On algorithmic solutions to simple allocation problems

We interpret solution rules to a class of simple allocation problems as data on the choices of a policy-maker. We study the properties of rational rules. We show that every rational rule falls into a class of algorithmic rules that we describe. The Equal Gains rule is a member of this class and it uniquely satisfies rationality, continuity, and equal treatment of equals. Its dual, the Equal Losses rule, uniquely satisfies continuity, equal treatment of equals, and two properties that constitute the dual of rationality: translation down and translation up

Towards a successful international greenhouse gas emissions trading

The inclusion of emissions trading in the Kyoto Protocol reflects an important decision to address climate change issues through flexible market mechanisms. In this paper, we have addressed a number of policy issues that must be considered in designing and implementing an international greenhouse gas (GHG) emissions trading scheme. These include how much of a Party’s assigned amounts of GHG emissions can be traded internationally; emissions trading models; competitiveness concern in the allocation of emissions permits; banking and borrowing; accountability; emissions trading system enlargement; and bubbles. Although our focus has been exclusively on emissions trading, we have discussed its relationship with the clean development mechanism, joint implementation and bubbles wherever necessary. By providing some new insights, the paper aims to contribute to the design and operationlization of an international emissions trading scheme.Bubbles; carbon tax; clean development mechanism; emissions trading; greenhouse gases; international competitiveness; joint implementation; Kyoto Protocol

Sequential Sharing Rules for River Sharing Problems

We analyse the redistribution of a resource among agents who have claims to the resource and who are ordered linearly. A well known example of this particular situation is the river sharing problem. We exploit the linear order of agents to transform the river sharing problem to a sequence of two-agent river sharing problems. These reduced problems are mathematically equivalent to bankruptcy problems and can therefore be solved using any bankruptcy rule. Our proposed class of solutions, that we call sequential sharing rules, solves the river sharing problem. Our approach extends the bankruptcy literature to settings with a sequential structure of both the agents and the resource to be shared. In the paper, we first characterise a class of sequential sharing rules. Subsequently, we apply sequential sharing rules based on four classical bankruptcy rules, assess their properties, and compare them to four alternative solutions to the river sharing problem.River Sharing Problem, Sequential Sharing Rule, Bankruptcy Problem, Water Allocation

Using emissions trading to regulate global greenhouse gas emissions

The inclusion of emissions trading in the Kyoto Protocol reflects an important decision to address climate change issues through flexible market mechanisms. This Article addresses a number of policy issues that must be considered in designing and implementing an international greenhouse gases (GHG) emissions trading scheme. These include emissions trading models, the initial allocation of emissions permits and its competitiveness concerns, banking and borrowing, the liability rules for non-compliance, and bubbles. The following conclusions emerge from the discussion. First, although emissions trading could take place either on an inter-governmental basis or on an inter-source basis, sub-national legal entities are the best entities to trade emissions permits. Allocating permits to individual emissions sources will facilitate private participation in emissions trading. Moreover, it has been argued that individual governments should be left free to devise their own ways of allocating assigned amounts. Second, it has been pointed out that although national emissions trading systems could be modelled as either upstream or downstream or hybrid systems, the distinguishing features of broad coverage and administrative simplicity would make an upstream system the more attractive approach. Moreover, national emissions trading systems should incorporate the maximum degree of flexibility in banking. Third, the liability rules are essential to the success of an international GHG emissions trading scheme. In general, a seller beware liability works well in a strong enforcement environment. In the Kyoto Protocol, however, it may not always work. By contrast, a buyer beware liability could be an effective deterrent to non-compliance, but the costs of imposing it are expected to be very high. To strike a middle ground, it has been suggested a combination of preventive measures with strong but feasible end-of-period punishments to ensure compliance with the Kyoto emissions commitments. Such measures aim to maximize efficiency gains from emissions trading and at the same time, to minimize over-selling risks.Annual retirement; auction; bubbles; buyer beware liability; carbon taxes; clean development mechanism; compliance reserve; compulsory insurance; emissions trading; grandfathering; greenhouse gases; international competitiveness; joint implementation; Kyoto Protocol; seller beware liability; World Trade Organization

A Revealed preference analysis of solutions to simple allocation problems

We interpret solution rules on a class of simple allocation problems as data on the choices of a policy-maker. We analyze conditions under which the policy maker’s choices are (i) rational (ii) transitive-rational, and (iii)representable; that is, they coincide with maximization of a (i) binary relation, (ii) transitive binary relation, and (iii) numerical function on the allocation space. Our main results are as follows: (i) a well known property, contraction independence (a.k.a. IIA) is equivalent to rationality; (ii) every contraction independent and other-c monotonic rule is transitive-rational;and (iii) every contraction independent and other-c monotonic rule, if additionally continuous, can be represented by a numerical function

Contributions to multi-issue bankruptcy problems with crossed claims

Un problema de bancarrota describe una situación en la que se debe repartir un patrimonio perfectamente divisible (que se suele denominar estado) entre un grupo de agentes que tienen demandas sobre él, siendo el patrimonio insuficiente para satisfacer todas las demandas. Una regla de bancarrota es un mecanismo que asigna a cada problema un reparto que cumple dos características básicas: primero, la racionalidad individual, es decir, los agentes no reciben más de lo que demandan, pero tampoco reciben menos de nada; y la segunda característica es que el mecanismo es eficiente, es decir, se reparte todo el patrimonio entre los demandantes. En esta tesis doctoral, se introduce un modelo novedoso de problemas de bancarrota con múltiples estados inspirado en un problema real de reducción de emisiones de diferentes familias de contaminantes, donde los contaminantes pueden pertenecer a más de una familia. Este modelo estudia situaciones con múltiples estados dónde cada agente reclama lo mismo a los diferentes estados en los que participa, es decir, cada agente tiene una única demanda, no una demanda (en general diferente) por cada uno de los estados. Este modelo es diferente de los problemas de bancarrota con múltiples estados que hay en la literatura. Los problemas de bancarrota con múltiples estados describen situaciones en las que hay un patrimonio perfectamente divisible que hay que distribuir entre varios estados, y hay un número de reclamantes que tienen demandas sobre cada uno de esos estados. Por lo tanto, hay un patrimonio a distribuir entre varios problemas y reclamantes con vectores de reclamos con tantas coordenadas como estados hay, de modo que la cantidad total de reclamos está por encima del patrimonio disponible. La pregunta es ¿cómo se debe repartir el patrimonio entre los múltiples estados y entre los reclamantes? Este problema ha sido resuelto por medio de reglas de asignación y existen varios enfoques en la literatura. Tres de ellos son mediante la solución de un problema de optimización, analizar el problema como un único problema de bancarrota y analizar el problema en dos etapas, primero distribuir el patrimonio entre los estados y después distribuir cada uno de los estados entre los reclamantes. En el caso de la investigación desarrollada en esta tesis, se tienen varios estados perfectamente divisibles, y los reclamantes tienen exactamente un reclamo que se usa en todos los estados simultáneamente a los cuales reclaman. A estos problemas se les ha denominado problemas de bancarrota con múltiples estados con demandas (o reclamos) cruzadas. Ahora, nuevamente, la pregunta es ¿cómo se debe asignar cada uno de los estados? Hasta donde sabemos, este problema es nuevo en la literatura, por lo que esta tesis doctoral viene a cubrir un vacío en la literatura de problemas de bancarrota. Además, para el nuevo modelo de problemas de bancarrota, se han introducido generalizaciones de la regla de recompensas iguales restringidas (constrained equal awards rule, CEA), de la regla proporcional, y de las reglas secuenciales con prioridades y su promedio, la regla de llegadas aleatorias (random arrival rule, RA). Para cada una de estas generalizaciones se ha realizado un análisis axiomático, obteniendo caracterizaciones para la generalización de la regla CEA y la generalización de la regla proporcional, quedando pendiente para futuras investigaciones la obtención de una caracterización para la generalización de la regla de llegadas aleatorias. La regla CEA es una de las principales reglas para resolver problemas de bancarrota. Esta regla simplemente divide lo más equitativamente posible el patrimonio entre los demandantes. La pregunta en el contexto de los problemas introducidos en esta tesis es qué sígnica lo más equitativamente posible. En el contexto de los problemas de bancarrota clásicos, lo más equitativamente posible significa que no hay demandante que puede obtener más que aquellos reclamos menores, excepto que estos últimos ya hayan recibido su reclamo completo. Este principio de lo más equitativamente posible se ha obtenido mediante la optimización sucesiva de varios problemas de optimización, siguiendo un esquema lexicográfico de programación lineal en el que al final de este se obtiene un reparto que consideramos que es la generalización de la regla CEA. Alternativamente, se proporciona un algoritmo para obtener esta misma solución mediante la aplicación de la regla CEA a los estados, actualizando los problemas en cada iteración. Así mismo, se realiza un estudio de sus principales propiedades y se caracteriza utilizando diferentes propiedades que son adaptaciones de propiedades básicas para problemas de bancarrota. En particular, se caracteriza la generalización de la regla CEA utilizando las propiedades de Pareto eficiencia, división igualitaria condicionada, consistencia, compensación completa condicionada y monotonía en los reclamos. Del mismo modo, en la investigación desarrollada en esta tesis doctoral se introduce una generalización de la regla proporcional, que llamamos regla proporcional restringida y que es definida mediante un proceso iterativo en el que se aplica la regla proporcional a cada uno de los estados, actualizando los problemas en cada iteración. Este proceso extiende de forma natural la regla proporcional al contexto de los problemas de bancarrota con múltiples estados con reclamos cruzados. Asimismo, se lleva a cabo un análisis axiomático de esta regla obteniendo una caracterización utilizando las propiedades de Pareto eficiencia, igual trato de los iguales, adjudicación mínima garantizada, consistencia y no manipulabilidad por división. Además, se extienden reglas secuenciales con prioridades y su promedio, la regla de llegadas aleatorias a los problemas de bancarrota de múltiples estados con reclamos cruzados. Como en los dos casos anteriores se lleva a cabo un análisis axiomático, pero no se obtiene una caracterización, por lo que cabe pensar en que sería necesario el uso de propiedades más técnicas como sucede en los problemas de bancarrota con múltiples estados. Por tanto, este es un punto que queda pendiente para futuras investigaciones. Finalmente, las generalizaciones de las reglas se aplican a la situación en la que cierta autoridad responsable de la calidad del agua en su región está interesada en controlar la contaminación del agua. En particular, están interesados en limitar la concentración de las tres categorías de contaminantes del agua. Por un lado, para cada una de estas categorías de contaminantes se han determinados niveles de concentración con el fin de mantener una calidad de agua razonable. Y, por otro lado, se controlan las principales sustancias mencionadas anteriormente para las que también existen límites máximos de concentración. Así, el problema a resolver por parte de la autoridad es como asignar nuevos límites a las sustancias, teniendo en cuenta los límites fijados para cada categoría de contaminantes. Por lo tanto, la autoridad enfrenta un problema de asignación con ciertas características especiales

Multi-issue bankruptcy problems with crossed claims

In this paper, we introduce a novel model of multi-issue bankruptcy problem inspired from a real problem of abatement of emissions of different pollutants in which pollutants can have more than one effect on atmosphere. In our model, therefore, several perfectly divisible goods (estates) have to be allocated among certain set of agents (claimants) that have exactly one claim which is used in all estates simultaneously. In other words, unlike of the multi-issue bankruptcy problems already existent in the literature, this model study situations with multi- dimensional states, one for each issue and where each agent claims the same to the different issues in which participates. In this context, we present an allocation rule that generalizes the well-known constrained equal awards rule from a procedure derived from analyzing this rule for classical bankruptcy problems as the solution to a sucession of linear programming problems. Next, we carry out an study of its main properties, and we characterize it using the well-known property of consistency

Banking Permits: Economic Efficiency and Distributional Effects

Most analyses of the Kyoto flexibility mechanisms focus on the cost effectiveness of “where” flexibility (e.g. by showing that mitigation costs are lower in a global permit market than in regional markets or in permit markets confined to Annex 1 countries). Less attention has been devoted to “when” flexibility, i.e. to the benefits of allowing emission permit traders to bank their permits for future use. In the model presented in this paper, banking of carbon allowances in a global permit market is fully endogenised, i.e. agents may decide to bank permits by taking into account their present and future needs and the present and future decisions of all the other agents. It is therefore possible to identify under what conditions traders find it optimal to bank permits, when banking is socially optimal, and what are the implications for present and future permit prices. We can also explain why the equilibrium rate of growth of permit prices is likely to be larger than the equilibrium interest rate. Most importantly, this paper analyses the efficiency and distributional consequences of allowing markets to optimally allocate emission permits across regions and over time. The welfare and distributional effects of an optimal intertemporal emission trading scheme are assessed for different initial allocation rules. Finally, the impact of banking on carbon emissions, technological progress, and optimal investment decisions is quantified and the incentives that banking provides to accelerate technological innovation and diffusion are also discussed. Among the many results, we show that not only does banking reduce abatement costs, but it also increases the amount of GHG emissions abated in the short-term. It should therefore belong to all emission trading schemes under construction.emission trading, banking

Greenhouse gases and Nutrients: The Interactions Between Concurrent New Zealand Trading Systems

Emissions trading and nutrient trading interact in critical ways. The agricultural sector is a major emitter of both nutrients and greenhouse gases in New Zealand. Thus the simultaneous implementation of such systems will have a large impact on the farmers in affected catchments. Many of the mitigation options that are available to farmers, for example reducing animal numbers, will reduce both nutrient loss and greenhouse gas emissions. Thus the combined cost of control could be much less than the sum of the costs of the separate systems. The allocation of units under each system will also affect the same people. Monitoring systems for each pollutant could have common elements but could also impose a double burden. The interactions between the two systems will complicate the decision making process for farmers and need to be considered when the policies are designed so they are as complementary as possible.Agribusiness, Agricultural and Food Policy, Environmental Economics and Policy, Farm Management, Resource /Energy Economics and Policy,

An Experimental Analysis of Compliance in Dynamic Emissions Markets

Two important design elements for emission trading programs are whether and to what extent firms are able to bank emissions permits, and how these programs are to be enforced. In this paper we present results from laboratory emissions markets designed to investigate enforcement and compliance when these markets allow permit banking. Banking is motivated by a decrease in the aggregate permit supply in the middle of multi-period trading sessions. Consistent with theoretical insights, our experiments suggest that high permit violation penalties have little deterrence value in dynamic emissions markets, and that the main challenge of enforcing these programs is to motivate truthful self-reports of emissions.compliance, enforcement, emissions trading, laboratory experiments, permit markets, permit banking