Equilibrium Pair Research Articles

Competition in Lending: Theory and Experiments*

A variation of the Rothschild-Stiglitz' equilibrium is examined in the context of com- petitive lending under adverse selection. The predictions of the model are tested in an experimental market setting. If equilibrium exists, the loan contracts offered and taken should separate projects by quality. When equilibrium exists, the experiments confirm the theory. The entrepreneurs with high-risk projects take bigger loans and pay higher credit spreads than those with low-risk projects. When equilibrium does not exist, which happens exactly when the candidate equilibrium does not provide a Pareto-optimal allocation, in half of the sessions loan trading stabilizes around the candid- ate equilibrium pair. In the other half, however, markets never settle down. This finding has important implications. When lenders can offer menus of contracts, as is usually the case in reality, the outcome may not be the zero-profit separating contracts of the standard model. Worse, fitting the standard model to field data may lead to serious biases in estimated parameters while falsely accepting the model's main restriction (separation).

Existence of best proximity pairs and equilibrium pairs

In this paper, using the fixed point theorem for Kakutani factorizable multifunctions, we shall prove new existence theorems of best proximity pairs and equilibrium pairs for free abstract economies, which include the previous fixed point theorems and equilibrium existence theorems.

Comparative Statics with Never Increasing Correspondences

This paper studies models where the correspondences (or functions) under consideration are never increasing (or weakly decreasing) in endogenous variables, and weakly increasing in exogenous parameters. Such models include games where endogenous variables are strategic substitutes for each other, and includes cases where additionally, some (but not all) endogenous variables are strategic complements. It is shown that the equilibrium set in such models is a non-empty, complete lattice, if, and only if, there is a unique equilibrium. Indeed, for a given parameter value, a pair of distinct equilibria are never comparable. Moreover, generalizing an existing result, it is shown that when a parameter increases, no new equilibrium is smaller than any old equilibrium. Furthermore, when functions under consideration are weakly decreasing in endogenous variables, a sufficient condition is presented that guarantees existence of increasing equilibria at a new parameter value.

Analytical Theories of Transport in Concentrated Electrolyte Solutions from the MSA

Ion transport coefficients in electrolyte solutions (e.g., diffusion coefficients or electric conductivity) have been a subject of extensive studies for a long time. Whereas in the pioneering works of Debye, Hückel, and Onsager the ions were entirely characterized by their charge, recent theories allow specific effects of the ions (such as the ion size dependence or the pair association) to be obtained, both from simulation and from analytical theories. Such an approach, based on a combination of dynamic theories (Smoluchowski equation and mode-coupling theory) and of the mean spherical approximation (MSA) for the equilibrium pair correlation, is presented here. The various predicted equilibrium (osmotic pressure and activity coefficients) and transport coefficients (mutual diffusion, electric conductivity, self-diffusion, and transport numbers) are in good agreement with the experimental values up to high concentrations (1-2 mol L(-1)). Simple analytical expressions are obtained, and for practical use, the formula are given explicitly. We discuss the validity of such an approach which is nothing but a coarse-graining procedure.

Kiglapait mineralogy IV: The augite series

Based on twenty-five new chemical analyses, augites from the Upper Zone of the Kiglapait layered intrusion, Labrador, span the range from En 7 3 to En 0 . disposed about a straight line sloping slightly upward from WO 4 0 to Wo 4 2 in the pyroxene quadrilateral. They contain little tetrahedral Al, which decreases with Fe enrichment as tetrahedral ferric Fe 3 + increases. Little or no jadeite or Ca-Tschermaks component is present. Titanium rises only slightly with Fe, and the acmite component is scattered near mole fraction 0.03. Excess cations relative to 6 oxygen atoms occur chiefly by solid solution toward olivine, the only co-crystallizing mafic silicate phase. Values of n β increase linearly over the range 1.670 at fictive En 1 0 0 to 1.7448 at En 0 . The position of the 150 powder X-ray diffraction peak shifts regularly from 5.0372 to 4.1727 degrees away from the 220 peak of silicon metal over the same composition range. Exsolution of orthopyroxene near (100) is succeeded up-stratigraphy by that of pigeonite near (001), and the switch occurs at about the same augite composition as the switch from external orthopyroxene to pigeonite in the Skaergaard intrusion. Exsolution of ilmenite in or near (100) and magnetite-ulvospinel near the a and c directions in (010) produces the black color of these augites in hand specimen. Subsolidus augite-olivine tie lines and exchange relations in Fe-Mg allow the distinction between equilibrium pairs and those affected by exchange with external Fe-Ti oxide minerals or with intercumulus liquid in Upper Border Zone lithologies. Liquids producing augite and olivine with plagioclase follow a Ca-depletion trend until crystallization of abundant olivine and titanomagnetite drives them on a Ca-enrichment trend, to a point near Mg-free augite. Activities of silica consistent with augite-olivine pairs range from <0.6 to 0.98. The Kiglapait augite series exemplifies the crystallization of a magma occupying the narrow regime between silica saturation and undersaturation, in extreme fractionation from troctolite to Mg-free syenite.

INFLUENCE OF ENVIRONMENTAL CHANGES ON COOPERATIVE BEHAVIOR IN THE PRISONER'S DILEMMA GAME ON AN ARTIFICIAL SOCIAL MODEL

In this paper, by simulations on an artificial social model, we analyze cooperative behavior of agents playing the prisoner's dilemma game, in which each of the agents has the two strategies: cooperate and defect. Because defect yields a better payoff whichever strategy an opponent chooses, it is rational for an agent to choose defect in a single game or a finite number of games. However, it is known that a pair of cooperates can also be a Nash equilibrium pair if the players do not know when the game is over or the game is infinitely repeated. To investigate such cooperative behavior, we employ an artificial social model called the Sugarscape and carry out simulations on the model. Arranging three kinds of environments in the Sugarscape, we examine cooperative behavior of agents who are essentially selfish, in a sense that they maximize their payoffs, and investigate influence of environmental changes on the cooperative behavior.

On existence of equilibrium pair for constrained generalized games

We obtain sufficient conditions for the existence of an equilibrium pair for a particular constrained generalized game as an application of a best proximity pair theorem.

How Multiserver Queues Scale with Growing Congestion-Dependent Demand

We investigate how performance scales in the standard M/M/n queue in the presence of growing congestion-dependent customer demand. We scale the queue by letting the potential (congestion-free) arrival rate be proportional to the number of servers, n, and letting n increase. We let the actual arrival rate with n servers be of the form λn=f(ξn)n, where f is a strictly-decreasing continuous function and ξn is a steady-state congestion measure. We consider several alternative congestion measures, such as the mean waiting time and the probability of delay. We show, under minor regularity conditions, that for each n there is a unique equilibrium pair (λ*n, ξ*n) such that ξ*n is the steady-state congestion associated with arrival rate λ*n and λ*n=f(ξ*n)n. Moreover, we show that, as n increases, the queue with the equilibrium arrival rate λ*n is brought into heavy traffic, but the three different heavy-traffic regimes for multiserver queues identified by Halfin and Whitt (1981) each can arise depending on the congestion measure used. In considerable generality, there is asymptotic service efficiency: the server utilization approaches one as n increases. Under the assumption of growing congestion-dependent demand, the service efficiency can be achieved even if there is significant uncertainty about the potential demand, because the actual arrival rate adjusts to the congestion.

Confinement-induced colloidal attractions in equilibrium.

The Poisson-Boltzmann theory for colloidal electrostatic interactions predicts that charged colloidal spheres dispersed in water should repel each other, even when confined by charged surfaces. Direct measurements on highly charged polystyrene spheres, however, reveal strong, long-ranged confinement-induced attractions that have yet to be explained. We demonstrate that anomalous attractions also characterize the equilibrium pair potential for more weakly charged colloidal silica spheres sedimented into a monolayer above a glass surface. This observation substantially expands the range of conditions for which mean-field theory incorrectly predicts the sign of macroions' interactions, and provides new insights into how confinement induces long-ranged like-charge attractions.

Relativistic Kinetic Theory of Waves in Equilibrium Magnetized Pair Plasma. General Dispersion Relations

A relativistic kinetic theory of parallel longitudinal and transverse waves in magnetized, equilibrium pair plasma is presented. On the basis of the relativistic Maxwell–Vlasov equation, the general dispersion relations for parallel propagating waves in equilibrium pair plasmas are derived by a correct analytical continuation on the whole complex frequency plane. These are used to prove that no parallel growing waves exist in magnetized pair plasma with isotropic distribution function. Only superluminal transverse waves with frequencies larger than a critical value depending on the magnetic field, undergo no Landau damping.

Solid-phase extraction NMR studies of chromatographic fractions of saponins from Quillaja saponaria.

The saponin mixture QH-B from the tree Quillaja saponaria var. Molina was fractionated by RP-HPLC in several steps. The fractions were analyzed by solid-phase extraction NMR (SPE-NMR), a technique combining the workup by solid-phase extraction with on-line coupling to an NMR flow probe. Together with MALDI-TOF mass spectrometry and comparison with chemical shifts of similar saponins, the structures of both major and minor components in QH-B could be obtained. The procedure described is a simple method to determine the structure of components in a complex mixture. The two major fractions of the mixture were found to contain at least 28 saponins, differing in the carbohydrate substructures. Eight of these have not previously been determined. The 28 saponins formed 14 equilibrium pairs by the migration of an O-acyl group between two adjacent positions on a fucosyl residue.

Charged particle layers in the Debye limit.

We develop an equivalent of the Debye-Hückel weakly coupled equilibrium theory for layered classical charged particle systems composed of one single charged species. We consider the two most important configurations, the charged particle bilayer and the infinite superlattice. The approach is based on the link provided by the classical fluctuation-dissipation theorem between the random-phase approximation response functions and the Debye equilibrium pair correlation function. Layer-layer pair correlation functions, screened and polarization potentials, static structure functions, and static response functions are calculated. The importance of the perfect screening and compressibility sum rules in determining the overall behavior of the system, especially in the r--> infinity limit, is emphasized. The similarities and differences between the quasi-two-dimensional bilayer and the quasi-three-dimensional superlattice are highlighted. An unexpected behavior that emerges from the analysis is that the screened potential, the correlations, and the screening charges carried by the individual layers exhibit a marked nonmonotonic dependence on the layer separation.

Rotational Brownian motion of a pair of linear molecules or dipoles with anisotropic interaction

The rotational Smoluchowski equation for the orientational distribution function of two identical linear molecules or dipoles with anisotropic interaction is solved by expansion in terms of a limited set of eigenfunctions of the operator for free rotational diffusion. The equilibrium self-correlation and pair time-correlation functions of the two axial unit vectors or dipole moments are evaluated for the special case of electrostatic or magnetostatic dipole interaction. The interactions appreciably influence the relaxation behavior.

Instantaneous normal mode analysis of Morse liquids

Instantaneous normal mode (INM) analysis of a set of bulk Morse systems is performed to monitor the changes in the curvature distribution that occur as a result of changing the range and curvature of the Morse potential. The liquids are bound by Morse pair potentials, Vα(r)=ε[e−α(1−(r/re))−1]2−ε, and share a common well-depth, ε, and equilibrium pair distance, re, but possess different values of range parameter, α, which is inversely correlated with the range and softness of the potential. INM analysis is used to index the changes in the curvature distribution of the potential energy surface that take place as the range parameter of the pair potential is varied and is shown to provide considerable insights into the accompanying dynamical changes. For example, the fraction of imaginary frequency modes, and therefore the diffusivity, is expected to rise with increasing temperature and decreasing range. In contrast, the Einstein frequency, which is a measure of the curvature of the effective potential well that traps a tagged particle in the liquid state, shows a nonmonotonic behavior with range. We also consider the behavior of INM spectra of liquids in relation to that of solids and gases. It is shown that INM analysis can be used to monitor the transition of a fluid from a liquidlike regime, dominated by collective rearrangements, to a gaslike regime, dominated by binary collisions. The transition to a collision-dominated regime is promoted by decreasing the range of the pair potential. Key INM spectral features are shown to undergo a discontinuous change on melting. Minimization of instantaneous configurations to the nearest saddle removes the imaginary frequencies in the solid phase but not in the liquid phase.

Computing Stationary Nash Equilibria of Undiscounted Single-Controller Stochastic Games

Given a two-person, nonzero-sum stochastic game where the second player controls the transitions, we formulate a linear complementarity problem LCP(q, M) whose solution gives a Nash equilibrium pair of stationary strategies under the limiting average payoff criterion. The matrix M constructed is of the copositive class so that Lemke's algorithm will process it. We will also do the same for a special class of N-person stochastic games called polymatrix stochastic games.

Transport equations for concentrated electrolyte solutions: Reference frame, mutual diffusion

Transport coefficients of dissociated electrolytes in aqueous solution are studied in the framework of the primitive model of ionic solutions in which the solvent is a dielectric continuum. Simple explicit expressions are obtained by using a combination of Smoluchowski equation for the dynamics and the mean spherical approximation (MSA) for the equilibrium pair correlation function. The case of symmetrical and dissymmetrical electrolytes is examined. In the case of the mutual diffusion, a reference-frame correction, that can be obtained from density measurements has to be taken into account for molar concentrations. The combined Smoluchowski/MSA theory of the primitive model is found to be self-consistent since it is able to describe simultaneously the different transport and equilibrium properties up to high concentrations (1–2 mol l−1).

Free volume and density and temperature dependence of diffusion coefficients of liquid mixtures.

A simple formula for the diffusion coefficient of liquid mixtures, expressed in terms of the work necessary to create a characteristic free volume in the liquid, is presented in the spirit of the Arrhenius activation theory and tested in comparison with available experimental data. If use is made of the generic van der Waals equation of state, the free volume appearing in the formula for the diffusion coefficient can be expressed in terms of the equilibrium pair correlation functions. The theoretical values for diffusion coefficients agree excellently with experimental values with regard to the density and temperature dependence of the diffusion coefficients of argon and krypton.

Theory of thermal conductivity of dense simple fluids

A theory of thermal conductivity of simple liquids is developed in a way parallel with the theory of shear and bulk viscosities reported in previous papers. A molecular theoretic expression for the thermal conductivity of simple liquids is presented, which consists of two distinctive parts: one that is given in terms of intermolecular forces and the structure of the liquid described by equilibrium pair correlation function and thus strongly depends on the density, and the other that is given in terms of the Chapman–Enskog thermal conductivity and thus independent of the density. The density dependent part of the thermal conductivity is given in terms of the intermolecular force, the equilibrium pair correlation function, and self-diffusion coefficient in a form similar to the shear and bulk viscosities of the liquid, or in terms of the shear viscosity in a form generalizing to liquids the Eucken relation of thermal conductivity and shear viscosity. The theoretical result obtained for thermal conductivity is tested against experimental data available on argon in the literature.

A differential game model of tariff war

We present a simple two(-country) by two(-good) differential game model of international trade in which the governments of the two countries play a tariff-setting game. We explicitly derive a unilateral optimum tariff rate and then a Markov-perfect equilibrium pair of tariff strategies (bilateral optimum tariff strategies) and compare the welfare level of each country among autarchic, free-trade, unilateral and bilateral optimum-tariff equilibria.

A competitive inventory model with the customer's general choice probability

We consider a single-period model with reallocation of excess demand such that two firms offer some product for customers who are uniformly distributed on a line segment market. This model results in one of the unit square games with pure strategies of continuous cardinary. Their purposes are to find the optimal ordering quantity that minimizes the total cost. We generate a matrix by arranging the ordering quantity obtained in the usual way as one of the strategies for each player and analyze our model in a way to find an equilibrium pair.