一致性成本分攤法則之公設法刻劃與策略性詮釋

Abstract

本篇論文主要探討在機場跑道成本分攤問題的架構下，不同的退化局結構設定是否會刻劃出不同的成本分攤法則。我們經由提供兩個一致性機場跑道成本分攤法則(限制利益均等法則與核仁)的公設法刻劃與策略性詮釋來回答上述問題。在機場跑道成本分攤問題的文獻中，有許多形式的退化局的設定，其中以左端點成本扣除法與右端點成本扣除法的設定最為被廣泛應用與討論。我們首先定義在這兩種不同的退化局設定法下之兩組雙邊一致性與逆一致性公設，分別稱之為左端點(右端點)成本扣除之雙邊一致性與左端點(右端點)成本扣除之逆一致性公設。我們利用左端點成本扣除之雙邊一致性與左端點成本扣除之逆一致性性質為基礎進行公設刻劃限制利益均等法則。此外我們設計一個具有此兩種性質之兩階段非合作延展式賽局，並利用此賽局來探討限制利益均等法則的策略性詮釋。我們證明此賽局存在唯一的一個子賽局完美均衡結果，且此均衡結果與限制利益均等法則所導出的分配結果一致。接下來我們使用右端點成本扣除之雙邊一致性與右端點成本扣除之逆一致性性質進行對核仁的公設刻劃。另一方面，我們設計一個具有此兩種性質之三階段非合作延展式賽局來提供核仁的策略性詮釋。我們證明此賽局存在唯一的一個子賽局完美均衡結果即為 核仁之成本分攤之分配結果。從本篇論文所得到之結果，可知在機場跑道成本分攤問題中不同的退化局設定無論是從公設法或是非合作賽局法的觀點下皆能夠刻劃出完全不同的成本分攤法則。此外本篇論文也描述限制利益均等法則與核仁此兩個成本分攤法則之根本差異。

This dissertation consists of two parts that develop axiomatic and strategic justifications for two consistent cost allocation rules, the constrained equal benefits (CEB) rule and the nucleolus, in the airport problem, which is concerned with sharing the cost of an airstrip among agents who need airstrips of different lengths. We justify these two cost allocation rules based on the two major kinds of consistency, Left-endpoint Subtraction (LS) bilateral consistency and Right-endpoint Subtraction (RS) bilateral consistency and converse consistency properties, LS converse consistency and RS converse consistency in the airport problem, respectively. The first part of this dissertation investigates the implications of LS bilateral consistency and LS converse consistency in the airport problem. First, on the basis of the two properties, we characterize the constrained equal benefits rule, which equalizes agents' benefits subject to no one receiving a subsidy. Second, we introduce a 2-stage extensive form game that exploits LS bilateral consistency and LS converse consistency. We show that there is a unique subgame perfect equilibrium outcome of the game and moreover, it is the allocation chosen by the constrained equal benefits rule. In the second part of the dissetation, we address whether different formulations of consistency and converse consistency axioms provide strategic justifications for different rules. First, we propose RS bilateral consistency and RS converse consistency in the airport problem, and find that the nucleolus, which lexicographically maximizes the welfare of the worst-off coalitions, satisfies the two properties. We then introduce a 3-stage extensive form game to implement the nucleolus that exploits the properties. As we show, there is a unique subgame perfect equilibrium outcome of the game and moreover, it is the allocation chosen by the nucleolus. This result together with which given in the first part of this dissertation provides a positive answer to the question.