在現代航空業中，細緻地設定機場之間的航班頻率是至關重要的。航班頻率直接影響市場份額和成本，並在各航空公司競爭激烈的環境中扮演關鍵的角色。隨著航空市場的蓬勃發展，航空公司之間的商業關係已經從簡單的競爭演變為聯盟與合作。在眾多合作策略中，代碼共享協議顯得尤為重要。

代碼共享作為一種合作方式，允許航空公司透過簽訂商業協議，在沒有親自運營的航班上銷售座位。這一做法通常在樞紐機場被廣泛應用，以提升長途航班或高頻短途航班之間的連接。統計數據顯示，超過一半的美國航空公司採用了代碼共享策略，尤其在鄰近熱門樞紐機場的航線上更為普遍。

雖然代碼共享在航空業被廣泛採用，然而值得注意的是，目前尚無全面的定量模型能同時處理代碼共享策略和航班頻率競爭的問題。有鑑於其重要性，本研究試圖建立一個頻率競爭模型，將代碼共享策略納入博弈論框架，並使用二階錐來描述其中的一些約束條件。為了找到該問題的納許均衡，我們運用二階錐體程序設計的最優性條件特性，建立了一個包含原始、對偶和互補鬆弛約束的KKT模型。所提出的模型採用定量計算，以確定每個航段的最佳頻率，並提供有關代碼共享、合適的合作夥伴以及航空公司之間利潤分配等相關決策的戰略啟示。

In the modern aviation industry, strategically setting flight frequencies between airports is a critical aspect, influencing market share and costs, and playing a pivotal role in the competitive dynamics among airlines. With the thriving aviation market, the nature of commercial relationships between airlines has changed from mere competition to the formation of alliances and collaborations. Among various cooperative strategies, the code-sharing agreement emerges as a particularly essential approach.

Code-sharing serves as a mechanism that allows airlines to sell seats on flights they do not operationally control, fostering participation through commercial agreements. This practice is frequently utilized in hub airports to improve connectivity between long-haul or high-frequency short-haul flights. Statistics indicate that more than half of U.S. airlines have embraced code-sharing strategies, with a notable prevalence on routes neighboring popular hub airports.

Despite the prevalence of codeshare in the airline industry, it is worth noting that there is no comprehensive quantitative model that addresses both codeshare strategy and flight frequency competition. Given its importance, this study attempts to develop a frequency competition model that incorporates code-sharing strategies in a game-theoretic context and uses second-order cones to characterize some of these constraints. To find the Nash equilibrium for this problem, we apply the nature of the optimality conditions of second order cone programming to build a KKT model containing primal, dual, and complementary slackness constraints. The proposed model employs quantitative calculations to determine the optimal frequency for each segment of the flight and provides strategic information on decisions related to code sharing, suitable partners, and profit sharing among airlines.

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