Stabilization through taxation inn-person games

In formulating solutions forn-person cooperative games, the concept of stability has played a dominant role. Although the core concept has the strongest stability, the core of a game is often empty. In this paper, the taxation system is incorporated into our framework, so that a modified solution concept, which enjoys the stability of core, can be developed. Various formulations based on principles such astaxation proportional to income andequity after tax are given.     

Two Approaches to the Problem of Sharing Delay Costs in Joint Projects

This paper concentrates on cost sharing situations which arise when delayed joint projects involve joint delay costs. The problem here is to determine fair shares for each of the agents who contribute to the delay of the project such that the total delay cost is cleared. We focus on the evaluation of the responsibility of each agent in delaying the project based on the activity graph representation of the project and then on solving the important problem of the delay cost sharing among the agents involved. Two approaches, both rooted in cooperative game theory methods are presented as possible solutions. In the first approach delay cost sharing rules are introduced which are based on the delay of the project and on the individual delays of the agents who perform activities. This approach is inspired by the bankruptcy and taxation literature and leads to five rules: the (truncated) proportional rule, the (truncated) constrained equal reduction rule and the constrained equal contribution rule. By introducing two coalitional games related to delay cost sharing problems, which we call the pessimistic delay game and the optimistic delay game, also game theoretical solutions as the Shapley value, the nucleolus and the -value generate delay cost sharing rules. In the second approach the delays of the relevant paths in the activity graph together with the delay of the project play a role. A two-stage solution is proposed. The first stage can be seen as a game between paths, where the delay cost of the project has to be allocated to the paths. Here serial cost sharing methods play a role. In the second stage the allocated costs of each path are divided proportionally to the individual delays among the activities in the path.     

INVESTIGATING TAX DISTORTIONS: AN APPLIED MODEL OF PETROLEUM EXPLORATION AND EXTRACTION DECISIONS

Abstract A numerical model is proposed for the testing of distortions caused by petroleum fiscal systems on the exploration and extraction activities of a profit‐maximizing firm. Traditional models have not been capable of testing for the distortions caused by the complex tax structures most often used by governments. Two tax combinations, as well as certain other taxes, are analyzed for distortions in the model. The model is parameterized using generic data because specific jurisdictions are not considered. The distortions due to rentals and royalties are as expected by theory. Property taxes show a new distortion result where production tilting is ambiguous.     

The consequences of irreversibility on optimal intertemporal emission policies under uncertainty

This paper investigates how irreversibility affects optimal intertemporal emission policies when negative stock externalities exist. In particular it discusses the effect of irreversible emission, i.e., it concerns the physical issue whether it is possible to recollect pollutants that have been emitted or not. We depict our analysis with the greenhouse effect as a topical example and model the uncertainty with respect to the future evolution of the world’s temperature (i.e., the uncertain factor that determines the costs) as Itô-process with the drift provided by current carbon-dioxide emissions. We show analytically that irreversibility affects the optimal emission policy only if the future impact of today’s emissions is uncertain. Under uncertainty, irreversibility leads to a conservationist policy such that emissions are reduced at any level of environmental concentration of the pollutant. The level where stopping emissions is optimal decreases in the presence of irreversibility. Furthermore, the expected duration of fossil fuel use is derived. A numerical example which is calibrated to roughly reflect the global CO₂ problem illustrates the analytical findings.     

On automorphisms of a distance-regular graph with intersection array {204, 175, 48, 1; 1, 12, 175, 204}

The research is focused on the question of proportional development in economic growth modeling. A multilevel dynamic optimization model is developed for the construction of balanced proportions for production factors and investments in a situation of changing prices. At the first level, models with production functions of different types are examined within the classical static optimization approach. It is shown that all these models possess the property of proportionality: in the solution of product maximization and cost minimization problems, production factor levels are directly proportional to each other with coefficients of proportionality depending on prices and elasticities of production functions. At the second level, proportional solutions of the first level are transferred to an economic growth model to solve the problem of dynamic optimization for the investments in production factors. Due to proportionality conditions and the homogeneity condition of degree 1 for the macroeconomic production functions, the original nonlinear dynamics is converted to a linear system of differential equations that describe the dynamics of production factors. In the conversion, all peculiarities of the nonlinear model are hidden in a time-dependent scale factor (total factor productivity) of the linear model, which is determined by proportions between prices and elasticities of the production functions. For a control problem with linear dynamics, analytic formulas are obtained for optimal development trajectories within the Pontryagin maximum principle for statements with finite and infinite horizons. It is shown that solutions of these two problems differ crucially from each other: in finite horizon problems the optimal investment strategy inevitably has the zero regime at the final stage, whereas the infinite horizon problem always has a strictly positive solution. A remarkable result of the proposed model consists in constructive analytical solutions for optimal investments in production factors, which depend on the price dynamics and other economic parameters such as elasticities of production functions, total factor productivity, and depreciation factors. This feature serves as a background for the productive fusion of optimization models for investments in production factors in the framework of a multilevel structure and provides a solid basis for constructing optimal trajectories of economic development.     

政府支出结构、扭曲性税收及内生贴现因子

在一个无穷期限模型中,假设经济主体具有完全理性,通过将常数贴现因子转换为关于效用水平的内生变量,利用跨期优化方法重新考虑了政府支出结构、扭曲性税收对宏观经济变量的影响.尤其关注这两种变量的长期和短期变化对资本积累路径的影响,理论模型表明,当贴现因子内生化后,政府支出结构和扭曲性税收对宏观经济的影响会更为复杂,尤其体现在生产性支出上.     

DYNAMIC CORRECTIVE TAXES WITH FLOW AND STOCK EXTERNALITIES: A FEEDBACK APPROACH

In confronting a consumer good whose production process is associated with both flow and stock externalities, a corrective tax is introduced to restore efficiency. The objective is to maximize social welfare over time when the stock pollutant obeys an arbitrary dynamic process. The model makes it possible to derive the optimal corrective tax as a closed form feedback control law. This feedback rule can be applied for qualitative purposes such as parameter analysis or studying the time path of the corrective tax. It can also be used for quantitative purposes, for example, evaluating an actual policy or assessment of the optimal tax for a certain case. It is here used to study how the optimal corrective tax, both as a function of time and as a function of the pollution level, depends upon the decay function. It is shown that, depending upon the initial conditions and the structure of the economy and the decay function, most outcomes are possible.     

Competitive insurance pricing with complete information,loss-averse utility and finitely many policies

In a recent paper, Ramsay and Oguledo (2012) show that in a competitive insurance market with complete information about individuals’ accident probabilities and production costs, which are proportional to the amount of insurance purchased and to the premium charged, only individuals whose accident probability is in a medium range are insurable and desire insurance. The purpose of this paper is to complement the analysis of Ramsay and Oguledo by considering production costs which are proportional to the number of policies offered by an insurer. In addition to the result of Ramsay and Oguledo we show that the group of individuals who obtain insurance is partitioned into several subgroups, where each subgroup is offered the same insurance policy. To derive this result we introduce the concept of incentive compatibility which ensures that an individual has no incentive to buy another policy. Assuming that individuals have loss-averse utility, we fully characterize the boundaries of these subgroups as the result of an undercutting process in premiums between the insurers.     

图博弈的过程比例解

本文对具有图结构合作博弈（图博弈）进行了研究，采用比例原则和过程化分配方法，定义了比例分配过程，并对其性质进行了分析。随后，针对比例分配过程的超有效情况，运用等比例妥协的方式给出满足有效性的过程比例解，并研究了稳定性。最后，将比例分配过程与过程比例解应用到破产问题中，得到图博弈过程比例解与破产问题比例规则等价的结论。     

Braids,conformal module and entropy

The conformal module of conjugacy classes of braids appeared in a paper of Lin and Gorin in connection with their interest in the 13th Hilbert Problem. This invariant is the supremum of conformal modules (in the sense of Ahlfors) of certain annuli related to the conjugacy class. This note states that the conformal module is inversely proportional to a popular dynamical braid invariant, the entropy. The entropy appeared in connection with Thurston?s theory of surface homeomorphisms. An application of the concept of conformal module to algebraic geometry is given.     

Simple-motion pursuit-evasion differential games,part 2: Optimal evasion from proportional navigation guidance in the deterministic and stochastic cases

The problem of the optimal evasion from a pursuer employing proportional navigation guidance is considered. Thus, we consider the problem of maximizing the time-to-capture when the problem parameters, namely, the speed ratio and the proportional navigation constant, are such that capturability of the evader is guaranteed.     

A Unified Approach to the Proportional Relation for Discrete-Time Single-Server Queues

It is well known that a simple relation called proportional relation holds for some queueing models, that is, the stationary queue length distribution of one system can be expressed as the product of a constant and the distribution of another system which is different only in the buffer capacity. Recently, the proportional relation has been verified for various discrete-time single-server queues with correlated arrivals, where it has been also shown that the proportional constant can be expressed in terms of the distribution of one system. This implies that the stationary queue length distribution of one system can be completely expressed in terms of the distribution of the other system. In this paper, we consider a generalized model of discrete-time single-server queue, which covers all previous ones, and give a simple and unified proof to the proportional relation as well as the expression of the proportional constant.     

An algorithm to solve the proportional network flow problem

The proportional network flow problem is a generalization of the equal flow problem on a generalized network in which the flow on arcs in given sets must all be proportional. This problem appears in several natural contexts, including processing networks and manufacturing networks. This paper describes a transformation on the underlying network that reduces the problem to the equal flow problem; this transformation is used to show that algorithms that solve the equal flow problem can be directly applied to the proportional network flow problem as well, with no increase in asymptotic running time. Additionally, computational results are presented for the proportional network flow problem demonstrating equivalent performance to the same algorithm for the equal flow problem.     

A queueing analysis of max-min fairness, proportional fairness and balanced fairness

We compare the performance of three usual allocations, namely max-min fairness, proportional fairness and balanced fairness, in a communication network whose resources are shared by a random number of data flows. The model consists of a network of processor-sharing queues. The vector of service rates, which is constrained by some compact, convex capacity set representing the network resources, is a function of the number of customers in each queue. This function determines the way network resources are allocated. We show that this model is representative of a rich class of wired and wireless networks. We give in this general framework the stability condition of max-min fairness, proportional fairness and balanced fairness and compare their performance on a number of toy networks.     

Nonlinear stability of Runge-Kutta methods applied to infinite-delay-differential equations

In functional differential equations (FDEs), there is a class of infinite delay-differential equations (IDDEs) with proportional delays, which aries in many scientific fields such as electric mechanics, quantum mechanics, and optics. Ones have found that there exist very different mathematical challenges between FDEs with proportional delays and those with constant delays. Some research on the numerical solutions and the corresponding analysis for the linear FDEs with proportional delays have been presented by several authors. However, up to now, the research for nonlinear case still remains to be done. For this, in the present paper, we deal with nonlinear stability of the Runge-Kutta (RK) methods for a class of IDDEs with proportional delays. It is shown under the suitable conditions that a (k, l)-algebraically stable RK method for this kind of nonlinear IDDE is globally and asymptotically stable.     

PQ oligopoly,proportional rationing,and randomly ordered consumers

In a PQ oligopoly, firms pick prices and quantities simultaneously, and unlike with the traditional Cournot and Bertrand models, market clearing is not imposed. It is thus necessary to specify the rationing rule. Proportional rationing is one of the popular choices, often justified through a notion of randomly ordered consumers with varied reservation prices. However, such a setting would render firm-specific demand a random variable, a fact overlooked in existing models. In the paper, we (1) formalise the notion of randomly ordered consumers into a new stochastic version of the proportional rationing scheme, (2) derive the probabilistic properties of firm-specific demand under this new scheme, and (3) show that the results of the stochastic and deterministic versions are not entirely consistent.     

Solving the 0–1 proportional knapsack problem by sampling

In this paper, we deal with the proportional knapsack problem that is a variation on the ordinary knapsack problem. In the proportional knapsack problem, we look at filling an urn with objects having two characteristics: color and weight. The colors of the objects in the urn should be proportional to the distribution of the colors in the object universe, and the total weight of the objects in the urn should be as close as possible to the capacity of the urn. The formulation of the problem was motivated by a real-life application from the area of finance, called a dollar roll. We show that the proportional knapsack problem is NP-hard, and then, using sampling, develop a heuristic procedure for solving the problem.Partial support from the Fund for the Promotion of Research and from the Alexander Goldberg Memorial Fund at Technion is gratefully acknowledged.     

Equal or proportional division of a surplus,and other methods

A cooperative venture yields a nonnegative surplus. Agents are differentiated by their opportunity costs only. Two surplus sharing methods (equal sharing, proportional sharing) are characterized with the help of four axioms. Separability and No Advantageous Reallocation deal with coalitional changes in the opportunity costs. Additivity and Path Independence take into account variations in the surplus level.Any triple of these axioms characterizes equalor proportional sharing. Any pair of axioms characterize a distinct, infinite family of methods, compromising between equal and proportional sharing.     

The sudden increase in ionospheric total electron content caused by the very intense solar flare on July 14, 2000

The present paper studies the sudden increase in total electron content (SITEC) on the ionosphere caused by the very intense solar flare on July 14, 2000. According to the well-known Chapman theory of ionization, we derive the relationship between the temporal variation rate, of the total electron content (TEC) and the flare parameters. It is shown that is proportional to the effective flare radiation flux, If, and inversely proportional to the Chapman function, ch(χ), of the zenith angle χ. TEC data observed by the GPS networks located in China, Southeast Asia and Australia during the very intense solar flare on July 14, 2000 are used to statistically investigate the relation between the observed and ch(χ). The analyses show that the two quantities are inversely proportional to each other, as the theory predicted. The present work shows that GPS observation is a powerful tool for studying solar flare effects on the ionosphere, I.e. The sudden ionospheric disturbances (SIDs). Because of its advantages of high precision, large geographical distribution and good temporal resolution, GPS TEC observation may reveal quantitatively the process of ionospheric disturbances caused by solar flares. Therefore, our results are of significance in the space weather research.     

Exponential sums,the geometry of hyperplane sections,and some diophantine problems

We estimate exponential sums with additive character along an affine variety given by a system of homogeneous equations, with a homogeneous function in the exponent. The proof uses the results of Deligne’s Weil Conjectures II and a generalization of Lefschetz hyperplane theorem to singular varieties. We apply our estimate to obtain an upperbound for the number of integer solutions of a system of homogeneous equations in a box. Another application is devoted to uniform distribution of solutions of a system of homogeneous congruences modulo a prime in the following sense: the portion of solutions in a box is proportional to the volume of the box, provided the box is not very small.