(Minimally) 'epsilon'-incentive compatible competitive equilibria in economies with indivisibilities

We consider competitive and budget-balanced allocation rules for problems where a number of indivisible objects and a fixed amount of money is allocated among a group of agents. In 'small' economies, we identify under classical preferences each agent's maximal gain from manipulation. Using this result we find the competitive and budget-balanced allocation rules which are minimally manipulable for each preference profile in terms of any agent's maximal gain. If preferences are quasi-linear, then we can find a competitive and budget-balanced allocation rule such that for any problem, the maximal utility gain from manipulation is equalized among all agents.

Conflict, wages, and multiple equilibria

Firms’ compensation practices affect the protection of investors’ interests and the degree of economic inequality by changing the stakes of engaging in appropriation activities versus respecting the status quo. We use a general equilibrium model where workers can either work peacefully or join a guerrilla movement that expropriates entrepreneurs. If workers are peaceful, they receive a competitive wage. If they join a guerrilla movement, they receive a share of the appropriated wealth, which depends positively on the number of guerrilla members. In this framework, we find one low-income, low-wage equilibrium with guerrilla activity and one peaceful, high-income, high-wage equilibrium. The peaceful equilibrium can be reached through redistribution policies, which can be implemented at the firm level. In essence, through their compensation policies entrepreneurs, not the state might be able to protect their assets against expropriation and simultaneously control the internal principal-agent problem.

AQA A2 Unit 4 Chemistry : kinetics, equilibria and organic chemistry.

Guía de apoyo para alumnos de educación secundaria de segundo ciclo que sigan la especificación de AQA (Assessment and Qualifications Alliance) en el nivel A2 del área de química. Está dividida en tres secciones: una introducción con consejos y técnicas para la realización del examen; una guía de contenido con los principales conceptos y temas (cinética, equilibrio, ácidos y bases, nomenclatura e isomería en química orgánica, compuestos del grupo carbonilo, química aromática, aminas, aminoácidos, polímeros, análisis y síntesis orgánica y determinación de estructura); y una sección con preguntas de examen y respuestas comentadas por un examinador.

A simple model of multiple equilibria and default. CEPS Working Document No. 366, 16 July 2012

This Working Document by Daniel Gros presents a simple model that incorporates two types of sovereign default cost: first, a lump-sum cost due to the fact that the country does not service its debt fully and is recognised as being in default status, by ratings agencies, for example. Second, a cost that increases with the size of the losses (or haircut) imposed on creditors whose resistance to a haircut increases with the proportional loss inflicted upon them. One immediate implication of the model is that under some circumstances the creditors have a (collective) interest to forgive some debt in order to induce the country not to default. The model exhibits a potential for multiple equilibria, given that a higher interest rate charged by investors increases the debt service burden and thus the temptation to default. Under very high debt levels credit rationing can set in as the feedback loop between higher interest rates and the higher incentive to default can become explosive. The introduction of uncertainty makes multiple equilibria less likely and reduces their range.

Real options and game theoretical approaches to real estate development projects: multiple equilibria and the implications of different tie-breaking rules

This paper contributes to a fast growing literature which introduces game theory in the analysis of real option investments in a competitive setting. Specifically, in this paper we focus on the issue of multiple equilibria and on the implications that different equilibrium selections may have for the pricing of real options and for subsequent strategic decisions. We present some theoretical results of the necessary conditions to have multiple equilibria and we show under which conditions different tie-breaking rules result in different economic decisions. We then present a numerical exercise using the in formation set obtained on a real estate development in South London. We find that risk aversion reduces option value and this reduction decreases marginally as negative externalities decrease.

Precise calculations of the existence of multiple AMOC equilibria in coupled climate models Part I: equilibrium states

This study examines criteria for the existence of two stable states of the Atlantic Meridional Overturning Circulation (AMOC) using a combination of theory and simulations from a numerical coupled atmosphere–ocean climate model. By formulating a simple collection of state parameters and their relationships, the authors reconstruct the North Atlantic Deep Water (NADW) OFF state behavior under a varying external salt-flux forcing. This part (Part I) of the paper examines the steady-state solution, which gives insight into the mechanisms that sustain the NADW OFF state in this coupled model; Part II deals with the transient behavior predicted by the evolution equation. The nonlinear behavior of the Antarctic Intermediate Water (AAIW) reverse cell is critical to the OFF state. Higher Atlantic salinity leads both to a reduced AAIW reverse cell and to a greater vertical salinity gradient in the South Atlantic. The former tends to reduce Atlantic salt export to the Southern Ocean, while the latter tends to increases it. These competing effects produce a nonlinear response of Atlantic salinity and salt export to salt forcing, and the existence of maxima in these quantities. Thus the authors obtain a natural and accurate analytical saddle-node condition for the maximal surface salt flux for which a NADW OFF state exists. By contrast, the bistability indicator proposed by De Vries and Weber does not generally work in this model. It is applicable only when the effect of the AAIW reverse cell on the Atlantic salt budget is weak.

Non-existence of competitive equilibria with dynamically inconsistent preferences

This paper shows the robust non-existence of competitive equilibria even in a simple three period representative agent economy with dynamically inconsistent preferences. We distinguish between a sophisticated and naive representative agent. Even when underlying preferences are monotone and convex, at given prices, we show by example that the induced preference of the sophisticated representative agent over choices in first-period markets is both non-convex and satiated. Even allowing for negative prices, the market-clearing allocation is not contained in the convex hull of demand. Finally, with a naive representative agent, we show that perfect foresight is incompatible with market clearing and individual optimization at given prices.

Climate determinism revisited: multiple equilibria in a complex climate model

Multiple equilibria in a coupled ocean–atmosphere–sea ice general circulation model (GCM) of an aquaplanet with many degrees of freedom are studied. Three different stable states are found for exactly the same set of parameters and external forcings: a cold state in which a polar sea ice cap extends into the midlatitudes; a warm state, which is ice free; and a completely sea ice–covered “snowball” state. Although low-order energy balance models of the climate are known to exhibit intransitivity (i.e., more than one climate state for a given set of governing equations), the results reported here are the first to demonstrate that this is a property of a complex coupled climate model with a consistent set of equations representing the 3D dynamics of the ocean and atmosphere. The coupled model notably includes atmospheric synoptic systems, large-scale circulation of the ocean, a fully active hydrological cycle, sea ice, and a seasonal cycle. There are no flux adjustments, with the system being solely forced by incoming solar radiation at the top of the atmosphere. It is demonstrated that the multiple equilibria owe their existence to the presence of meridional structure in ocean heat transport: namely, a large heat transport out of the tropics and a relatively weak high-latitude transport. The associated large midlatitude convergence of ocean heat transport leads to a preferred latitude at which the sea ice edge can rest. The mechanism operates in two very different ocean circulation regimes, suggesting that the stabilization of the large ice cap could be a robust feature of the climate system. Finally, the role of ocean heat convergence in permitting multiple equilibria is further explored in simpler models: an atmospheric GCM coupled to a slab mixed layer ocean and an energy balance model

Spectral nonlocality, absolute equilibria and Kraichnan-Leith-Batchelor phenomenology in two-dimensional turbulent energy cascades

We study the degree to which Kraichnan–Leith–Batchelor (KLB) phenomenology describes two-dimensional energy cascades in α turbulence, governed by ∂θ/∂t+J(ψ,θ)=ν∇2θ+f, where θ=(−Δ)α/2ψ is generalized vorticity, and ψ^(k)=k−αθ^(k) in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow (α=1), regular two-dimensional flow (α=2) and rotating shallow flow (α=3), which is the isotropic limit of a mantle convection model. We re-examine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general α, and point out their limitations. Using an α-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Non-local triads contribute increasingly to the energy flux as α increases. More importantly, the energy cascade is downscale in the self-similar inertial range for 2.5<α<10. At α=2.5 and α=10, the KLB spectra correspond, respectively, to enstrophy and energy equipartition, and the triad energy transfers and flux vanish identically. Eddy turnover time and strain rate arguments suggest the inverse energy cascade should obey KLB phenomenology and be self-similar for α<4. However, downscale energy flux in the EDQNM self-similar inertial range for α>2.5 leads us to predict that any inverse cascade for α≥2.5 will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for α≥2.5 is significantly steeper than the KLB prediction, while for α<2.5 we obtain the KLB spectrum.