Strict Equilibrium Research Articles

A Nash equilibrium against gun control

This work constructs a non-cooperative, static game of gun control between the citizen and a pacifistic society characterised by law enforcement imperfection, by which the retention of firearms and the certitude of punishment against all crimes emerge both as a strict Nash equilibrium, in pure strategies, and as a strict dominant strategy equilibrium. The reason is that ratified by the Second Amendment to the American Constitution, discerning the necessity of a militia to the individual and societal security of a free state, by which the right of the people to keep and bear arms cannot be infringed.

Strict Vector Equilibrium Problems of Multi-Product Supply–Demand Networks with Capacity Constraints and Uncertain Demands

This paper considers a multi-product, multi-criteria supply–demand network equilibrium model with capacity constraints and uncertain demands. Strict network equilibrium principles are proposed both in the case of a single criterion and multi-criteria, respectively. Based on a single criterion, it proves that strict network equilibrium flows are equivalent to vector variational inequalities, and the existence of strict network equilibrium flows is derived by virtue of the Fan–Browder fixed point theorem. Based on multi-criteria, the scalarization of strict network equilibrium flows is given by using Gerstewitz’s function without any convexity assumptions. Meanwhile, the necessary and sufficient conditions of strict network equilibrium flows are derived in terms of vector variational inequalities. Finally, an example is given to illustrate the application of the derived theoretical results.

Uniformly strict equilibrium for repeated games with private monitoring and communication

AbstractCooperation through repetition is an important theme in game theory. In this regard, various celebrated “folk theorems” have been proposed for repeated games in increasingly more complex environments. There has, however, been insufficient attention paid to the robustness of a large set of equilibria that is needed for such folk theorems. Starting with perfect public equilibrium as our starting point, we study uniformly strict equilibria in repeated games with private monitoring and direct communication (cheap talk). We characterize the limit equilibrium payoff set and identify the conditions for the folk theorem to hold with uniformly strict equilibrium.

Blockchain-based Decentralized Reward Sharing: The Case of Mining Pools

We introduce a reciprocity protocol , an innovative approach to coordinating and sharing rewards in blockchains. Inherently decentralized and implementable, it puts emphasis on incentives rather than forcing specific sharing rules from the outset. Analyzing the non-cooperative game the protocol induces, we identify a robust, strict, and Pareto-dominant symmetric equilibrium. In it, even self-centered participants show extensive systemic reciprocity. Thus, despite a setting that is generally unfavorable to reciprocal behavior, the protocol enables users to build trust between themselves by taking on a role akin to a social contract.

Robustness Against Indirect Invasions in Asymmetric Games with Continuous Strategy Spaces

Strategies which are robust against indirect invasions (RAII) have been studied in the literature for symmetric games. In this paper, we introduce the notion of RAII profiles for asymmetric games with continuous strategy spaces. For these games, we prove that the set of all indirect neutral mutants of a RAII profile is equivalent to a minimal evolutionarily stable set. Furthermore, globally strong uninvadable profiles are shown to be RAII profiles. We also discuss connections between evolutionarily stable sets and strict equilibrium sets of profiles.

Continuous level-k mechanism design

In de Clippel et al. (2019), it is shown that, perhaps surprisingly, the set of implementable social choice functions is essentially the same whether agents have bounded depth of reasoning or rational expectations. The picture is quite different when taking into account the possibility of small modeling mistakes. While continuous (strict) equilibrium implementation becomes very demanding (Oury and Tercieux (2012) – OT), continuity in level-k implementation obtains essentially for free. A decomposition of the conditions implied by the OT implementation notion confirms that it is the use of equilibrium, and not continuity per se, that is responsible for the difference.

Analysis of a Thermodynamic Determination of the Surface Tension of a Two-Component Vapor–Liquid System

A numerical analysis is performed of a thermodynamic determination of the surface tension (ST) of a vapor–liquid binary mixture and interfacial tension (IT) between two liquid phases as the excess value of free energy ΔF of a two-phase system with and without for a phase boundary. Calculations are made in the simplest version of the lattice gas model (LGM), allowing for the interaction of nearest neighbors in a quasi-chemical approximation. Each node of a two-component mixture in the LGM system can be occupied by mixture components A + B and vacancy V. The two main ways of calculating ST, expressed in terms of different partial contributions Miq to excess free energy ΔF (where i = A, B, V are vacancies; 1 ≤ q ≤ κ, q is the number of the monolayer inside the boundary; and κ is its width), are compared, as are calculations of ST and IT as excess free energy ΔF for a lattice model with no vacancies. The ambiguity of ST and IT values depending on the type of Miq functions is obtained by calculating the temperature dependence for a flat boundary and the dependence of ST and IT on droplet size at a fixed temperature. The role of vacancies in the LGM as the main mechanical characteristic of the system under the condition of strict phase equilibrium in three equilibria (mechanical, energy, and chemical) is discussed.

Two Strongly Truthful Mechanisms for Three Heterogeneous Agents Answering One Question

Peer prediction mechanisms incentivize self-interested agents to truthfully report their signals even in the absence of verification by comparing agents’ reports with their peers. We propose two new mechanisms, Source and Target Differential Peer Prediction, and prove very strong guarantees for a very general setting. Our Differential Peer Prediction mechanisms are strongly truthful : Truth-telling is a strict Bayesian Nash equilibrium. Also, truth-telling pays strictly higher than any other equilibria, excluding permutation equilibria, which pays the same amount as truth-telling. The guarantees hold for asymmetric priors among agents, which the mechanisms need not know ( detail-free ) in the single question setting . Moreover, they only require three agents , each of which submits a single item report : two report their signals (answers), and the other reports her forecast (prediction of one of the other agent’s reports). Our proof technique is straightforward, conceptually motivated, and turns on the logarithmic scoring rule’s special properties. Moreover, we can recast the Bayesian Truth Serum mechanism [ 20 ] into our framework. We can also extend our results to the setting of continuous signals with a slightly weaker guarantee on the optimality of the truthful equilibrium.

Mediated talk: An experiment

We experimentally compare mediated (cheap) talk with direct (cheap) talk. Theory, guided by a characterization of equilibria in both environments, suggests that mediated talk has the potential to improve information sharing and welfare relative to direct talk. We sharpen the theory prediction by invoking Crawford's (2003) language-anchored level-k analysis. In the experiment, we find that mediated talk can indeed facilitate information transmission. We also find, however, that this requires that the language employed conforms with the mediation mechanism: mediation mechanisms improve information sharing for a variety of conforming languages, but fail to do so with a nonconforming language. These experimental findings match the predictions from the language-anchored level-k analysis. Strikingly, this is the case even when a whole array of alternative selection criteria (including iterative deletion of dominated strategies, strict equilibrium, Pareto efficiency, etc.) make a unique common prediction that sharply disagrees with the language-anchored level-k prediction.

Model comparisons for two-temperature plasma equations of state

When a plasma is generated in the laboratory, energy is often deposited preferentially into either the electrons or the ions, giving rise to a quasiequilibrium state in which the two species, electrons and ions, are well described by two effective temperatures, Te and Ti. Accurate hydrodynamic modeling of such a two-temperature plasma requires an equation of state that captures the relevant many-body physics without assuming a strict local thermodynamic equilibrium. Several models have been proposed within the literature, which extend conventional statistical approaches, each employing a different combination of assumptions for modifying the equilibrium equations. In this work, we compare the predictions for several models, presenting derivations of the internal energy and pressure for each microscopic model within a unified framework so that the assumptions of each model may be more easily compared to one another. We find that for sufficiently weak coupling, all models agree with one another. However, as the coupling strength is increased, the disagreement between the models becomes more pronounced. Moreover, the relative sizes of the corrections predicted by each model depend on which species has the higher temperature, Te > Ti vs Te < Ti.

Eigenmode analysis of perturbations in the primordial medium at and before recombination

Context. Anisotropies of the cosmic microwave background are thought to be due to perturbations of the primordial medium, which, post recombination, lead to the formation of galaxy clusters and galaxies Aims. The perturbation wave modes of the primordial medium at and before recombination, consisting of a fully ionised baryonic plasma, a strong black body radiation field, and cold dark matter, are analysed. Methods. We use the linear perturbation theory of the relativistic equations of motion, utilising a strict thermodynamic equilibrium model that relates the radiation energy density to the plasma temperature. Results. It is shown that a wave mode corresponding to the postulated baryon acoustic waves exists with a phase velocity close to the speed of light, but the participation of the dark matter in this mode is very small. Instead, the dark matter has its own dominant mode in the form of gravitational collapse, with very little participation by the baryonic plasma. Conclusions. In view of this very weak coupling between baryons and dark matter, the initial conditions postulated for computer simulations of large-scale structure and galaxy formation – which assume that after recombination, when galaxy formation is getting underway, baryon and dark matter density perturbations are spatially coincident and are equal in terms of fractional amplitude – may be unjustified. Additionally, the possible non-coincidence of baryon and dark matter perturbations at the last scattering surface has implications for the analysis of cosmic microwave background anisotropies.

Continuous implementation with direct revelation mechanisms

We investigate how a principal's knowledge of agents' higher-order beliefs impacts their ability to robustly implement a given social choice function. We adapt a formulation of Oury and Tercieux (2012): a social choice function is continuously implementable if it is partially implementable for types in an initial model and “nearby” types. We characterize when a social choice function is truthfully continuously implementable, i.e., using game forms corresponding to direct revelation mechanisms for the initial model. Our characterization hinges on how our formalization of the notion of nearby preserves agents' higher order beliefs. If nearby types have similar higher order beliefs, truthful continuous implementation is roughly equivalent to requiring that the social choice function is implementable in strict equilibrium in the initial model, a very permissive solution concept. If they do not, then our notion is equivalent to requiring that the social choice function is implementable in unique rationalizable strategies in the initial model. Truthful continuous implementation is thus very demanding without non-trivial knowledge of agents' higher order beliefs.

The repetitive local sampling and the local distribution theory

AbstractMolecular simulation is a mature and versatile tool set widely utilized in many subjects. However, its methodology development has been struggling with a tradeoff between accuracy and speed, significant improvement of both is necessary to reliably substitute many expensive and laborious experiments in molecular biology and nanotechnology. Previously, the ubiquitous severe wasting of computational resources in molecular simulations due to repetitive local sampling was raised, and the local free energy landscape approach was proposed to address it. The core idea is to first learn local distributions, and followed by dynamic assembly of which to infer global joint distribution of a target molecular system. When compared with conventional explicit solvent molecular dynamics simulations, a simple and approximate implementation of this theory in protein structural refinement harvested acceleration of about six orders of magnitude without loss of accuracy. While this initial test revealed tremendous benefits for addressing repetitive local sampling, there are some implicit assumptions need to be articulated. Here, I present a more thorough discussion of repetitive local sampling; potential options for learning local distributions; a more general formulation with potential extension to simulation of near equilibrium molecular systems; the prospect of developing computation driven molecular science; the connection to mainstream residue pair distance distribution based protein structure studies; and the fundamental difference of the averaging strategy from potential of mean force. This more general development is termed the local distribution theory to release the limitation of strict thermodynamic equilibrium in its potential wide application in general soft condensed molecular systems.This article is categorized under: Molecular and Statistical Mechanics > Free Energy Methods Data Science > Artificial Intelligence/Machine Learning

Strict pure strategy Nash equilibrium in large finite-player games when the action set is a manifold

We present results on the relationship between non-atomic games (in distributional form) and approximating games with a large but finite number of players. Specifically, in a setting with differentiable payoff functions, we show that: (1) The set of all non-atomic games has an open dense subset such that any finite-player game that is sufficiently close (in terms of distributions of players’ characteristics) to a game in this subset and has sufficiently many players has a strict pure strategy Nash equilibrium (Theorem 1), and (2) any equilibrium distribution of any non-atomic game is the limit of equilibrium distributions defined from strict pure strategy Nash equilibria of finite-player games (Theorem 2). This supplements our paper Carmona and Podczeck (2020b), where analogous results are established for the case where the action set of players is a subset of some Euclidean space, with non-empty interior, and payoff functions are such that equilibrium actions are in the interior of the action set. The goal of the present paper is to remove these assumptions.

Partially mixed lower bound constant stress tetrahedral element for Finite Element Limit Analysis

A numerical analysis of the limit state for solids, with an adequately described structural geometry, is often a computationally demanding task, and there is a need for an effective method. The existing solid elements for Finite Element Limit Analysis (FELA) are either computationally expensive or require a stress cutoff of the yield surface for triaxial stress states. This paper presents an effective partially mixed lower bound tetrahedral constant stress solid element that converges rapidly and does not require modification of the yield surface. The element is based on a partially relaxed formulation of the lower bound theorem by providing strict equilibrium of the normal tractions on the element faces and a relaxed equilibrium of the shear/tangential tractions at the vertices. The performance of the element is shown in four examples applying either the von Mises yield criterion, or the Modified Mohr–Coulomb yield criterion with the possible inclusion of reinforcement. The examples show fast convergence and good performance even for relatively coarse meshes.

Preference revelation games and strict cores of multiple‐type housing market problems

AbstractWe consider multiple‐type housing market problems as introduced by Moulin (1995) and study the relationship between strict strong Nash equilibria and the strict core (two solution concepts that are defined in terms of the absence of weak blocking coalitions). We prove that for lexicographically separable preferences, the set of all strict strong Nash equilibrium outcomes of each preference revelation game that is induced by a strictly core stable mechanism is a subset of the strict core, but not vice versa, that is, there are strict core allocations that cannot be implemented in strict strong Nash equilibrium. This result is extended to a more general set of preference domains that satisfy strict core non‐emptiness and a minimal preference domain richness assumption.

Heavy-element Rydberg transition line emission from the post-giant-evolution star HD 101584

Context. We report the detection of two lines at millimetre wavelengths towards the immediate surroundings of the post-giant and most likely post-common-envelope star HD 101584 using high-angular-resolution ALMA observations. The circumstellar environment of this object is rich in different molecular species, but we find no viable identifications in terms of molecular lines. Aims. We aim to determine whether or not these lines can be attributed to the Rydberg transitions – X30α and X26α – of neutral atoms of elements heavier than carbon. Methods. A simple model in strict local thermodynamic equilibrium for a warm-gas environment of the moderate-temperature star (Teff ≈ 8500 K) was constructed to corroborate our findings. A geometrically thin, disc-like geometry seen face-on was chosen and a distance of 1 kpc. Results. The observed flux densities of the lines and the continuum at 232 and 354 GHz can be reproduced using ≈10−3 M⊙ of gas at a temperature of ≈2800 K and a hydrogen density of ≈1012 cm−3, assuming solar abundances for the elements. The gas lies within a distance of about 5 au from the star (assuming a distance of 1 kpc). The ionisation fraction is low, ≈3 × 10−5. The origin of such a region is not clear, but it may be related to a common-envelope-evolution phase. With these conditions, the line emissions are dominated by Rydberg transitions within the stable isotopes of Mg. A turbulent velocity field in the range 5.5–7.5 km s−1 is required to fit the Gaussian line shapes. An upper limit to the average magnetic field in the line-emitting region of 1 G is set using the Zeeman effect in these lines. Conclusions. We speculate that Rydberg transitions of heavy elements may be an interesting probe for the close-in environments of other moderate-temperature objects like AGB stars, red supergiants, yellow hypergiants, and binaries of various types.

Neptune's Spatial Brightness Temperature Variations from the VLA and ALMA

Abstract We present spatially resolved (0.″1–1.″0) radio maps of Neptune taken from the Very Large Array and Atacama Large Millimeter/submillimeter Array between 2015 and 2017. Combined, these observations probe from just below the main methane cloud deck at ∼1 bar down to the NH4SH cloud at ∼50 bar. Prominent latitudinal variations in the brightness temperature are seen across the disk. Depending on wavelength, the south polar region is 5–40 K brighter than the mid-latitudes and northern equatorial region. We use radiative transfer modeling coupled to Markov Chain Monte Carlo methods to retrieve H2S, NH3, and CH4 abundance profiles across the disk, though only strong constraints can be made for H2S. Below all cloud formation, the data are well fit by 53.8 − 13.4 + 18.9 × and 3.9 − 3.1 + 2.1 × protosolar enrichment in the H2S and NH3 abundances, respectively, assuming a dry adiabat. Models in which the radio-cold mid-latitudes and northern equatorial region are supersaturated in H2S are statistically favored over models following strict thermochemical equilibrium. H2S is more abundant at the equatorial region than at the poles, indicative of strong, persistent global circulation. Our results imply that Neptune's sulfur-to-nitrogen ratio exceeds unity, as H2S is more abundant than NH3 in every retrieval. The absence of NH3 above 50 bar can be explained either by partial dissolution of NH3 in an ionic ocean at GPa pressures or by a planet formation scenario in which hydrated clathrates preferentially delivered sulfur rather than nitrogen onto planetesimals, or a combination of these hypotheses.

Chlorine drying with hygroscopic ionic liquids

The chlorine (Cl2) drying technology using ionic liquids (ILs) as absorbents was proposed for the first time and systematically investigated from the molecular level scaled up to the industrial level. The hygroscopic IL [EMIM][CH3SO3] was screened as a suitable absorbent from 238 potential IL candidates consisting of 14 cations and 17 anions, by calculating the Cl2 and H2O solubility and separation selectivity of Cl2 to H2O in different ILs based on the COSMO-RS model. The microscopic atomic and molecular insights into the separation mechanisms were deeply revealed by using COSMO-RS model analyses (i.e., σ-profiles, σ-potentials, excess enthalpies, entropies, and Gibbs free energies) and quantum chemistry calculation (binding energies and weak interaction analyses). The Cl2 solubility in pure IL and H2O + IL systems were predicted by the COSMO-RS model, and the results agree with the microscopic mechanism identification. Moreover, the strict equilibrium stage model employed with the COSMO-RS model parameters was built to perform the process simulation, and continuous Cl2 drying with ILs was conceptually designed and optimized at industrial scale. It was confirmed that [EMIM][CH3SO3] is a very promising absorbent leading to a less IL amount, a much lower energy consumption than the other IL [EMIM][BF4], which has a very bright industrialization potential used for Cl2 drying technology.

Mathematical model of liquefied natural gas evaporation and analysis of original composition effect on evaporation speed

Subject of Research. The paper proposes a model for predicting evaporation of liquefied natural gas (LNG) stored in tanks of regasification terminals. The model is a combination of the strict thermodynamic LNG vapor-liquid equilibrium and heat transfer realistic models. Analysis of the initial composition effect and the stock of LNG, the initial content of nitrogen and the value of the outside air temperature on the LNG evaporation rate is carried out. Method. A numerical experiment using a mathematical model of the LNG evaporation process was based on the LNG composition data and its storage time in aboveground tanks. The proposed method provided a number of advantages compared to previously developed models: the heat input to the low-temperature part of the LNG storage tank was calculated taking into account the outdoor temperature and the LNG composition; the evaporation coefficient was not an input parameter, but was calculated as part of the simulation; the LNG density was calculated by experimental correlation. Main Results. An important parameter in assessing the LNG loss from its evaporation is the nitrogen content in the liquid, which evaporates at a higher rate than methane, the main LNG component. Analysis of the initial composition effect on the LNG evaporation rate has shown that the growth of the nitrogen content in the initial mixture causes noticeable decrease in the evaporation rate due to the nitrogen priority evaporation and, as a consequence, the growth of latent mixture heat vaporization. Analysis of the initial LNG supply value at the evaporation rate has shown that a large degree of the tank filling causes an outstripping reduction in losses from evaporation. The result is an earlier reduction in the amount of boil-off gas (BOG, stripping gas) for more filled tank. Analysis of the outdoor temperature effect on the rate of LNG evaporation has shown that the ambient temperature change of 1 °C leads to the decrease in the BOG amount by 0.2 %. Practical Relevance. The proposed mathematical model of the LNG evaporation process reduces BOG formation during long-term storage, maintain the original LNG quality, optimizes the operational parameters of regasification terminals, and provides the consumers with reliable supply of high-quality natural gas.