Question

Using concepts from game theory, explain why an airline that is in competition with several other firms “has promised to maintain services on the route for the long term,” despite losses.

In your explanation, use a payoff matrix with hypothetical payoffs, with (for simplicity) only two players: "United" and "South West Airlines". Be sure to explain the payoffs and identify any Nash equilibria and the likely eventual outcome.

Answer 1

A) Game theory is the process of modeling the strategic interaction between two or more players in a situation containing set rules and outcomes. While used in a number of disciplines, game theory is most notably used as a tool within the study of economics.

As the global economy is becoming more and more connected, the aviation industry is one of the fastest transportation sectors. Commercial airlines carried more than 4.5 billion passengers in 2019 and are expected to generate 581 billion U.S. dollars in global revenue in 2020. Air transportation also plays an important role for tourism, contributing to economic growth, especially in developing countries. The number of international tourist arrivals increased from 1.32 billion arrivals in 2017 to 1.4 billion in 2018; more than half of tourists chose to reach their destination by air transportation.

Aviation provides the only rapid worldwide transportation network, which makes it essential for global business. It generates economic growth, creates jobs, and facilitates international trade and tourism.

The mobility of men and material by air is called air transport. It is the fastest means of transport. It is very useful for long distances and saves time.

The Parliament passed the Air Transport Corporation Act in 1953 under which the Indian Airlines Corporation was to run domestic services and Air India is to run external services.

Vayudoot and Pawan Hans are the two airlines added to civil aviation recently. Vayudoot operates in remote stations not covered by Indian Airlines. Pawan Hans provides helicopter services to remote places. In 1972, International Airport Authority of India (IAAI) was established and in 1986 National Airport Authority of India (NAAI) was installed.

The Director General of Civil Aviation (DGCA) is responsible for maintenance of civil aerodromes. After the implementation of economic reforms, Govt. has been following the policy of open skies and private airlines have been permitted to operate in the field of civil aviation.

Advantages of Air Transport:

The following are the main advantages:

1. High Speed:

It is the fast speed means of transport. Passengers and goods can be transported easily from one place to the other.

2. Minimum Cost:

Unlike railways and road transport, there is no need to spend money on the construction of any track or road, only airports have to be constructed.

3. Strategic Importance:

An airway has great strategic importance. It can be used for internal and external security.

4. Easy transport of costly and light goods:

It is quite convenient to send costly, light and perishable goods through air transport.

5. Free from physical barriers:

Air transport is free from physical barriers like river, mountains and valleys etc.

6. Useful for Agriculture:

Air transport is useful for aerial spray on pests and insects which cause harm to crops.

7. Useful in natural calamities:

During earth quake, flood, accidents and famine air transport is used for rescue operations.

B) Payoff Matrix. In game theory, a payoff matrix is a table in which strategies of one player are listed in rows and those of the other player in columns and the cells show payoffs to each player such that the payoff of the row player is listed first.Payoff Matrix. An matrix which gives the possible outcome of a two-person zero-sum game when player A has possible moves and player B moves. The analysis of the matrix in order to determine optimal strategies is the aim of game theory.

In game theory, a payoff matrix is a table in which strategies of one player are listed in rows and those of the other player in columns and the cells show payoffs to each player such that the payoff of the row player is listed first.

Payoff of a game is incremental gain/benefit or loss/cost that accrue to a player by executing its strategy given the strategy of the other player. The payoff depends on the context of the game. For example, firms deciding about their advertising budgets worry about their revenue, firms undertaking new investment in plant and machinery are interested in finding their rate of return and so on.

A payoff matrix is an important tool in game theory because it summarizes the necessary information and helps us determine whether a dominant strategy and/or a Nash equilibrium exist. It has application in oligopoly models, etc.

Presentation

If the row player has n strategies and the column player has m strategies, the number of cells in the matrix must be n × m and a total number of 2 × n × m payoff values must be there.

A payoff matrix lists the name of the row player to the left of the matrix and the name of the column player above the matrix. The strategies of the row player form the rows of the matrix and the strategies of the column player form its column. The payoff to the row player is always listed first in each cell but the actual presentation may vary as follows:

• The payoffs may be separated using a comma such that the payoffs to the row player appears to the left of the comma and the payoffs to the column player are listed to the right of the comma.
• Alternatively, the row payoff is listed in the bottom left of each cell and column payoff is shown in the upper right corner of the cell. Sometimes a diagonal is drawn inside the cell to separate the two payoffs. The example below illustrate different presentation methods.

Example

Let us consider two telecommunication operators: Row and Column. Currently, they share the market equally. There is a $50 million worth of untapped market. If Row expands its network, it will be able to capture the whole $50 million revenue if Column does not expand its network, and vice versa. Similarly, if both expand their network, Row will get $20 million additional revenue and Column $30 million, but if no one expands its network, both gets zero additional revenue.

Let us create a payoff matrix for this game.

a)There are two players: Row and Column and each has two strategies i.e. to expand or not to expand. Hence, there must be four cells in the matrix.

b)We list Row as the player whose strategies are listed in rows in red and Column as the player whose strategies are tabulated in columns in blue.

c)The upper left cell corresponds a strategy in which both firms expand. In such an eventuality, Row gets $20 million (which appears first) and Column gets $30 million (which appears last).

d)The lower left cell corresponds to a strategy when Row does not expand but Column expands. The payoff to Row and Column in this case is 0 and $50 million, respectively. This payoff reverses in the upper right corner which represents payoff when Row expands but Column does not.

e)The lower right cell represents a situation in which neither firm moves to capture the market, and both get a payoff of zero.

The following table shows the different ways in which the payoff matrix may be presented.

Payoffs represent revenue gain in millions of USD	Column
Expand	Not Expand
Row	Expand	20,30	50,0
Not Expand	0,50	0,0

Payoffs represent revenue gain in millions of USD	Column
Expand	Not Expand
Row	Expand	30 20	0 50
Not Expand	50 0	0 0

Payoffs represent revenue gain in millions of USD	Column
Expand	Not Expand
Row	Expand	30 20	0 50
Not Expand	50 0	0 0

The following table shows the different ways in which the payoff matrix may be presented.