Types Of Equilibria Research Articles

Neoclassical transport benchmark of global full-f gyrokinetic simulation in stellarator configurations

A global full-f gyrokinetic simulation code, GT5D, is extended to incorporate stellarator equilibria, provided by a widely used three-dimensional equilibrium code, VMEC [S. P. Hirshman and O. Betancourt, J. Comput. Phys. 96, 99 (1991)]. An interface code is newly developed, in which the so-called VMEC coordinates are transformed into the coordinates of GT5D. The following benchmark calculations in a typical LHD equilibrium are carried out for the numerical verification of GT5D in stellarator configurations. First, zonal flow damping tests are performed, and good agreement in the residual levels with an analytical theory is confirmed. Second, the neoclassical transport and the ambipolar radial electric field computed by a global δf neoclassical transport code, FORTEC-3D [S. Satake et al., Plasma Fusion Res. 3, S1062 (2008)], are successfully reproduced.

Social Incentive Mechanism Based Multi-User Sensing Time Optimization in Co-Operative Spectrum Sensing with Mobile Crowd Sensing.

Co-operative spectrum sensing emerging as a significant method to improve the utilization of the spectrum needs sufficient sensing users to participate. Existing related papers consider only the limited secondary users in current sensing system and assume that they will always perform the co-operative spectrum sensing out of obligation. However, this assumption is impractical in the realistic situation where the secondary users are rational and they will not join in the co-operative sensing process without a certain reward to compensate their sensing energy consumption, especially the ones who have no data transmitting in current time slot. To solve this problem, we take advantage of the mobile crowd sensing to supply adequate co-operative sensing candidates, in which the sensing users are not only the secondary users but also a crowd of widely distributed mobile users equipped with personal spectrum sensors (such as smartphones, vehicle sensors). Furthermore, a social incentive mechanism is also adapted to motivate the participations of mobile sensing users. In this paper, we model the interactions among the motivated sensing users as a co-operative game where they adjust their own sensing time strategies to maximize the co-operative sensing utility, which eventually guarantees the detection performance and prevents the global sensing cost being too high. We prove that the game based optimization problem is NP-hard and exists a unique optimal equilibrium. An improved differential evolution algorithm is proposed to solve the optimization problem. Simulation results prove the better performance in our proposed multi-user sensing time optimization model and the proposed improved differential evolution algorithm, respectively compared with the non-optimization model and the other two typical equilibrium solution algorithms.

Are We Really Solving the Dynamic Traffic Equilibrium Problem with a Departure Time Choice?

The dynamic traffic equilibrium problem has been a pivotal area of research in transportation for a few decades. The current state-of-the-art research in this area generally considers simultaneous departure time and route choice. In this paper, we theoretically prove that, in the simplest standard bottleneck model with a sufficient number of commuters, a dynamic user equilibrium (DUE) cannot be reached through a day-to-day evolution process of travelers’ departure rate—a central idea behind the iterative dynamic traffic equilibrium algorithms prevalent in the literature. We carry out our exploration with the proportional swap system and then extend our analysis to other typical dynamic equilibrium algorithms such as the network tatonnement process, the simplex gravity flow dynamics, the projected dynamical system, and the evolutionary traffic dynamics. Our investigation indicates that any algorithm analogous to the five categories of systems must be cautious in terms of convergence when it is applied to solve the DUE problem with a departure time choice, and hence puts forward a general question: Are we really solving the DUE problem with a departure time choice?

New family of 4-D hyperchaotic and chaotic systems with quadric surfaces of equilibria

This paper reports 4-D hyperchaotic and chaotic systems with various quadric surfaces of equilibria. A known and systematic search procedure is used to generate the proposed systems. Six cases have non-degenerate quadric surfaces (ellipsoid, spheroid, sphere, elliptic hyperboloid of one sheet, circular hyperboloid of one sheet) type of equilibria and two cases have degenerate quadric surfaces (elliptic cylinder, circular cylinder) type of equilibria. All the cases in the new systems have coexistence of chaotic attractors. Chaotic natures of the new systems are confirmed by using various numerical tools. MATLAB simulation results are further validated by circuit implementations.

Typical equilibrium state of an embedded quantum system.

We consider an arbitrary quantum system coupled nonperturbatively to a large arbitrary and fully quantum environment. In the work by Ithier and Benaych-Georges [Phys. Rev. A 96, 012108 (2017)2469-992610.1103/PhysRevA.96.012108] the typicality of the dynamics of such an embedded quantum system was established for several classes of random interactions. In other words, the time evolution of its quantum state does not depend on the microscopic details of the interaction. Focusing on the long-time regime, we use this property to calculate analytically a partition function characterizing the stationary state and involving the overlaps between eigenvectors of a bare and a dressed Hamiltonian. This partition function provides a thermodynamical ensemble which includes the microcanonical and canonical ensembles as particular cases. We check our predictions with numerical simulations.

Coordinated Pricing Analysis with the Carbon Tax Scheme in a Supply Chain*

ABSTRACTThe carbon tax is a cost‐efficient scheme to curb emissions, and it has been implemented in Australia, British Columbia, and other places worldwide. We aim to analyze its effect on dynamic pricing in a supply chain with multiple suppliers and one manufacturer. The profit‐maximizing manufacturer makes final products using raw materials from suppliers with heterogeneous prices and emission rates. A two‐stage game model is built over an infinite time horizon for this issue. In the first stage, suppliers face price‐dependent demand to set their prices and production rates under the constraint of inventory capacity. Then, in response to the carbon tax scheme, the manufacturer evaluates the procurement prices and emission rates of suppliers to control its emission volumes and sets the sales price of its product. This article predominately focuses on the optimal pricing strategies in a decentralized supply chain. The open‐loop equilibrium and Markovian Nash equilibrium for the dynamic pricing game models of both suppliers and the manufacturer are derived, respectively. The equilibrium prices of suppliers and the manufacturer can be solved based on both irreversible actions and real‐time states. These two types of equilibria can be regarded as the solutions of two different models in specific situations. To analyze the effect of sourcing diversity on pricing strategies and emissions control for the manufacturer, the more general equilibrium price for the manufacturer in an n‐suppliers oligopoly is studied. Numerical examples are presented to illustrate the equilibrium and its monotonicity with various parameter settings.

Investigating the critical slip surface of soil slope based on an improved black hole algorithm

Analysing the stability of soil slopes and investigating critical slip surfaces present an important and very complicated optimisation problem. In this paper, we solve this problem by introducing and modifying a new global optimisation (black hole algorithm) technique to form a new global optimisation algorithm for continuous optimisation (the improved black hole algorithm). By combination with typical mature limit equilibrium analysis (the Spencer method and the Morgenstern-Price method), the improved black hole algorithm was used to find the critical slip surface of soil slope. Thus, this paper proposed a new method for finding the critical slip surface of soil slope. Finally, the proposed method was verified through two typical numerical soil slope cases and was compared with the black hole algorithm and other extant studies. The results indicated that the applicability, validity and effectiveness of the improved black hole algorithm showed an improvement over previous studies and over the black hole algorithm. Moreover, the proposed method was applied for one highway landslide, and the determined critical slip surface was well agreement with the real one.

Time-dependent seafloor roughness simulations using a coupled spectral ripple-biological decay model

Ever changing hydrodynamic conditions in the nearshore continuously affect biological communities and sediment features on the seafloor. Seafloor sediments have complicated interactions with the co-existing biological flora and fauna on the seabed. For example, ripple formation by waves and ripple degradation from biological activity are opposing forces occurring continuously. Simulating this complex natural environment is challenging due to these dynamic interactions of processes that span across a wide range of length and time scales. Existing seafloor models are often based on equilibrium conditions and neglect any change due to biological effects. Additionally, typical equilibrium ripple models provide only geometric dimensions, not a roughness spectrum necessary for acoustic applications. We present a time-varying spectral seafloor model, NSEA, that predicts the spatial and temporal evolution of seafloor roughness accounting for both the evolution and degradation of ripples due to hydrodynamics and biology. Model predictions are compared to high-frequency sector-scanning sonar data collected off the coast of Panama City, FL, during the Target and Reverberation Experiment (TREX13) and at the US Army Corps of Engineers Field Research Facility in Duck, NC. The sector-scanning sonar imaged ~15 square meters of the seafloor every 12 min for up to four weeks in depths up to 20 m.

General Equilibrium Model for an Asymmetric Information Economy Without Delivery Upper Bounds

AbstractIn this paper, we introduce production into the standard general equilibrium model with asymmetric information, which was proposed by Dubey et al. (Cowles Foundation Discussion Paper 2000; Econometrica 2005). In such an economy, there is no rational explanation for producers’ delivery upper bounds while the endowments naturally limit consumers’ deliveries. However, we show that the typical equilibrium allocation of the asymmetric information economy necessarily and substantially depends on such exogenous upper bounds (Example 1 and Theorem 1). In other words, an equilibrium existence theorem without such upper bounds, even if such exists, will typically fail to treat the asymmetric information problem, e.g., the adverse selection problem. Hence, to treat the equilibrium existence problem under the informational asymmetry appropriately, we have to extend the standard model so that the delivery upper bounds need not to be specified explicitly. For this purpose, we propose a quite natural and realistic assumption with respect to the technological condition related to the market delivery, i.e., the existence of some small standardization, commoditization, and/or transaction costs of market deliveries is shown to be sufficient (Theorem 3).

Peer-to-Peer Markets with Bilateral Ratings

We consider a platform that matches service providers with potential customers. Ratings of a service provider reveal the quality of his service while ratings of a consumer reveal the cost to serve her. Under a competitive search framework, we study how bilateral ratings influence market competition and segmentation. Two types of equilibria exist under bilateral ratings. In the first type, low-cost consumers only apply to high-quality service providers, who post a higher price, have longer queues and are less likely to accept an application than low-quality providers. High-cost consumers apply to all service providers and have a lower acceptance rate. In the second type of equilibria, both high- and low-quality service providers serve all consumers. Across all equilibria, equilibrium prices may decrease as the fraction of high-quality providers increases, as consumers become more costly to serve, and as the platform's commission rate increases. Compared with a platform with unilateral ratings where only service providers are rated, a platform with bilateral ratings may soften service providers' competition, leading to higher equilibrium prices. Lastly, we find that in the case of incomplete market coverage, high-quality service providers may charge lower prices than low-quality providers in equilibrium, because by charging a lower price, a high-quality service provider attracts more consumer applications, which enables him to cherrypick a low-cost consumer, while a low-quality service provider faces with consumers with higher serving costs and thus charge a higher price to make up the serving cost.

Round-Robin Tournaments with Limited Resources

We propose a theoretical model of a round-robin tournament with limited resources motivated by the fact that in a real-world round-robin sport tournament participating teams are sometimes forced to distribute their effort over an extended period. We assume that the participating teams have a limited amount of effort that must be distributed between all matches. We model the outcome of each match as a first-price sealed-bid auction. Results are aggregated after all matches are played with respect to the number of wins. The teams distribute their effort striving to maximize the expected payoff at tournament completion. For a three team tournament, we describe the set of all subgame perfect Nash equilibria in pure strategies. For tournaments with a relatively low first prize, we found two types of equilibria: ‘effort-saving’ and ‘burning out’, both leading to unequal payoffs. In contrast, for tournaments with a large first prize a limited budget of effort, in general, does not allow for the first or the last move advantage to be exploited.

Mobility of copper and zinc in near-surface groundwater as a function of the hypergenic zone lithology at the Kampinos National Park (Central Poland)

In the paper, we assess the mobility of copper and zinc in two sections, Granica and Kampinos, of the glacial and post-glacial sediments in the Kampinos National Park (Poland) and its buffer zone. The Granica section is practically devoid of carbonates and clay fraction, and the environment is markedly acidic. The other section, Kampinos, is characterized by a considerable content of carbonates (up to 20%) and clay fraction (up to 34%) with high sorption potential. The bonds of Zn2+ and Cu2+ cations with the solid phase occur mainly through adsorption and formation of salts, and through creation of chelated and complex connections. We found that, while sorption of Cu2+ within the shallow groundwater zone under typical natural environment equilibrium conditions depends mainly on the content of the sorbing solid phase (i.e. organic matter and metal oxides and hydroxides), sorption of Zn2+ within the shallow groundwater zone depends mainly on the fluctuating acidity and ionic strength of the groundwater, and to a lesser extent on the content and nature of the solid phase. The sorption process within the Kampinos section occurred predominantly on to three sorption media: clay fraction, organic matter and amorphous forms of Fe, Al and Mn. In the Granica section, because of the absence of clay fraction, sorption of the two metals occurred mainly with the organic matter and amorphous forms of Fe, Al and Mn. In addition, the sorption potential of the two metals in this section was low, because of the acidic pH of the environment, i.e. high availability of exchangeable hydrogen in the sorption complex. The concentrations of copper and zinc in the soil (So) were examined using both: the Lindsay and Norvell’s and aqua regia methods. The methods of variable extraction capacity yielded very similar results for copper. In addition, the study found that the amounts of extracted zinc depended on the type of solution. The highest concentrations of zinc and copper were observed using the extraction with aqua regia. The results from determining zinc and copper concentrations (So) in the soil and rocks and the results of hydrochemical modelling show that the mobility of these two elements is highly limited by sorption processes; moreover, zinc is less effectively adsorbed than copper in these sections.

On the geometric conditions for multiple stable equilibria in clamped arches

Curved structures, such as beams, arches, and panels are capable of exhibiting snap-through buckling behavior when loaded laterally, that is they can exhibit multiple stable equilibria, sometimes after any external loading is removed. This is a consequence of highly nonlinear force-deflection relations with perhaps multiple crossings of the zero-force axis for typical equilibrium paths. However, the propensity to maintain a stable snapped-through equilibrium position (in addition to the nominally unloaded equilibrium configuration) after the load is removed depends on certain geometric properties. A number of clamped arches are used to illustrate the relation between geometry (essentially the shape) and corresponding equilibrium configuration(s), and especially those conditions for which the initial equilibrium configuration is the only stable shape possible. Furthermore, related results are obtained when a change in the thermal environment may cause a system to exhibit a stable snapped-through equilibrium even when the system at ambient thermal conditions does not. Some representative examples are produced using a 3D printer for verification purposes.

Dynamic Certification, Reputation for Quality and Industry Standard

We study firm's incentives to invest and build reputation for quality, when quality can be certified at a cost. We consider two types of equilibria: one in which certification decisions are made based on firm's reputation and the second in which they are made based on the time since last certification. We show that reputation-based certification has a very limited effect on incentives to invest in quality, so that in equilibrium the firm invests only its reputation is the lowest. We also show that the firm in this case suffers from an over-certification trap in which the benefits of reputation are dissipated by excessive certification. These problems can be avoided with time-based certification, which can allow first-best investment in quality for sufficiently small certification cost, despite investment being unobservable. We also show that the optimal certification duration results in the firm certifying when its reputation is high.

Empirical Distribution of Equilibrium Play and Its Testing Application

We show that in any n-player, m-action normal-form game, we can obtain an approximate equilibrium by sampling any mixed-action equilibrium a small number of times. We study three types of equilibria: Nash, correlated, and coarse-correlated. For each one we obtain upper and lower bounds on the number of samples required for the empirical distribution over the sampled action profiles to form an approximate equilibrium with probability close to 1.These bounds imply that using a small number of samples we can test whether or not players are playing according to an approximate equilibrium, even in games where n and m are large. In addition, our results substantially improve previously known upper bounds on the support size of approximate equilibria in games with many players. In particular, for the three types of equilibria we show the existence of approximate equilibrium with support-size polylogarithmic in n and m, whereas the previously best-known upper bounds were polynomial in n (Hémon et al. [Hémon S, de Rougemont M, Santha M (2008) Approximate nash equilibria for multi-player games. Algorithmic Game Theory (Springer), 267–278], Germano and Lugosi [Germano F, Lugosi G (2007) Existence of sparsely supported correlated equilibria. Econom. Theory 32(3):575–578], Hart et al. [Hart S, Mas-Colell A, Babichenko Y (2013) Simple Adaptive Strategies: From Regret-Matching to Uncoupled Dynamics, Vol. 4 (World Scientific Publishing Company)]).

Peer-to-Peer Markets with Bilateral Ratings

We consider a platform that matches service providers with potential customers. Ratings of a service provider reveal the quality of his service while ratings of a consumer reveal the cost to serve her. Under a competitive search framework, we study how bilateral ratings influence market competition and segmentation. Two types of equilibria exist under bilateral ratings. In the first type, low-cost consumers only apply to high-quality service providers, who post a higher price, have longer queues and are less likely to accept an application than low-quality providers. High-cost consumers apply to all service providers and have a lower acceptance rate. In the second type of equilibria, both high- and low-quality service providers serve all consumers. Across all equilibria, equilibrium prices may decrease as the fraction of high-quality providers increases, as consumers become more costly to serve, and as the platform's commission rate increases. Compared with a platform with unilateral ratings where only service providers are rated, a platform with bilateral ratings may soften service providers' competition, leading to higher equilibrium prices. Lastly, we find that in the case of incomplete market coverage, high-quality service providers may charge lower prices than low-quality providers in equilibrium, because by charging a lower price, a high-quality service provider attracts more consumer applications, which enables him to cherrypick a low-cost consumer, while a low-quality service provider faces with consumers with higher serving costs and thus charge a higher price to make up the serving cost.

Modeling the Impacts of Free Trade Agreements on Domestic Transportation Gateways, Corridors, and Ports

Canada has recently made progress with several free trade agreements (FTAs), and although the government has carried out considerable analysis of their potential impact on the Canadian economy, little to no work has been done to assess the potential impact on Canada's transportation system. The objective of the research was to estimate the impacts of recent and forthcoming FTAs on Canada's domestic trade infrastructure. This study extended a typical computable general equilibrium simulation of an FTA by estimating high-level domestic supply chain characteristics (i.e., subnational region of origin or destination, sub-national region of exit or entry, international transportation mode, port of clearance) and by converting the resulting trade flows to freight flows measured in tonnage. The results indicate that the Comprehensive Economic and Trade Agreement (CETA) between Canada and the European Union (EU) may have had large impacts on Canada's Continental and Atlantic Gateways, especially at the Port of Montreal, Quebec, as a result of trade creation with the EU. CETA also has had impacts on various crossings at the U.S. border as a result of trade diversion with the United States. Simulations, however, suggested that the Canada–Korea Free Trade Agreement has had relatively small impacts, mostly concentrated in the Asia-Pacific Gateway, particularly at the Port of Vancouver, British Columbia. Although the impacts were FTA-specific, this research demonstrated the need to consider FTAs in commodity forecasting and freight transportation planning, because they could make sizable changes to future freight flows on domestic transportation infrastructure.

Best-shot versus weakest-link in political lobbying: an application of group all-pay auction

We analyze a group political lobbying all-pay auction with a group specific public good prize, in which one group follows a weakest-link and the other group follows a best-shot impact function. We completely characterize all semi-symmetric equilibria. There are two types of equilibria: (1) each player in the best-shot group puts mass at the upper bound of the support, whereas each player in the other group puts mass at the lower bound of the support; (2) players in the best-shot group put masses at both the lower and the upper bounds, while the other group randomizes without a mass point. An earlier and longer version of this study was circulated under the title “The Group All-pay Auction with Heterogeneous Impact Functions.” We appreciate the comments of an Associate Editor and two anonymous referees, Kyung Hwan Baik, Walter Enders, Matt Van Essen, Paan Jindapon, David Malueg, Paul Pecorino, Seth Streitmatter, Ted Turocy, the participants at the 2015 conference of ‘Contest: Theory and Evidence’ at the University of East Anglia, and the seminar participants at the University of Alabama and Korea University. Iryna Topolyan gratefully acknowledges the support from the Charles Phelps Taft Research Center. Any remaining errors are our own.

Typical equilibrium beach profile models and their significances from different segments of a headland-bay beach

This study introduces three typical models on equilibrium beach profile, and discusses the application limitations of these models. Then this study examines the selections for applying these models on different coastal segments of a headland-bay beach in west Guangdong, South China, and explores the physical significances of those parameters in the models. The results indicate that: (1) Bodge’s model is more in line with the equilibrium beach profile of the tangential or transitional segment, whereas Lee’s model is more consistent with the shadow profile; (2) most of the parameters in three models have clear physical significances in accordance with the actual characteristics of this headland-bay beach; and (3) both the selections for the equilibrium beach profile from different segments and significances of most of the parameters in three models are in essence correlated with the morphodynamic states at various coastal locations.

Arms build‐up and arms race in optimal economic growth

AbstractI analyze a model of strategic interdependence between two economies linked by investments in defensive capital for deterrence purposes. I adapt a two‐agent dynamic setting where weapon production affects consumption. Individually both economies determine their balanced growth path by taking this interdependence into account in different grades of awareness. I associate two types of equilibria with internal or external determinants for defense production analogous to scenarios of arms build‐up or arms race. I find that a defense sector is compatible with economic growth but a tight arms race can harm growth.