| 摘要: | 本計畫將考慮以下成本負擔問題。該成本負擔問題具有下列的特性:模型中的經濟個體對某個公共設施有一特定需求。不同的經濟個體對該公共設施有不同的需求。滿足特定經濟個體的需求必須耗費一定的成本,不同經濟個體有不同的需求成本。經濟個體依照需求成本的大小被排列(從小到大)，滿足某一特定經濟個體的需求意謂著所有需求成本比該經濟個體還小的個體都被滿足並且不須任何額外的成本。該成本負擔問題有幾個實用例子,最有名的例子就是所謂的灌溉渠道成本負擔問題:每一個農莊主人必須負擔維持本身使用的渠道(從灌溉口到該農莊主人的農田的末端)的成本，距離灌溉口越遠的人將會使用到距離灌溉口較近的人所使用到的渠道。我們將從規範的角度來探討“該如何＂向所有使用該渠道的農莊主人索取維護整個渠道的費用？一個成本負擔方法或法則是一個函數，此函數結合每一個這類成本負擔問題一個成本負擔的向量，此向量指出每一個農莊主人該負擔的數額。 “什麼樣＂的成本負擔法則這群相關經濟個體最能接受。本研究將採用公設法來回答這個問題。公設法的本質是藉由形式化一些成本負擔法則的性質來對法則和法則之間進行比較，最終希望能釐清性質與性質之間的邏輯關係和探討能否刻畫某個或某些成本負擔法則基於這些性質。本研究將提出一個新的成本負擔法則的性質並探討該性質與其他性質間的意涵。該性質是一種是獨立性性質，稱之為 independence of predecessors。假設某個農莊主人所使用的渠道遭到破壞導致維護該渠道的成本增加x單位，此非預期的成本增加造成任何會使用到該渠道的農莊主人的維護成本也增加x單位，然而未使用到該渠道的人則不會增加任何維護成本。一個合理的成本負擔法則不應該向這些成本未增加的人索取額外的費用，也就是說，這群人應該負擔與原先相同的數額。本研究的第一年希望能夠釐清在線型的成本負擔問題(例如：灌溉渠道成本負擔問題)那些成本負擔法則滿足這個性質並且刻畫所有滿足該性質的成本負擔法則。本研究的第二年希望能夠把對這個性質的研究拓展到樹狀的網路成本負擔問題，並探討在樹狀的網路成本負擔問題中何種成本負擔法則滿足此性質和刻畫滿足這種性質的所有成本負擔法則。藉此，希望能對一些日常生活中常被運用的成本負擔法則提供一套公設化的理論基礎，同時也希望對解決這類問題的決策者提供一些建議。 ; We consider a class of cost sharing problems with the following features. Agents are ordered in terms of their needs for a public facility, and satisfy- ing an agent with a certain need implies satisfying all agents with smaller needs at no extra cost. How should the cost of maintaining or building the facility be distributed? An example is the so-called \airport problem." Di®erent airlines need airstrips of di®erent lengths. The larger a plane, the longer the airstrip it needs. Accommodating a given plane implies accommodating all smaller planes at no extra cost. To accommodate all planes, the airstrip must be long enough for the largest plane. How should the cost of the airstrip be shared among the airlines? A division rule is a function that associates with each problem of this kind a \contributions vector." The purpose of this project is to propose an invariance property, \in- dependence of predecessors" of division rules, and study its implications for the model under consideration. The property says that if the cost parameter of an airline, say ci, increases by a positive amount ®, the cost parameters of the airlines whose cost parameters are smaller than ci re- main unchanged, and the cost parameters of all other airlines increase by ®, then those airlines whose cost parameters are smaller than ci should contribute the same amounts as they did initially. Besides independence of predecessors, we consider a variable-population property, downstream-substraction consistency. It is an application for air- port problems of a general principle of \consistency." Suppose that there are n airlines indexed by 1; : : : ; n and airline i's cost parameter ci rep- resents the cost of building the part of the airstrip airline i uses, which we call \segment i." For simplicity, assume that c1 < ¢ ¢ ¢ < cn. Consider a contribution vector x chosen by a rule for the problem just de¯ned. Imagine that airline i pays its contribution xi and \leaves," and reassess the situation from the viewpoint of the remaining airlines. It is of course natural to think of xi as a contribution to segment i. So, for airline i's successors, which also use segment i (the airlines with higher indexes than i), it is clear that their cost parameters should be revised down by xi. For airline i's predecessors, which only use part of segment i, it is less clear how the revision should be carried out: To which part of segment i should xi be imputed? Several proposals have been made. One of them is to think of xi as a contribution to the part of segment i that airline i uses but its predecessors do not. Then, if xi · ci ¡ ci¡1, none of airline i's predecessors bene¯ts from airline i's contribution. Thus, their cost pa- rameters remain unchanged; otherwise, some of airline i's contribution, namely xi ¡ (ci ¡ ci¡1), would be regarded as a contribution to the part of the airstrip that airlines i and i ¡ 1 use but the other predecessors do not. So, ci¡1 will be revised down by that quantity; if xi · ci ¡ci¡2, none of airline i ¡ 1's predecessors bene¯ts from airline i's contribution. Thus, their cost parameters remain unchanged; otherwise, some of airline i's contribution, namely xi ¡(ci ¡ ci¡2), would be regarded as a contribution to the part of the airstrip that airlines i, i¡1, and i¡2 use but the other predecessors do not. So, ci¡2 will be revised down by that quantity; and so on. In general, the cost parameter of each of airline i's predecessors, say airline k, is revised down by the maximum of zero and xi ¡ (ci ¡ ck). Downstream-subtraction consistency (Potters and SudhÄolter, 1999) of the rule requires that for the reduced problem just de¯ned, each of the re- maining airlines should pay the same amount as it did initially. We ¯rst work with the simple and basic model, examine the implica- tions of the two properties and hope to give as explicit as possible a de-scription of the family of division rules satisfying them. Second, we plan to extend the model to the situations in which the structures imposed on the set of agents are more rich. The extended model is the so-called network problems. We then undertake the systematic study of the implications of the two properties (of course, we have to extend the properties in the extended model) and if possible, give a complete description of the family of division rules satisfying them. ; 研究期間 9708 ~ 9807 |
