自1978年美國國內航空業務放鬆管制以來，航空公司開始將票價和服務頻率作為最重要的兩個競爭手段，因此在競爭性航線中提供更多的航班以爭奪頻率，是有效增加其收益和利潤的方法。

此篇論文主要分為兩部分。首先，我們在現有的頻率競爭模型中，改善一個航空公司的賽局模型，將其線性化。第二部分則是實現演算法以獲得線性整數的納什均衡解。隨後，我們欲利用美國三級機場的經驗數據，驗證本篇的模型和方法，並提出一個可以有效提高航空公司利潤的適當策略。然而，我們的演算法在固定的有限多邊形維度下，也可用於計算線性賽局的整數解。

最後，由於我們研究中每個玩家可以處理的策略數量是有限的，因此在該領域的未來研究中，我們仍然需要改進模型和演算法使得我們的賽局策略能更加全面。

Since passenger deregulation of the U.S. domestic airline industry in 1978, airlines have been using fares and service frequency as the two most important instruments of competition. Competitive routes offer more flights is the approach to compete for frequencies to increase their profits.

Our dissertation is mainly divided into two parts. First, we improved and linearized an equilibrium programming model for airlines based on an existing frequency competition model. The second part moves on to implements an algorithm to obtain the linear integer Nash equilibrium sets. Afterwards, we want to validate the proposed model and method with empirical data from coordinated airports in U.S., then propose a proper strategy which can improve an airline’s profit. Our algorithm can also be applied to deal with the lattice points on linear integer game when the dimension of the polytope is fixed.

Finally, due to the limited number of strategies that can be handled in our study, in future studies in this field, we still need to improve the accuracy of model and the efficiency of algorithm to make the game strategies more comprehensive.

摘要
Abstract
Contents
List of Tables----------------------------------ii
List of Figures--------------------------------iii
Chapter 1 Introduction---------------------------1
1.1 Motivation-------------------------------1
1.2 Research Purpose and Contribution--------2
1.3 Thesis Organization----------------------3
Chapter 2 Literature Review----------------------4
2.1 Airline Frequency Competition------------4
2.2 Linear Integer Nash Equilibrium----------5
2.3 Short Rational Generating Function-------5
Chapter 3 Problem Formulation--------------------8
3.1 The Model----------------------------------8
3.2 Algorithm---------------------------------11
Chapter 4 Numerical Experiment------------------15
4.1 Parameter Estimation--------------------15
4.2 Empirical Analysis----------------------16
Chapter 5 Conclusions and Future Direction------21
References--------------------------------------23

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