium) cautioned by the Sonnenschein–Mantel–Debreu theorem. We show that aggregation pathologies should be expected to arise frequently in homogeneous exchange economies, but dwindle and eventually disappear as economies grow diverse. When subjects actually trade, general equilibrium predictions are accurate in most cases, and the failures occur only in economies a priori classified as fragile to preference instability. Our study uses individual‐level experimental data to address longstanding questions in general equilibrium theory that are unanswerable using prior methods.

An improved dispersive contribution for the COSMO-SAC-Phi equation of state

In this work, the COSMO-SAC-Phi equation of state [Fluid Phase Equilib. 488 (2019) 13–26] is refined by the introduction of a new equation to describe dispersive effects. The proposed modification is inspired by the well-known rules of consistency for α-functions, used in cubic equations of state. The results for 38 representative compounds have shown that the proposed modification is able to improve the correlation of pure compound experimental data of saturation pressures and saturated liquid volume, with average deviations of 0.96% and 0.73%, respectively. Densities of pure compounds under conditions beyond the saturation region were also well predicted. Vapor-liquid equilibrium predictions of binary mixtures demonstrated, for most cases, that the modified equation was superior to the original COSMO-SAC-Phi model, PSRK, and Soave-Redlich-Kwong with the classical van der Waals mixing rule. The modified model was also able to produce very good predictions for liquid-liquid equilibrium, being similar to UNIFAC-LLE at low temperatures, but exhibiting a much better performance at higher temperatures (and pressures).

Competitive Attention, Superstars and the Long Tail

We propose a model of competitive attention based on two key premises: i) People have limited information processing capacities and ii) consideration sets are formed according to relative salience. The equilibrium predictions we obtain can help to understand, and connect, diverse empirical phenomena, such as the Paradox of Choices, the Power Law dispersions of key market data (sales, profits, online clicks,...), the relation between advertising expenditures and market shares, the evolution of market inequality, or why evidence favoring a “Long Tail” effect is mixed at best.

Reference Dependent Prices in Bargaining: An Experimental Examination of Precise First Offers

Evidence from psychology and marketing suggests that those who make a first in bargaining get a better deal than those who make a round first offer. We report on a series of experiments designed to test for and improve our understanding of the first offer (PFO) effect in bargaining and whether it likely reflects rational optimizing or equilibrium behavior. Our experiment varies whether decisions are incentivized and whether the PFO effect can emerge as an equilibrium of a cheap-talk signaling game. We find evidence of a PFO effect when subjects read a vignette and make unincentivized individual decisions. When monetary incentives are added to the vignette, we still find the PFO effect, but it is not robust. In a bilateral bargaining situation with a cheap-talk equilibrium, we can not find the PFO effect, which is inconsistent with the equilibrium predictions. Moreover, the PFO effect reemerges in a setting in which initial offers are generated by a random device and thus provides a strong refutation of the signaling model. Our evidence suggests that optimizing and equilibrium accounts of the PFO effect are inadequate. Understanding initial offers as reference points, which subtly change perceptions about the kinds of acceptable counteroffers, provides a plausible account of a new finding on which prior explanations are silent: precise offers induce more precise counteroffers.

Delegation and Overhead Aversion with Multiple Threshold Public Goods

Experimental studies have modeled individual funding of social projects as contributions to a threshold public good. We examine donors’ behavior when they face multiple threshold public goods and the possibility of coordinating their contributions via an intermediary. Employing the experimental design developed in Corazzini, Cotton, and Reggiani (2020), we vary both the size of a ‘destination rule’, which places restrictions on the intermediary’s use of a donor’s funds, as well as the overhead cost of the intermediary, modeled as a sunk cost incurred by the intermediary whether or not any of the public goods are successfully funded. We show that subjects behave in line with equilibrium predictions with regard to the size of the destination rule, only increasing their contributions in the presence of a relatively high destination rule that prevents expropriation by the intermediary. However, we find that the positive effect of a high destination rule is undone in the presence of overhead sunk costs on the intermediary, thus providing evidence in favor of the sunk-cost bias and ‘overhead aversion’ that are commonly exhibited by donors exhibit when selecting charities.

Effects of residual disinfectants on the redox speciation of lead(ii)/(iv) minerals in drinking water distribution systems.

This study investigated the reaction kinetics on the oxidative transformation of lead(ii) minerals by free chlorine (HOCl) and free bromine (HOBr) in drinking water distribution systems. According to chemical equilibrium predictions, lead(ii) carbonate minerals, cerussite PbCO3(s) and hydrocerussite Pb3(CO3)2(OH)2(s), and lead(ii) phosphate mineral, chloropyromorphite Pb5(PO4)3Cl(s) are formed in drinking water distribution systems in the absence and presence of phosphate, respectively. X-ray absorption near edge spectroscopy (XANES) data showed that at pH 7 and a 10 mM alkalinity, the majority of cerussite and hydrocerussite was oxidized to lead(iv) mineral PbO2(s) within 120 minutes of reaction with chlorine (3 : 1 Cl2 : Pb(ii) molar ratio). In contrast, very little oxidation of chloropyromorphite occurred. Under similar conditions, oxidation of lead(ii) carbonate and phosphate minerals by HOBr exhibited a reaction kinetics that was orders of magnitude faster than by HOCl. Their end oxidation products were identified as mainly plattnerite β-PbO2(s) and trace amounts of scrutinyite α-PbO2(s) based on X-ray diffraction (XRD) and extended X-ray absorption fine structure (EXAFS) spectroscopic analysis. A kinetic model was established based on the solid-phase experimental data. The model predicted that in real drinking water distribution systems, it takes 0.6-1.2 years to completely oxidize Pb(ii) minerals in the surface layer of corrosion scales to PbO2(s) by HOCl without phosphate, but only 0.1-0.2 years in the presence of bromide (Br-) due the catalytic effects of HOBr generation. The model also predicts that the addition of phosphate will significantly inhibit Pb(ii) mineral oxidation by HOCl, but only be modestly effective in the presence of Br-. This study provides insightful understanding on the effect of residual disinfectant on the oxidation of lead corrosion scales and strategies to prevent lead release from drinking water distribution systems.

Analysis of various approaches to accurately prediction of phase equilibrium of binary helium systems based on the Peng-Robinson equation of state

The paper presents a detailed algorithm for calculating the vapor-liquid phase equilibrium for multicomponent systems based on the Peng-Robinson equation of state. Various approaches are considered that make it possible to improve the quality of predicting phase equilibrium by the example of eight binary helium systems containing nitrogen, argon, carbon dioxide, methane, ethane, propane, isobutane, and n-butane. The influence of the acentric factor and the binary interaction parameter on the accuracy of the helium systems phase behavior predicting is analyzed. The optimal interaction coefficients for the presented systems are found under the assumption that this parameter does not depend on temperature. The temperature range of applicability of various approaches is determined, which makes it possible to maximize the description of the phase behavior of helium systems.

New modified PC-SAFT pure component parameters for accurate VLE and critical phenomena description

The theory of Perturbed Chain Statistical Associating Fluid (PC-SAFT) is largely applied in many industrial fields. It requires three parameters: the segment number (m), the hard-core segment diameter (σ), and the segment-segment interaction energy parameter (ε/k) for every pure non-associating fluid. By convention, they are determined by fitting vapor pressure and liquid density data. However, the shortage behind these parameters adopted by their respective authors is that they give excessive values of critical temperatures and critical pressures, which are crucial to forecasting vapor-liquid critical pressure and composition of the mixture at high pressures and temperatures.In this paper, a new approach is proposed to evaluate PC-SAFT parameters of different substances from diverse chemical families. Good fits of saturation pressure and vapor densities values of 94 pure substances are obtained, with an overall AARD of 0.89% and 1.50% respectively.The proposed method requires as input the critical pressure (Pc), the critical temperature (Tc), and the acentric factor (ω). By using these parameters, PC-SAFT estimates with accuracy the critical properties of pure compounds as well as the successful prediction of vapor-liquid equilibria for many non-associating binary systems at critical regions including mixtures containing ammonia, comparing with other literature values. But the limitation of this method is reflected in underestimated liquid densities.

An experiment on deception, reputation and trust

An experiment is designed to shed light on how deception works. The experiment involves a twenty period sender/receiver game in which period 5 has more weight than other periods. In each period, the informed sender communicates about the realized state, the receiver then reports a belief about the state before being informed whether the sender lied. Throughout the interaction, a receiver is matched with the same sender who is either malevolent with an objective opposed to the receiver or benevolent always telling the truth. The main findings are: (1) in several variants (differing in the weight of the key period and the share of benevolent senders), the deceptive tactic in which malevolent senders tell the truth up to the key period and then lie at the key period is used roughly 25% of the time, (2) the deceptive tactic brings higher expected payoff than other observed strategies, and (3) a majority of receivers do not show cautiousness at the key period when no lie was made before. These observations do not match the predictions of the Sequential Equilibrium and can be organized using the analogy-based sequential equilibrium (ABSE) in which three quarters of subjects reason coarsely.

Machine Learning Approaches for Prediction of Phase Equilibria in Poly (Ethylene Glycol) + Sodium Phosphate Aqueous Two-Phase Systems

In this research, liquid-liquid equilibrium (LLE) data were experimentally obtained for the ternary systems of (water + carboxylic acid + dipropyl ether) at T = 298.2 K and P = 101.3 kPa. The carboxylic acids used in this study were isobutyric acid, valeric acid, and isovaleric acid. All these systems are according to Treybal classification, Type-2 systems because the two binary subsystems are partially miscible. The lowest distribution coefficients and separation factors were calculated for isobutyric acid (40 and 329, respectively). The authenticity of the experimental equilibrium data was identified from Hand and Othmer-Tobias correlations. The experimental tie-line data were correlated by using the nonrandom two-liquid (NRTL) and universal quasi-chemical (UNIQUAC) activity coefficient models. RMSD values are between 0.0112 and 0.0155 for the NRTL model, and are between 0.0083 and 0.0153 for UNIQUAC model.

Attainment of equilibrium via Marshallian path adjustment: Queueing and buyer determinism

We examine equilibration in a market where Marshallian path adjustment can be enforced, or not, as a treatment: a posted offer market either with buyer queueing via value order, or random order, respectively. We derive equilibrium predictions, and run experiments crossing queueing rules with either human or deterministically optimizing robot buyers under both locally stationary and non-stationary marginal cost. Results on rate of convergence to competitive equilibrium are obtained, and Marshallian path adjustment is established as conducive to attaining competitive equilibrium.

Measurement and prediction of solid-liquid equilibria in the ternary system (KCl-SrCl2-H2O) at 273 and 308 K

Solubilities of ternary system (KCl-SrCl2-H2O) were determined using the isothermal dissolution equilibrium method at 273 and 308 K. According to the obtained experimental results, the phase diagrams of the system at 273 and 308 K were plotted respectively. The results show that the ternary system has a invariant point, two univariate solubility curves and two crystallization regions corresponding to KCl and SrCl2•6H2O at 273 and 308 K, no solid solution was found in the phase diagram. Based on Pitzer and H-W model, the Pitzer single salt parameters of KCl (β(0), β(1), Cϕ) and SrCl2 (β(0), β(1), β(2), Cϕ) and the interaction parameters of mixed ions (θK, Sr, ΨK, Sr, Cl) were used to calculate the solubilities of the ternary system at 273 and 308 K, and the results show that the calculated values agree well with the experimental values in this work.

Examination of inorganic gaseous species and condensed phases during coconut husk combustion based on thermodynamic equilibrium predictions

Multi-component thermodynamic equilibrium predictions of coconut husk combustion products were performed in this work. The calculation results showed that the concentration of the chlorine species in the flue gas and ash were clearly influenced by the combustion temperature. At temperatures below 820 °C the highest concentration was HCl(g), and above 820 °C was KCl(g). Chlorine species were also observed in ash, as KCl–NaCl–RbCl solid solution (when the combustion temperature was lower than 700 °C), and KCl–NaCl–K2SO4–Na2SO4 liquid solution (in the range of 600–960 °C). At low combustion temperatures (600 °C), chlorine retention in solid ash was the most effective. Speciation of inorganic gaseous species and condensed phases were investigated also during flue gas cooling from 1000 to 200 °C. Major condensed phase compositions were dominated by alkali metal salts in both solid and liquid phase states. In addition, the Gibbs energy of substance formation, and Gibbs reaction energy, in order to thoroughly interpret the thermodynamic predictions were determined. Finally, thirty seven eutectic points for binary systems calculated in the “Phase Diagram” module of the FactSage package were presented. For the purposes of interpreting the results, the melting point ranking for pure substances and binary systems were created.