Multiple Equilibria Research Articles

Dynamics of the Agulhas Current Influenced by the North–South Shift of Subtropical Front

Abstract The influence of meridional shift of the oceanic subtropical front (STF) on the Agulhas Current (AC) regime shifts is studied using satellite altimeter data and a 1.5-layer ocean model. The satellite observations suggest the northward shift of the STF leads to the AC leaping across the gap with little Agulhas leakage, and the southward shift of the STF mainly results in the AC intruding into the Atlantic Ocean in the forms of a loop current and an eddy-shedding path, while there are three flow patterns of AC for moderate latitude of the STF. The ocean model results suggest no hysteresis (associated with multiple equilibrium states) exists in the AC system. The model reproduces similar AC regimes depending on different gap widths as in the observations, and model results can be used to explain the observed Agulhas leakage well. We also present the parameter space of the critical AC strength that results in different AC flow patterns as a function of the gap width. The vorticity dynamics of the AC regime shift suggests that the β term is mainly balanced by the viscosity term for the AC in the leaping and loop current paths, while the β and instantaneous vorticity terms are mainly balanced by the advection and viscosity terms for the AC in the eddy-shedding path. These findings help explain the dynamics of the AC flowing across the gateway beyond the tip of Africa affected by the north–south shift of the STF in the leaping regime or penetrating regime.

Panel-Pin Model for Kinematic and Equilibrium Analysis of Rigid Origami

In this study, the mathematical model referred to as the panel-pin model is proposed for analyzing the infinitesimal-deformation mechanism and the large-deformation equilibrium path of a rigid origami composed of rigid faces (panels) and subjected to deformation only at its crease lines. The panel-pin model represents a rigid origami as a structure of rigid panels pin-connected at the vertices and has the following advantages: 1) consistent formulation of compatibility equations for any type of the rigid origami structure; 2) systematic computation of vertex displacements, folding angles, and their derivatives; and 3) ease of accounting for gravity acting on the panels. The infinitesimal mechanism of the panel-pin model is studied according to the standard procedure for mechanisms and linkages, and an equilibrium path is traced as the trajectory of equilibrium points obtained by minimizing the total potential energy of the model with a rotational spring along each crease line. The numerical examples with multiple degrees of freedom of the mechanism show that the multiple equilibrium paths can be obtained by assigning the initial imperfection, and this is also confirmed by the physical model.

Firm Competition and Cooperation with Norm‐Based Preferences for Sustainability

We analyze firms' incentives to coordinate on the introduction of a sustainable product variant when consumers' preferences for sustainability depend on the perceived social norm, which in turn is shaped by average consumption behavior. We show that such preferences could lead to multiple equilibria. If the level of competition among potential adopters is very low and adoption of the sustainable variant allows them to sufficiently expand their aggregate market share, they will coordinate on introducing the sustainable variant when a lenient legal regime makes this feasible. If competition among them is intense and market expansion under the sustainable variant is very limited, coordination can forestall the adoption of the sustainable variant. Our analysis thus both confirms and qualifies the notion of a sustainability “first‐mover disadvantage” as a justification for an agreement between competitors, which has gained traction in antitrust. We also provide empirical evidence for norm‐based sustainability preferences.

Evolutionary game analysis of shared parking market diffusion under government management

Abstract The imbalance between supply and demand in urban settings poses a significant barrier to the sustainable advancement of urban transportation. Shared parking serves as a viable solution to mitigate these challenges. Nevertheless, for its sustained growth, a regulatory mechanism enforced by the government is imperative. To promote shared parking market diffusion, we construct an evolutionary game model that incorporates the government, enterprises and parking demanders. It explores stabilization strategies for these stakeholders and identifies multiple equilibrium states under different parameter conditions. The results show that the rate and stability of these evolutionary strategies are constrained by the mutual benefits derived by the three parties. Furthermore, such stakeholders are reciprocally influenced by their willingness to engage in shared parking to varying degrees. Government subsidies serve as a determining factor for the strategic choices made by both enterprises and demanders, albeit at different evolutionary rates. Demanders who have a higher value of time tend to park on-street, thereby influencing enterprise strategies. To foster the long-term growth of the shared parking market, the government must enact appropriate subsidy policies, maintain consistent regulations and advocate for increased subsidies for parking demanders to reduce the effect of temporal heterogeneity on parking behavioural choices.

Trading and Shareholder Democracy

ABSTRACTWe study shareholder voting in a model in which trading affects the composition of the shareholder base. Trading and voting are complementary, which gives rise to self‐fulfilling expectations about proposal acceptance and multiple equilibria. Prices and shareholder welfare can move in opposite directions, so the former may be an invalid proxy for the latter. Relaxing trading frictions can reduce welfare because it allows extreme shareholders to gain more weight in voting. Delegating decision‐making to the board can help overcome collective action problems at the voting stage. We also analyze the role of index investors and social concerns of shareholders.

Unified flash calculations with isenthalpic and isochoric constraints

In the unified flash procedure, a persistent set of unknowns and equations are solved in equilibrium calculations, allowing for simultaneous phase stability and split calculations. For fluids in a subcritical thermodynamic state characterized by pressure and temperature, modeling both liquid and gas phases with inequality conditions for phase fractions has been shown to incorporate the tangent-plane criterion and results in a consistent formulation of compositions for both present and absent phases. However, applications such as high-enthalpy systems in subsurface flow require a state definition using other state variables than pressure and temperature, as well as the capability to represent supercritical phases. Furthermore, the robustness of the flash across a wide range of state values is required if equilibrium dynamics are to be included in a flow and transport problem.This work introduces constraints in terms of enthalpy and volume to allow pressure and temperature to vary in the unified setting. The constraints are shown to arise from equilibrium conditions for the relevant state functions to be minimized. To increase the range of applicability, a modified extension procedure for the compressibility factor was devised, as well as procedures for the flash initialization.The unified formulation is extendable to allow isenthalpic and isochoric flash calculations. The initialization was devised using methodologies from the negative flash and Rachford–Rice equations. Extensive numerical tests with multiple equilibrium definitions in terms of state variables were performed. Gas–liquid, binary and a multicomponent mixture using Peng–Robinson EoS showed consistency of results which are verified using third-party code.

Insider Trading with Semi-Informed Traders and Information Sharing: The Stackelberg Game

This paper presents a financial Stackelberg game model with two partially informed risk neutral insiders. Each insider receives a private signal about the stock value and competes with the other insider under a Stackelberg setting. Linear strategies for the game’s participants are considered and normal distributions for the fundamentals are assumed. Based on the Stackelberg game and the Backward Induction theory, the unique linear equilibrium is characterized. The findings reveal that the level of partial information might increase/decrease the insiders’ profits as well as the market parameter in the Stackelberg setting relative to the Cournot setting. Additionally, this paper considers the information sharing scenario between the two insiders competing in this Stackelberg game. The results show that multiple equilibria exist in contrast to the information sharing scenario in the Cournot game where the Nash equilibrium is unique.

Complex Dynamic Analysis for a Rent-Seeking Game with Political Competition and Policymaker Costs

This paper investigates the dynamics of rent-seeking games that include political competition and policymaker cost model. The local asymptotic stability of multiple equilibrium points and Nash equilibrium points are studied. In the rent-seeking model, the existence and stability of Flip bifurcation and Neimark–Sacker bifurcation are examined, and the corresponding theorems and conditions are derived. The theoretical conclusions of the paper are verified by numerical simulations with different parameters. The simulation graphics show that the rent-seeking game model exhibits rich dynamic behaviors, such as multi-periodic orbits, Flip bifurcation, Neimark–Sacker bifurcation, and chaotic sets.

Pushing towards shared mobility

This paper provides a theoretical argument for preferential treatment of shared vehicles (SV) over private ones by municipal parking authorities. When all parked vehicles are treated equally, multiple equilibria may exist: (i) a “private” one, in which travellers are hesitant to switch to SV because the latter are hard to find, and (ii) a “shared” equilibrium, in which travellers use shared mobility because the city is saturated with vacant SV. The latter equilibrium, if it exists, is shown to yield higher welfare. Municipal parking discounts for SV reduce the amount of investment required for a “big push” towards the shared equilibrium, or even make it the only equilibrium.

Electrostatic interactions between charge regulated spherical macroions.

We study the interaction between two charge regulating spherical macroions with dielectric interior and dissociable surface groups immersed in a monovalent electrolyte solution. The charge dissociation is modelled via the Frumkin-Fowler-Guggenheim isotherm, which allows for multiple adsorption equilibrium states. The interactions are derived from the solutions of the mean-field Poisson-Boltzmann type theory with charge regulation boundary conditions. For a range of conditions we find symmetry breaking transitions from symmetric to asymmetric charge distribution exhibiting annealed charge patchiness, which results in like-charge attraction even in a univalent electrolyte-thus fundamentally modifying the nature of electrostatic interactions in charge-stabilized colloidal suspensions.

Dynamics in a behavioral-epidemiological model for individual adherence to a nonpharmaceutical intervention.

The SARS-CoV-2 pandemic has highlighted the importance of behavioral drivers in epidemic dynamics. With the relaxation of mandated nonpharmaceutical interventions (NPIs) formerly in place to decrease transmission, such as mask-wearing or social distancing, adherence to an NPI is now the result of individual decision-making. To study these coupled dynamics, we embed a game-theoretic model for individual NPI adherence within an epidemiological model. When the disease is endemic, we find that our model has multiple (but none concurrently stable) equilibria: one each with zero, complete, or partial NPI adherence. Surprisingly, for the equilibrium with partial NPI adherence, the number of infections is independent of the transmission rate. Therefore, in that regime, a change in the rate of pathogen transmission, e.g., due to another (mandated) NPI or a new variant, has no effect on endemic infection levels. On the other hand, we show that vaccination successfully decreases endemic infection levels, and, unexpectedly, also reduces the number of susceptibles at equilibrium when there is partial adherence. From a game-theoretic perspective, we find that highly effective NPIs lead at most to partial adherence. As this effectiveness decreases, partially effective NPIs initially lead to increases in population-level adherence, especially if the risk is high enough. However, a completely ineffective NPI results in no adherence. Furthermore, we identify parameter regions where the individual incentives may not align with those of society as a whole. Overall, our findings illustrate complexities that can arise due to behavioral-epidemiological feedback and suggest appropriate measures to avoid more pessimistic population-level outcomes.

Integrated stochastic multicriteria acceptability analysis and data envelopment analysis with fixed-sum outputs: an application for evaluating participating nations in the Winter Olympics Games

Along with the popularity of Olympic Games, evaluating and ranking participating nations has become one of the hottest issues in recent years. Data envelopment analysis (DEA) is extensively used for participating nations’ performance evaluation, while the prior literature mainly addresses the maximum efficiency by ignoring the weights diversity, which might lead to unreasonable and biased results. By considering the fixed-sum medals constraint, this paper proposes an integrated approach of stochastic multicriteria acceptability analysis (SMAA) and DEA for evaluating the participating nations. The proposed approach addresses the weights diversity and multiple equilibrium efficient frontiers by investigating the overall feasible space, and two strategies are considered to guarantee the fairness concern for calculating the efficiencies. Besides, the proposed approach provides both rank acceptability and holistic acceptability index to obtain the complete ranking from the best to the worst and to get the relative ranking relationship in the overall feasible space. The proposed approach can provide more reasonable performance measurements since it explores different rank positions and improves the whole satisfaction of all participating nations. Finally, the proposed approach is applied to empirically analyze the participating nations in the Winter Olympic Games from 2010 to 2022 and some valuable analytical results are provided.

Facultative Mutualisms and θ-Logistic Growth: How Larger Exponents Promote Global Stability of Co-Existence Equilibria

We investigate the stability of co-existence equilibria for two-species models of facultative mutualism for which birth and death are modeled as separate processes, with possibly distinct types of density dependence, and the mutualistic contributions are either linear or saturating. To provide a unifying perspective, we first introduce and discuss a generic stability framework, finding sufficient stability conditions expressed in terms of reproductive numbers computed at high population densities. To this purpose, an approach based on the theory of monotone dynamical systems is employed. The outcomes of the generic stability framework are then used to characterize the dynamics of the two-species models of concern, delineating between decelerating (lower-powered) and accelerating (higher-powered) density dependences. It is subsequently seen that accelerating density dependences promote the stability of co-existence equilibria, while decelerating density dependences either completely destabilize the system via promoting the unboundedness of solutions or create multiple co-existence equilibria.

Stability of switched systems with multiple equilibria: A mixed stable–unstable subsystem case

Stability of switched systems with multiple equilibria: A mixed stable–unstable subsystem case

Social networks and voter turnout.

This paper develops a model of voter turnout that embeds Riker and Ordeshook's (1968 Am. Pol. Sci. Rev. 62, 25-42 (doi:10.2307/1953324)) calculus of voting into the context of a social network. In the model, an individual's expressive benefits to voting depend on the behaviour of their social contacts. We show that there may be multiple equilibria and analyse how these equilibria depend on the structure of the network. We discuss six empirical implications of the model for turnout, some of which suggest novel answers to longstanding puzzles in the turnout literature, such as: why are higher income individuals more likely to vote even in cases when registration costs are low? Why is turnout so difficult to predict? Why does lowering registration costs disproportionately increase turnout among high-income voters? And why do we observe inertia in turnout across elections?

Acceptable discourse: Social norms of beliefs and opinions

This paper develops a theory of social norms of beliefs and opinions, which provides an account of political correctness and the backlash against it. Social norms about opinion expression emerge as equilibria of a signaling game in which expressing an unpopular opinion leads to bad judgments about one’s values, but may also be attributed to one’s factual beliefs. Multiple equilibria may co-exist, corresponding to norms with more or less conformity and social pressure. Additionally, motivated reasoning and persuasion allow norms to influence privately held opinions and underlying factual beliefs. This gives us a new account of normative social influence on beliefs. People convince each other, and themselves, of the beliefs that make their opinions more socially acceptable. The theory helps us understand how public discourse shapes beliefs, for example, when communities with stronger norms of political correctness keep a lid on racist opinions, yet believe that racism is more prevalent.

Impact of Fear on Searching Efficiency of Prey: A Prey–Predator Model with Weak Allee Effect

Reduced population growth at low density has important implications for conservation, colonization success, and wildlife management. In this context, the Allee effect, i.e. the positive relationship between per capita growth rate and biomass of small population density, is a crucial biological phenomenon since it is directly related to population extinction. The present paper deals with a two-species interacting model with a predator–prey relationship, where the prey population experiences the mate-finding Allee effect caused by the predator. We assume that the searching efficiency of prey individuals decreases linearly with predator density due to predation fear and investigate how predation intensity affects predator–prey dynamics. Moreover, we consider the Monod–Haldane type functional response for predator–prey interactions, which shows group defense of prey against the predator. We provide detailed mathematical analyses, including the positivity and boundedness of solutions, all biologically feasible equilibria, and their local and global stabilities. From our detailed mathematical analyses, we observe that when the carrying capacity of prey is low, at most one interior equilibrium exists, and system dynamics is simple compared to the case with high carrying capacity in which multiple coexistence equilibria may exist. We discuss three codimension-one bifurcations mathematically, e.g. Hopf bifurcation, transcritical bifurcation, saddle-node bifurcation. We notice bistability in the system when there are two interior equilibria with high carrying capacity. However, a unique attractor exists when there is only a single interior equilibrium and both populations persist. We perform extensive numerical simulations by varying two parameters simultaneously and explore how the system dynamics become complex when carrying capacity is high compared to low carrying capacity. Moreover, we discuss other important biological phenomena, e.g. the paradox of enrichment, bubbling phenomenon, etc.

A novel variational inequality approach for modeling the optimal equilibrium in multi-tiered supply chain networks

We present a novel variational inequality model (VIM) to capture the complex real decision-making process in multi-tiered supply chain networks (MSCN) without strictly limiting the features of related functions. The VIM is formulated with the equilibrium conditions on links as the optimization goal and the flow conservation condition as the main constraints. We transform the VIM into a series of equivalent Non-Linear Programming Models (NLPMs) to solve. To address this challenge, we propose a novel population-based heuristic algorithm called the Multiscale Model Learning Algorithm (MMLA). The MMLA is inspired by the learning behavior of individuals in a group and can converge to an optimal equilibrium state of the MSCN. The MMLA has two key operations: zooming in on the search field and learning search in a learning stage. The excellent performers, called medalists, are imitated by other learners. With the increase in learning stages, the learning efficiency is improved, and the searching energy is concentrated in a more promising area. We employ sixteen benchmark optimization problems and two supply chain networks to demonstrate the effectiveness of the MMLA and the rationality of the equilibrium models. The results obtained by MMLA for the NLPM show that the MMLA can solve the equilibrium model effectively, and multiple optimal equilibrium states may exist for an MSCN. The flexibility of the NLPM makes it possible to consider more complicated decision-making mechanisms in the model.

The Authoritarian Commons: Divergent Paths of Neighborhood Democratization in Three Chinese Megacities

Abstract Can a liberal commons emerge in an authoritarian regime? Based on an in-depth investigation of the ongoing self-governance movement among hundreds of millions of homeowners in China, this Article examines the tension between authoritarianism and liberal commons for the first time. Empirically, this Article reveals a striking contrast: in Shanghai, 94% of condominium complexes have established homeowners’ associations, a kind of liberal commons, compared with 41% in Shenzhen, and only 12% in Beijing. It is posited in this Article that the authoritarian commons (i.e., the dynamic interactions between the authoritarian state and homeowners’ efforts to create a liberal commons in their neighborhoods) features multiple equilibria that depend on the state capacity and the risks posed by the self-governance movement. A highly capable state facing an intermediate degree of risk can make the institutional reforms necessary to accommodate the grassroots democracy. This research of the authoritarian commons brings the state back to the economic theories of property rights, and brings property, and more specifically, space and territorial control to the study of authoritarianism. It also deepens our understanding of authoritarianism and development.

Multiple equilibrium states in large arrays of globally coupled resonators

Multiple equilibrium states in large arrays of globally coupled resonators