3.2. Some Typical Examples of Competitive Games in the Tourism Business

In this case, company E can choose a row strategy, while company F can choose a column strategy.

According to the position table III.3, there are four possible outcomes for two companies E and F, which are recorded in four cells of this position table. Cell A shows the outcome when both companies choose the normal price strategy: the profit of each company is 10. Cell B shows the outcome when company E chooses the normal price strategy and company F chooses the war price strategy: the profit of company E is -20, the profit of company F is -100. Conversely, cell C shows the outcome when company E chooses the war price strategy and company F chooses the normal price strategy: the profit of company E is -100, the profit of company F is -20. Cell D shows the outcome when both companies choose the war price strategy: the profit of each company is -50.

Table III.3: Position table in the bioligopolistic price war game between two shipping companies E and F

Company F

Pbt Pct

Company E

Pbt

A	10	B	-100
10		-20
C	-20	D	-50
-100		-50

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Pct

(ii) Optimal strategy and optimal equilibrium:

The optimal strategy is the best strategy one can choose, regardless of the opponent's strategy.

Analyzing the position table III.3 row by row, we can determine that the optimal strategy of company E is the normal pricing strategy. Indeed, if company E chooses the normal pricing strategy, then depending on the strategy chosen by company F, company E will have a profit of 10 (small profit) or -20 (small loss). Meanwhile, if company E chooses the war pricing strategy, also depending on

According to the opponent's strategy, company E will have a profit of -100 (too big a loss) or -50 (too big a loss).

Also exactly the same as above, if we analyze position table III.3 by column, we can determine that the optimal strategy of company F is the normal price strategy.

The optimal equilibrium is the outcome that occurs when all players in a game choose the optimal strategy.

According to position table III.3, when both companies E and F choose the optimal strategy of normal pricing, the outcome is the optimal equilibrium in cell A: each company has a profit of 10.

In competitive market games, when one knows very little about one's opponents' strategies, the rational decision one usually makes is the optimal strategy, that is, the strategy that is best in the sense that it depends least on the strategies of one's opponents.

(iii) Nash equilibrium:

As discussed above, in competitive games, people only adopt optimal strategies when they know very little about their opponents. In real competition, people know more about their opponents, because every opponent tries to maximize profits. Therefore, the optimal equilibrium is not the most interesting state in competitive games.

Consider the monopolistic game between two ocean passenger transport companies E and F, in which each firm is considering whether to maintain a normal pricing strategy (Pbt) or adopt a high pricing strategy (Pc) to capture additional monopoly profits. Suppose the outcomes of this game are given in position table III.4.

Table III.4: Position table in the monopolistic game between two shipping companies E and F

Company F

P C Pbt

Company E

A	200	B	220
100		-30
C	-40	D	30
150		20

Pbt

Analyzing the four possible outcomes in the confrontation game, the following observations can be drawn:

- When both companies adopt the normal pricing strategy, they earn low profits; the profits of companies E and F are 20 and 30 respectively.

- When both companies collude to adopt a high monopoly pricing strategy, they gain additional high monopoly profits; the profits of companies E and F are 100 and 200 respectively.

- When one company maintains a normal price strategy and the other company applies a high price strategy, the company that maintains the normal price strategy will attract more customers and earn higher profits, while the other company will fall into a situation where there are too few customers and suffer losses (negative profits). This situation is represented by cells B and C.

Now let us analyze the overall development of this game. First, both companies adopt the normal pricing strategy, then the outcome occurs in cell D: the profits of companies E and F are 20 and 30 respectively. With the same goal of maximizing profits, these two companies seek to increase profits. They collude and adopt a high monopoly pricing strategy to gain more of the high monopoly profits. This situation is shown in cell A: the profits of companies E and F are 100 and 200 respectively. However, it does not last long because

The desire for profit is limitless for each company. They collude with each other for profit, they can also secretly break the collusion for profit. In reality, it often happens that company E or company F secretly breaks the collusion, arbitrarily reduces the price to attract customers, and of course, the profit of this company will increase. This situation is illustrated in cell B or cell C. When company E breaks the collusion, the result will occur in cell C: the profits of company E, F are 150 and -40 respectively. And when company F breaks the collusion, the result will occur in cell B: the profits of company E, F are -30 and 220 respectively. This "deceptive" behavior

pushed the competitor into a loss-making situation and was quickly exposed, forcing this competitor to also adopt a normal pricing strategy. So outcome D occurred again.

The equilibrium that occurs in cell D is an optimal equilibrium. Moreover, it is also a Nash equilibrium. This equilibrium was discovered by the mathematician John Nash in 1951 and is named after him.

A Nash equilibrium is an equilibrium in which no player can improve his position, even if he knows in advance the strategy of his opponent.

According to the position table III.4, it is easy to verify that the equilibrium occurs at

Cell D is a Nash equilibrium, meaning that when knowing in advance that company F's strategy is the normal pricing strategy, company E cannot choose any strategy other than the normal pricing strategy, and vice versa, when knowing in advance that company E's strategy is the normal pricing strategy, company F cannot improve its position by applying a strategy other than the normal pricing strategy.

III.3.2. Some typical examples of competitive games in tourism business

(i) Advertising games

Suppose two travel companies E and F are equally competitive and are considering whether to conduct advertising campaigns.

The possible outcomes in this game are given in position table III.5, where the numbers in each cell represent the profits of firms E and F, respectively.

Table III.5: Position table of advertising games

Company F

Ads No Ads

Company E

A	5	B	2
10		15
C	8	D	3
6		10

No advertising

Analyzing by rows, it is easy to see that the optimal strategy of company E is advertising strategy. Similarly, analyzing by columns, it can be seen that the optimal strategy of company F is advertising strategy. Thus, cell A represents the optimal equilibrium. Moreover, when this equilibrium occurs, each company cannot improve

can maintain its position by ceasing advertising, so cell A also represents a Nash equilibrium.

(ii) Product selection game

Suppose two restaurants are facing a tourist food service market in which two types of food (seafood and river fish) can be successfully marketed if each type of food is supplied by only one restaurant. In this case, the position table of the two restaurants is given in Table III.6, where the numbers in the cells are the profits of restaurant E and restaurant F, respectively.

Table III.6: Position table of the product choice game

F Restaurant

Seafood River fish and shrimp

Restaurant E

Seafood

A	-2	B	10
-2		10
C	10	D	-2
10		-2

River fish and shrimp

In this game, each restaurant is impartial about which product it will supply. If it were possible to cooperate, the two restaurants would probably compromise on dividing the market, with each restaurant specializing in supplying only one type of product.

The strange thing about this game is that there is no optimal equilibrium, but there are two Nash equilibria, shown in cells B and C. This means that, knowing in advance which product the other restaurant chooses to supply, the remaining restaurant has no choice but to choose the remaining product.

In the reality of the food and tourism business in Vietnam, restaurants that sell the same type of food are often concentrated in a row, attracting consumers to eat there. However, this concentration is the main reason leading to fierce competition between restaurants. The competitive advantage often leans towards restaurants with good food quality, reasonable prices, parking, etc.

(iii) Non-cooperative game:

Game theory also sheds light on the need for cooperation in economic life, although we already know that Adam Smith's "Invisible Hand" produces efficient resource allocation in perfectly competitive markets from the motive of profit maximization or utility maximization.

In many situations, noncooperative behavior leads to economic inefficiency or social suffering. A classic example of this is the arms race between the United States and the Soviet Union before 1990, in which noncooperative behavior between them led to huge expenditures on nuclear-armed militaries.

Another typical example is the non-cooperative environmental pollution game in the hotel and restaurant sector. Position table III.7 shows the possible outcomes in the non-cooperative environmental pollution game of two hotels E and F, where the numbers in each cell represent the profits of hotel E and hotel F, respectively.

Table III.7: Position table of the non-cooperative game for the environmental pollution problem of hotels E and F

F Hotel

Less pollution More pollution

Hotel E

Less pollution

A	90	B	100
90		90
C	90	D	100
100		100

Heavy pollution

In the non-cooperative pollution game, each unregulated profit-maximizing hotel will dump pollutants (raw wastewater, food waste, etc. ) into lakes and oceans. If each individual hotel tries to clean up the environment, it will suffer from diminishing profits. The non-cooperative Nash equilibrium in cell D will lead to a situation of high pollution. When

In that case, the government can come up with a common wastewater treatment solution. And the forced cooperation equilibrium in cell A will reduce the profit of each hotel, but in return, the environment will be clean.

The above game demonstrates how the action of the "Invisible Hand" can lead to a breakdown of perfect competition. This is an inefficient Nash equilibrium. Government intervention to force the cooperative equilibrium in cell A to occur is always an effective solution in keeping the environment clean.

(iv) Repetitive game:

Positioning tables are a useful tool for competitive analysis. However, they are not the only tools used for this purpose. In competitive analysis, one can use graphs, network diagrams, etc. It can be illustrated

This is done by a game of repeated discounts between hotels E and F to attract customers.

Figure III.1 depicts a repeated discounting game between two hotels E and F, in which hotel E always initiates a discount, and in response, hotel F follows suit. The vertical vectors such as A 0 B 0 , A 1 B 1 , A 2 B 2 , etc. represent

represents the price reduction behavior of hotel E, and the horizontal vectors B 0 A 1 , B 1 A 2 , etc. represent the price reduction response behavior of hotel F. Because the

By cutting prices first, hotel E attracts more customers. Behavior

Hotel E's price reduction is the cause of hotel F's reciprocal price reduction. Finally, we can easily see that this type of competition for customers must lead to prices below the cost of production and put both hotels into a loss-making situation.

A large-scale rebate game occurred in the hotel industry in Vietnam in late 1997 and 1998, when the financial and currency crisis in Thailand was spreading to many Asian countries , causing a sharp decline in tourist arrivals to Asia . In the rebate game,

In this regard, private and joint venture hotels are always proactive in reducing prices.

State-owned hotels have been passively reducing prices and are suffering heavy losses.

A 0

A 1

B 0

A 2

B 1

B 2

P 0

Price of hotel E

P 1 P 2

0 P 2 P 1 P 0