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1.0 Introduction简介
20世纪世界运输史上发生了两个重要的变化，即飞机和高速铁路的运营（Fischer and Kamerschen，2003）。与邻国日本和西方发达国家相比，中国的高速铁路起步较晚，但发展速度很快（Liu and Kuang，2010）。据2014年底统计，全国铁路总里程已超过11万公里，高速铁路总里程已超过1.5万公里（张、杨、卫，2009）。高速铁路在短途客运市场上具有航空运输所不具备的独特优势。许多短途航线，由于高铁的开通，航空的时间优势已经不复存在，客运量已经下降甚至停飞（wei，2007）。中国高速铁路的快速发展将使运输市场的竞争更加激烈。在中短途市场上，高速铁路以其与航空运输一样快的速度、不断改进的服务和固有的准时性，对民航业产生了巨大的影响。面对如此强大的竞争对手，中国各大航空公司需要依靠自身独特的飞行优势、成熟的运营机制、积极的市场开拓、稳定的业务来源、以及应对挑战的定价策略。本文以中国南方航空公司为例，探讨如何运用博弈论制定价格策略，使其价格能够吸引消费者，保证其合理收益。本文首先回顾了博弈论的相关文献，然后介绍了如何计算高铁与飞机的均衡价格，然后分析了南航应如何根据计算结果制定价格策略。
Two important changes have taken place in the history of world transportation in the 20th century, namely the operation of aircraft and high-speed railways (Fischer and Kamerschen, 2003). Compared with neighboring Japan and developed countries in the West, China's high-speed railways started late, but its development speed is rapid (Liu and Kuang, 2010). According to statistics at the end of 2014, the total mileage of the national railway has exceeded 110,000 kilometers, and the total mileage of high-speed railway has exceeded 15,000 kilometers (Zhang, Yang and Wei, 2009). High-speed railways have a unique advantage that air transport does not have in the short-haul passenger transport market. Many short-haul air routes, because of the opening of high-speed rail, the time advantage of aviation no longer exists, the passenger load has dropped or even grounded (Wei, 2007). The rapid development of China's high-speed railways will make the competition in the transportation market more intense. In the short- and medium-haul market, high-speed railways have a great impact on civil aviation by virtue of the speed which is as fast as that of air transportation, continuous improvement of services and inherent punctuality. Faced with such a strong competitor, China's major airlines need to rely on their unique flight advantages, mature operating mechanisms, active market development, stable business sources, and pricing strategies to meet the challenges. The aim of this essay is to take China Southern Airlines as an example to explore how to use game theory to formulate a price strategy so that its price can attract consumers and guarantee its reasonable income. This paper first reviews the relevant literature of game theory, then introduces how to calculate the equilibrium price of high-speed rail and aircraft, and then analyzes how the Southern Airlines should formulate a price strategy based on the calculation results.
2.0 Main body主体
2.1 China Southern Airlines南航
南航总部设在广州，成立于1995年3月25日（中国南方航空，2018年）。是中国运输机数量最多、航线网络最发达、客运量最大的航空公司。数据显示，近10年来，南航机票价格涨幅不到1%（中国南航，2018年）。在中国年平均通胀率超过8%的背景下，这表明中国南方航空公司始终利用低成本竞争参与市场竞争。其中一个主要原因是中国高铁的崛起。一方面，高铁继续采用低价手段抢占南航市场份额，南航不得不频频打折。随着人力和运营成本的不断提高，南航的利润空间越来越小。对于南航来说，了解价格战的根本原因，合理定价，摆脱恶性价格竞争，对于南航的健康发展具有重要意义。
China Southern Airlines was headquartered in Guangzhou and established on March 25, 1995 (China Southern, 2018). It is the airline with the largest number of transport aircraft, the most developed route network and the largest passenger traffic in China. The data shows that the price of air tickets of China Southern Airlines has risen by less than 1% in the past 10 years (China Southern, 2018). In the context of China's annual average inflation rate of more than 8%, it shows that China Southern Airlines always uses low-cost competition to participate in market competition. One of the main reasons for that is the rise of China's high-speed rail. On the one hand, high-speed rail continues to use low-cost methods to seize the market share of China Southern Airlines, and Southern Airlines has to make frequent discounts. With the continuous improvement of manpower and operating costs, the profit margin of China Southern Airlines is getting smaller and smaller. For China Southern Airlines, understanding the essential reasons for price wars, determining a properly price, and getting rid of vicious price competitions are of great significance to the healthy development of China Southern Airlines.
2.2 Game theory
In a game, based on whether the participants can negotiate freely before taking any action, and whether the mutually beneficial action plan or strategy can reach a binding agreement, a game can be divided into cooperative game and non-cooperative game (Nash, 1951). A reasonable and predictable feature of a cooperative game is that it is Pareto optimal: if a different strategy can be used to simultaneously improve the situation of two participants, they will definitely agree to do that (Sehipper, Nijkamp and Rietveld, 2007). However, in reality, competitors in many cases find it difficult to reach a binding agreement, so the solution in the competition in this case cannot reach the Pareto optimality, but only the Pareto suboptimal (Hsu, Lee and Liao, 2001). One of the most typical examples is the prisoner's dilemma often studied. A study of the prisoner's dilemma found that oligopolists often struggled with a prisoner's dilemma when deciding their pricing strategy (Netessine and Shumsky, 2005). They must decide whether to take aggressive pricing to gain a larger market share at the expense of competitors' losses, or to adopt a more moderate pricing strategy to coexist with competitors in the current state of their respective market share and obtain higher profits than when competition is fierce (Anjos, Cheng and Currie, 2004). This is the inevitable result of a non-cooperative game. In a non-cooperative game, to accurately predict the behavior of rational participants in a game, it needs to introduce a concept of “Nash Equilibrium”, which refers to that in non-cooperative game strategies, in the case where other people do not change their strategies, the strategy of all players is the best for themselves. At the Nash (1951) equilibrium point, every player in the game has no motivation to change their strategy alone. Cooperative game refers to a binding agreement between players, such as price alliances between oligopolistic companies, etc. (Nash, 1951).
2.3 The price game between high-speed rail and aviation industry in China
Aviation industry
Unchanged fare fare reduction
High-speed rail Unchanged price 5 10 -10 15
Price reduction 15 -5 -5 -5
Table 1 Simulation of price game of China Southern Airlines with China's high-speed rail Shao (2015)
The following is a game that simulates the price strategy of aviation and high-speed rail according to game theory.
If high-speed rail reduces price and aviation industry keeps the price unchanged, then high-speed rail will profit 15, aviation industry will lose 5, the overall profit will be 10; if both high-speed rail and aviation industry keep the price unchanged, then high-speed rail will profit 5 and aviation industry will profit 10, the overall profit will be 15; if high-speed rail keeps the price unchanged, and aviation industry reduces price, then high-speed rail will lose 10 and aviation industry will profit 15, the overall profit will be 5; if both high-speed rail and aviation industry reduce price, then high-speed rail will lose 5 and aviation industry will lose 5 neither, the overall loss will be 10.
For the high-speed rail, the price cut is obviously better than the maintenance. The expected return of the high-speed rail price reduction is 10 (15-5), and the retained income is -5 (5-10). The high-speed rail is for its own maximizing returns will inevitably reduce prices. From the perspective of China Southern Airlines, price cut is also better than maintenance, because the profit of its price cuts are 10 (15-5), the maintenance income is 5 (10-5), and it will most probably choose to cut prices. Or it can be said that this price war will definitely be provoked by high-speed rail, because the price cut will definitely bring higher profits and encroach on the aviation market share, and aviation has to choose to cut prices in order to meet the challenges of high-speed rail. Therefore, both the high-speed rail and the aviation industry have chosen to reduce prices as a strategy. From the perspective of revenue, they lose 5 and the overall loss is 10. The overall benefit at this time is the worst. This is the Nash equilibrium situation pointed out above. When each individual seeks to maximize the benefits, the overall interests are not optimal or even the worst, that is, the non-cooperative game can only reach the Pareto suboptimal.#p#分页标题#e#
In such a game, the two sides cut prices for the maximization of their own interests, but the result is not worth the loss. Therefore, this maximizing behavior is a damage of other sides’ profits at the expense of damaging its own interests. The result at this time is not only the dissatisfaction of aviation and high-speed rail, but also the more importantly, the government is even more dissatisfied, because all the assets of aviation and high-speed rail are state-owned assets, and the result of the game between the two is actually leading to the loss of state-owned assets.
Since the rapid development of China's high-speed rail, in order to attract more consumers as soon as possible, the high-speed rail continues to improve service quality, and the high-speed rail fare continues to decrease, and the management level of high-speed rail is also improving (Courty, 2003). The income of high-speed rail has brought huge impact on the aviation industry. In order to compete for the market, high-speed rail and aviation have implemented price cuts in disguise, and in some local areas, there have even experienced vicious price competition events. From the overall perspective of the transportation industry, the government has introduced a series of measures to control the price war between the two sides. But can the high-speed rail and aviation industry really avoid cutting prices? According to the theory of game theory, this is impossible, because the current high-speed rail and civil aviation fares are higher than their respective unit costs, and now China’s high-speed rail and airline fares are far from falling to the marginal cost of the two, the high-speed rail and airlines will continue to reduce prices in the foreseeable future, the two sides will use discounts, concessions, and many means to reduce prices in disguise. These disguised means are to make the price reduction behavior more concealed, when their competitor keeps its prices unchanged, they get the most benefit, but since the two operators are playing the same strategy, both of them try to get more benefits by reducing the price in disguise, which makes the newly established balance broken and they continue to suffer losses. We know that only when the price of high-speed rail and airlines falls to the same level as the marginal cost, the market will reach a stable equilibrium. At this time, no additional profit is available to both parties, the market is close to a perfectly competitive market, and consumers are the biggest beneficiary. This is not a good thing for the long-term interests and sustainable development of high-speed rail and airlines. As the result of the price war, it has made the aviation industry and high-speed rails miserable, the next consideration for the two industries must be to find a competitive strategy to get rid of such prisoners' dilemmas.
2.4 Equilibrium price
In the high-speed rail and civil aviation market of the Wuhan-Guangzhou line, in the face of impact of fast and relatively cheap high-speed railway, civil aviation companies have to compress capacity to ensure profits. At present, the price of the first-class seat of high-speed rail between Wuhan and Guangzhou is 738.5 yuan (RMB, similarly hereinafter), the price of second-class seat is 463.5 yuan, the average fare is 518.5 yuan, and the price of civil aviation ticket of the same distance is about 675 yuan, about 50% of the full price, coupled with various taxes and fees of 80 yuan, the total cost is about 755 yuan.
Under the premise that in the future, fare fluctuations may be carries out when market operation and income management of high-speed railway is implemented, airlines will encounter greater market pressure, in order to ensure greater market share and more revenue. With the LINGO software, Shao (2015) used fare, driving speed and punctuality rate as parameters to construct a model of game between high-speed rail and air fares, showing that the optimal fare for high-speed railway is designed to be an average of 482 yuan (685.5 yuan for first-class seats and 431 yuan for second-class seats). The best fare for civil aviation is about 610 yuan. If other external factors remain constant, the high-speed rail and civil aviation have no incentive to change their fares under this balanced fare combination.
Actual fare Balanced fare
High-speed rail 518.5 482
Aviation 675 610
Difference 156.5 128
Table 2 Actual fare & Balanced fare (Shao, 2015)
At present, the average fare of the high-speed rail in China is 518.5 yuan, and the equilibrium price is 482 yuan. The full price of civil aviation tickets of the Wuhan-Guangzhou route is 1,350 yuan, and the current average discount is 5%: 675 yuan. The equilibrium fare is 610 yuan, which is about 4.5% of the full price, which slightly lower than the actual fare.
At present, the average fare difference between the high-speed rail and the civil aviation actually is 156.5 yuan (RMB). The difference between the two in the balanced fare combination is 128 yuan. It shows that the gap between high-speed rail and air fare in reality is 28.5 yuan larger than the equilibrium price gap.
This result shows that from the perspective of equilibrium price difference, the fare of civil aviation is still high, and there is room for downward adjustment. As for the current fare of high-speed rail, the fare of China Southern Airlines is reduced from 675 to 646.5 yuan, which is appropriate. Of course, if the fare of high-speed rail continues to fall, then China Southern Airlines will maintain its own fare at a price of 128 yuan more than the fare of the high-speed rail, namely, the equilibrium price. This is theoretically reasonable.
Compared with civil aviation and other modes of transportation, high-speed railways are high-speed, fast-moving, and there is not much difference in the utility and value of the two. The reduction in fare difference can be effectively preventing the imbalance caused by passengers’ being inclined to a certain mode of transportation due to the unfair price gap in the transportation market.
According to the equilibrium fare, the profit of high-speed rail and civil aviation are 0.451 yuan/person kilometer (the cost is 0.324 yuan//person kilometer) and 0.686 yuan/person kilometer (the cost is 0.45 yuan//person kilometer) respectively, which are higher than their respective unit costs. Under the balanced fare combination, both the high-speed rail and the civil aviation can obtain a certain positive return.
2.5 Recommendation
2.5.1 Price adjustment
From the above calculation of the balanced fare, it can be seen that in order to cope with the fare fluctuation of the high-speed rail, the average fare of the ticket of the Wuhan-Guangzhou route can be reduced from 675 yuan to 610 yuan to reach the equilibrium fare. Because high-speed railway and air transportation are high-quality modes of transportation, they all have similar characteristics of emphasis on service and fast delivery. The target customer groups of the two are similar in their demand for transportation products. After the price hike of the high-speed rail, in most cases, the fare will be properly lowered to increase the attendance rate, which will inevitably impact airlines’ revenue. Therefore, civil aviation must also reduce prices accordingly. However, proper price reduction means that civil aviation needs to grasp the price reduction range, which is neither unprofitable nor will it cause a more violent price war from the high-speed railway.
2.5.2 Frequent flyer program
Frequent flyer program is a major feature of airline operations and competition (Sehipper, Nijkamp and Rietveld, 2007). It promotes the means of accumulating mileage or points and rewarding mileage and gifts to passengers who frequently take a company's flights (Anjos, Cheng and Currie, 2004). This is a unique means for airlines to attract business travelers and improve their competitiveness. Frequent flyers are mostly business travelers, they are not sensitive to price, and have a lifetime value, thus they are one of airlines’ most important sources of profit. High speed railway in this respect is difficult to have natural conditions to compete with airlines. Therefore, airlines should continue to improve the frequent flyer program, provide personalized services for their high-net-worth customers, and build a barrier for themselves in price competition.
2.5.3 Competition and cooperation
Civil aviation and high-speed rail are not completely competitive. In general, there is a kind of competing relationship between high-speed rail and civil aviation. They cooperate in competition and compete in cooperation. Both parties must seize the same source of customers in similar markets and bring a large amount of transportation demand to each other. From the perspective of maximizing social welfare, high-speed rail and civil aviation need to rationally distribute passenger flow according to the network coverage and infrastructure construction of both parties, and reach a memorandum on price adjustment to avoid vicious competition.
2.5.4 Improving service
In addition to price, there are many influencing factors that affect passengers’ choosing transportation modes, such as service level, speed, comfort, on-time rate, and personal preference. Air transportation has always been distinctive and special in the transportation system since its extensive use. It has a natural speed advantage and a service reputation that has been maintained for many years. These external factors can reduce the price sensitivity of passengers. In terms of the punctuality rate and convenience that may be weaknesses judged by passengers, civil aviation needs to be strengthened by strengthening management and adopting multi-channel ferry.#p#分页标题#e#
3.0 Conclusion
The rapid development of China's high-speed rail has brought great impact to Chinese industry companies represented by China Southern Airlines. According to the analysis of game theory, high-speed rail has reason to adopt price reduction strategy to participate in market competition, because it can bring more market share and benefits to them. At the same time, according to further analysis of game theory, it can be seen that in order to obtain more market share and benefits, high-speed rail and aviation companies have reason to conduct multiple and repeated price wars and launch malicious competition. From the perspective of game theory, the price war may be beneficial to a enterprise itself in the short term, but in the long run, the price war will ultimately damage the overall interests, that is, it is pointed out by the game theory that when each individual is seeking to maximize benefits, the overall interests are not optimal or even the worst, that is, non-cooperative games can only reach Pareto suboptimal. If they can find a balanced price, it may help to ease the price war between high-speed rail and aviation, because under the equilibrium price conditions, the other party can neither raise the price, otherwise it will further lose the market; nor can it lower the price, because there will be a loss.
Judging from the current actual situation, the average fare of China Southern Airlines is 675 yuan, and the average fare of high-speed rail is 518.5. After calculation, the actual price difference between the two is 156.5 yuan. The equilibrium price of China Southern Airlines is 610 yuan, and the equilibrium price of high-speed rail fares is 482 yuan. The difference between the two equilibrium prices is 128 yuan. It shows that the current price of China Southern Airlines needs to be reduced, and it needs to be reduced to around 638 yuan. That is, as long as the actual average price of China Southern Airlines can maintain the difference of 128 of the actual average price of the high-speed rail, they can achieve the Nash equilibrium status. Of course, in order to avoid the vicious price war with high-speed rail, China Southern Airlines need to improve their services, frequent flyer programs, and cooperation with high-speed rail.
References
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