If we were to posit that there is a connection between Maximus, general of the Roman Empire and protagonist of the film Gladiator, game theory and how Airbus or Boeing set the price of their planes, or how airlines set the price of their tickets, is it credible?
Well, if we combine fact and fiction, so be it. In 2001, the Australian actor Russell Crowe, known for his roles in Gladiator, Master and Commander, Cinderella Man and American Gangster, among other hits, played John Nash, The mathematician and winner of the 1994 Nobel Prize in Economics, who for many will be remembered for having inspired the film «A Beautiful Mind«, the title of the film from which the GAME THEORY entered popular culture thanks to the award-winning film.
The “Nash equilibrium”, as applied to the airline industry, does not imply that the best joint outcome for the companies is achieved, but only the best outcome for each and every company considered individually.
The Game Theory is a branch of mathematics and economics which, using models, analyses and studies situations called games, in which two or more players must interact and decide what decision to take based on the decisions that others may take.
John Nash went down in history for his fundamental contribution to Game Theory, in particular, for being the creator of the Nash equilibrium, a «solution concept», where each individual player does not gain any incentive by modifying his strategy as long as the other players maintain theirs. In this way, each player is executing the best possible “move” considering the moves of the other players.
If we translate this concept to the business world, in a Nash equilibrium each firm executes the best possible ”move” taking into account the moves of the other firms. It does not imply that the best joint outcome for the firms is achieved, but only the best outcome for each firm individually.
Application of Nash Equilibrium in the aeronautics sector
From tenders for aeronautical and airport infrastructure projects; closed auctions or public tenders, first price, second price; aeronautical pool contracts; budgets for technological developments for production and technology in the aeronautical industry; aircraft production between Airbus vs Boeing; ticket prices set by airlines or the competition between two airlines on a given route, depend on it. Let us look at several examples.
How would this theory be applied in the case that several airlines are fighting on the same route?
In economic terms, the Nash equilibrium describes the market for a good in which there is a set of competing airlines, each of which separately decides how to price its tickets in order to maximise its profits.
If, for example, Ryanair decides to offer more flights than its potential demand, it will face higher costs; if it decides to produce less than demand, it will not be able to satisfy all its customers.
And how does any airline adopt the best strategy based on the decisions of the other airlines that are its competitors? The best strategy would be to change the price.
Suppose there are several airlines operating the same route offering the same services to the passenger, i.e. none is of better quality than the other. In this case, the airline that sets the lowest price will be the one that takes the largest share of the market. But of course, the minimum price would be the one that at least covers its operating costs. Therefore, the minimum price would be the one that at least covers its operating costs, Nash's break-even in this context would be a price lower than its rivals, but higher than its operating costs..
Airlines behave like pure strategists, taking into account the moves of all their competitors in order to win the game, their main objective being to gain as much market share as possible.
Another scenario where this balance applies is in the operation of airports.
There are countries like Spain where one company, in this case AENA, has a monopoly on airports, but what happens, for example, in London? In the British capital there are several operators that operate its 6 airports: Heathrow, Gatwick, Stansted, Luton, London City Airport and Southend. How is the competition between them?
To analyse the assumption we can create a game in which there are several airports that share a catchment area and have one or more airlines operating in each of them.
It is about vertical structures formed by an airport and the airline entering into a contract or agreement under which commercial revenues are shared.
In this case, although airports compete to attract the same passengers, it is actually the airlines that compete with each other, as airports are buildings that have no mobility or attractiveness of their own. Therefore, they set up vertical structures to analyse airport competition.
As these airlines offer substitute services, passengers are faced with the dilemma of deciding which airline-airport to choose for their flight.
To solve the game we can obtain the perfect Nash equilibrium in subgames. On the one hand, each airport-airline decides the variables of the contract where commercial revenues are shared and, on the other hand, airlines compete to the Cournot and decide on the number of passengers to be carried.
Another interesting case in which to apply Game Theory is that of the airline alliances.
Why do airline alliances exist? Why are all the major leading airlines part of one of them?
In the air transport sector, airlines conduct collaborative strategies in most cases, acting in parallel and simultaneously through alliance agreements.
The exception is Ryanair, which has developed a different strategy from its competitors, acting rationally and applying the strategy it considers optimal for its unique interests.
At present, the airline industry has found itself in Nash equilibrium, The result is that legacy airlines secure long-haul flights and low-cost carriers secure short-haul flights. The result is that the legacy airlines are guaranteed long-haul flights and the low-cost carriers short-haul flights.
However, new strategies emerge from time to time, for example, the low-cost sector has also “appropriated” strategies such as monopolising a secondary airport for a single company. This is the case of Stansted (London) by Ryanair.
Taken as a whole, if one airline gains market share in the air transport sector, this has an effect on all competition. This is a clear example of zero-sum game, where airlines cannot reach prior agreements. In the end, mathematics also provides an answer to the behaviour of the airline market.
