Why Do Airlines Not Make Money

 

Seemingly since the beginning of aviation history there has been discussion and speculation on the remarkable inability of the industry to generate profits. This is even more so the case now, when a number of the world's airlines are bankrupt. The failure of aviation, or at least of airlines, to produce a reasonable rate of return on investments has been a fact pondered by many at great length but never satisfactorily understood. Somehow the industry seems to violate the most basic principles of economics and business.

Complaints about the lack of profitability in the airline industry surface during periodic downturns, but the problem has been there since the industry started. Statistics shows a long history of losses for airline industry and yet at the same a phenomenal growth in traffic. The airline industry is a complex one and the apparently contradictory statistics only underscores this fact.

Airlines Profits in Perspective

Profits by definition are surplus of income over expenditure; i.e.; the difference between revenue and expenditure. The table at Annexure 1 shows operating profits for the airlines industry from 1947 to 2007 a period long enough to qualify as the ‘long run’ of the Marshallian economics. The table throws up some interesting results. The industry made operating profits in 45 of the 61 years. From 1962 to 1979 it had a long period of uninterrupted operating profit. Though operating profit during this period remained positive they nevertheless, exhibit severe slowdowns. Besides, the magnitude of profit has been modest for most of the years. The period of losses is more frequent from 1980 onwards; since then for every three consecutive years of losses there are seven or eight consecutive years of profit. If we look more closely at the table then it would be seen that the long period of uninterrupted operating profits coincided with the period of regulation of the industry in force almost in all the countries of the world during the period. The USA, which at that time accounted for more than 50% of world traffic

deregulated its airline industry in 1978 and since then the trend in operating profit, has changed altogether. Furthermore, the period of losses coincide with periods of recession. Another thing that is not as obvious in the table but comes out quite clearly in the graph is the volatile and cyclic nature of the industry; post 1978 in particular. 

The picture seen in operating profit as a percent of revenues shows disturbing trend. As can be seen from the table at Annexure 2 since 1947 the airlines have managed to clock a return of more than 5% only on 13 occasions and have not been able to achieve double digit return even once. It may surprise many at our choice of 5% as the benchmark, after all while evaluating a project we generally use discount factor of 12%, that is an investment is considered worthwhile unless it brings in a return of

12%. To lessen the surprise let us point out that the average returns that the airlines have realized in these 61 years is 2.30%; our benchmark that is double the average is therefore reasonable. The remarkable thing is that the average does not change much with change in policy; during the regulation period it was 2.25% after deregulation it improved marginally to 2.34%. Also, to be noted here is that we are talking here of gross margin that does not include the cost of borrowings. The highest return achieved during the regulation period was 9.5% (1965, 1966) and 6.1% (1988) after deregulation.

We now turn our attention to net profit and net margin. Here the picture is even more dismal. In 31 out of 61 years the industry made losses. Even the profit making years are not great ones their magnitude is usually fairly low. In fact, if we add up all the losses and set it off against all the profits then the net figure comes to $17,000 million or 278 million a year. Hence the remark made in the early 1990s by former CEO of American Airlines Robert Crandall that the colossal losses made by the industry negated all the profit made since 1903.

As for net profit as percent of revenue, the best that the industry could achieve was 6.1% in 1966 apart from that only on one occasion margin has been more than 5%. The 61 year average is a miserable 0.12%.

The analysis above shows that the airlines industry has not been a profitable one. And this appears to be so almost since the beginning of the industry. The evidence points towards a very depressing state of financial health of the airlines.

Where Does the Problem Lie

The above analysis raises the issue of what causes this intriguing behaviour of the airline industry. The answer lies in the nature of the industry. One of the widely accepted theories of economics holds that unfettered competition does not work very well in certain industries commonly known as natural monopoly. Natural monopolies often result in infrastructure and capital-intensive industry; examples are water supply, electricity, public transport and the like. An utility is often created because it is the only way to ensure crucial infrastructure investments are made; if multiple firms operate they may not be able to afford to upgrade their systems overtime.  Economists have for long argued that natural monopolies whose activities fall within the ambit of public utilities should be provided protection by allowing them to function as monopolies but within a regulated market.

Indeed many of the elements of the infrastructure of the airline industry are natural monopolies. For example, it would not be more efficient to have multiple air-traffic control firms competing against one another. By disallowing construction of a second airport within a radius of 150 kilometres of an existing airport, airports in India are allowed to function as natural monopoly in a limited sense. But airlines themselves are never thought of as a utility and this in our opinion is a myopic view. There are a number of reasons why airlines should be treated as a public utility. Civil aviation like other transport industries generates important external benefits. The returns from air transport are not restricted to the industry itself, but encompass wider effects on the economy at large. Airlines are often used to serve important national, social and economic objectives of the government. The national airline of a country is seen purely as a symbol pf prestige; or as a means of encouraging trade and investment; or as a way of stimulating the development of tourism; or as an important source of foreign exchange; or as a vehicle for supporting the development of a domestic aero space industry; or as a way of guaranteeing the availability of standby fleet with fully trained personnel in case of emergency. The importance that governments give to some of these nationalist and mercantile objectives may be declining over the years but they are still highly significant.  

The consequence of refusal to accept airline industry, as a public utility infrastructure while granting some of its constituents the benefits of monopoly has been that on the supply side airlines have to pay monopoly price for the services consumed and on the demand side it has to live by the market determined price. Living by the market price would not have been such a bad thing had the market itself been a rational place like any other competitive marketplace. Sadly this is not the case. As the Fortune magazine once observed, ‘for all its ineffable allure, though, the airline industry is like the banana business.’[1] Airplane seats are a commodity - despite heroic attempts at product differentiation, passengers think one airline's seat is pretty much like another's - and when a plane takes off with empty seats, the commodity is spoiled. It is better by far, from an airline's point of view, to lure passengers from competitors at deep discounts than not to sell seats at all. Airlines sell a perishable product, and it's like the last banana in the store; one can either get a penny for it or one can get nothing for it, so airlines sell it for a penny.

Combine these characteristics and what do you get? Vicious, endless fare wars that in most businesses would quickly thin out the players but that in airlines have helped produce a record of chaos and wreckage rare in any industry and almost incredible in one so important to the nation's and world's economy.

The commonly accepted view so far has been that pricing madness and mammoth losses have resulted from bad policy, bad management, and bad luck - problems that have masked progress toward an eventual, conventional settling down of the industry. However, a small but growing group of industry experts believe the conventional explanation of chronic airline turmoil is wrong. The new view says the trouble isn't bad luck; it's the very nature of the business. Loosely associated with Lester Telser,[2] a prominent economist at the University of Chicago, they argue that the airline industry is an economic machine programmed for self-destruction or something close to it.

The argument, at its simplest, goes like this: No matter how many employees are laid off or labour concessions gained, the fixed costs of aviation - planes, fuel, facilities - are destined to remain relatively high. The marginal costs of adding passengers on a partly filled flight are negligible. So the airlines need not charge much to make that perishable seat worth selling. The result is now a days’ roughly 90% of airline passengers buy their tickets at a discount, paying on average just a third of the full fare. Thus in an industry with high fixed costs and low marginal costs, competition produces a market that never settles down. Economists say such a market has an "empty core."[3]

The essence of neo classical demand theory is built on the premise that through a process of bidding and counter bidding between the seller and the buyer the parties arrive at a price at which neither the seller makes an excess profit nor the buyer makes an excess gain. With both the buyer and the seller satisfied with the transaction the market will attain a state of equilibrium such a market guarantees that no one in the market is worse off than before and at least one person is better off than before. This is known as Pareto the position where social welfare is at the optimum. The attainment of equilibrium is made possible due to the presence of large number of buyers and sellers.

Without challenging the central proposition of the neo classical demand theory the core theory makes the additional proposition that it is not always necessary for a competitive market to attain an equilibrium price. According to core theory a market can perpetually remain in disequilibria if certain conditions are fulfilled. Telser describes these conditions using the word ‘Chaos”. According to Telser, there is chaos when "price cutting is extreme, most firms in the industry are losing money, and yet it is plain that buyers want the product and are willing to pay higher prices than those currently prevailing."[4]

If we look at the airline industry we find it meets all the requirements of a competitive market; it has large number of buyers and sellers, there is no restriction to firm’s entry or exit nor is there any restraint on price. Theoretically therefore, the industry should at some stage reach the equilibrium state yet experience shows that it never happens. The relentless pressure to sell seats and at least recover the short run marginal cost makes airlines to resort to extreme price cutting and offering seats at ridiculous fares (e.g. for Rs. 99) even when the passengers are willing to pay much higher fare, thus fulfilling Telser’’s criteria of an industry with an empty core. The chaos so created never settles down, airlines are known to sell seats even when the aircraft is on the verge of takeoff! In the process the gap between the marginal and average cost gets so large that airlines generally are not able to recover their long run average cost and thus fail to make any money.

The above discussions highlight that the unrestricted ability to contract and re-contract among buyers and sellers within an industry allows fares to be bid down to non-profitable levels. To the extent that one or more airlines have excess operating capacity, attracting additional customers by lowering price (provided such price is above marginal cost) creates additional operating profit (or reduces operating loss) for the individual airline. The important feature is the effect of excess capacity, not necessarily the cause of that excess capacity.

Another condition that must be fulfilled for an empty core to exist is the presence of avoidable cost[5]. The presence of avoidable cost lends another peculiarity to the airline industry and contributes towards the industry’s poor profitability. Once an airline has incurred the sunk cost[6] and created operating capacity the actual operation of the aircraft requires the incurrence of large avoidable cost irrespective of level of utilisation. This results in what economists call a U shaped cost curve. Once however, an airline has committed to particular fleet and schedule it cannot change output without incurring substantial adjustment cost. The airlines get caught in a no win situation – not flying saves avoidable cost but incurs adjustment cost; flying on the other hand results in higher expenditure but lower revenue.

On the supply side the cost conditions of an airline are such that cost per mile flown falls as the number of miles flown increases. However, technological constraints imply that, only reducing aircraft capacity can increase distance flown. Further, cost per passenger falls as the number of seats filled on an aircraft rises up to full capacity. Taken together this implies that marginal cost starts increasing well before the payload at maximum range is reached. The airline industry has generally operated with excess productive capacity. Further airlines tend to cut prices to short-run marginal cost in the face of excess capacity that occur due to variations in demand, which pushes prices below that required to operate an efficient set of schedules.

On the demand side an airline faces seasonal and cyclical demand. Thus, matching capacity to demand in the airline industry moves it toward an empty core, or an unstable equilibrium.

Policy Implications

The study was undertaken with the objective to examine and explain why airlines do not make money. Examination of historical data on both gross and net profit established the fact that over the long run airline industry does not indeed make any money, it at best breaks even. The reasons for this intriguing state of the industry can be found in the nature or peculiarities of the industry. Since individual airlines deal with a commodity that is perishable they are always under pressure to sell their stock of available seats. Presence of excess capacity in the industry compounds the situation further. This leads to fierce price war among airlines that results in seats being sold at a price much below what the market can bear. What is worse, in their effort to maximise their short run revenue the airlines end up with fares that are below the long run average cost. Poor financial return then puts even more pressure on the airlines to maximise capacity utilisation that once again starts the cycle of under pricing and the resultant consequences.

Analysing the behaviour of the airline industry and noting its unique features economists like Telser, Button, Nyshadham, Raghavan, Pirrong, Sjostrom and others have found an explanation in the core theory. Their theory states that a competitive market through a process of coalition among its members arrives at a price that establishes equilibrium in the market, which lends stability to the market; this stability forms the core of the market. However, they also found that there are certain industries that due to their special characteristics perpetually remain unstable, i.e.; at no point the industry attains an equilibrium price. Typically firms in such industry often have to sell their products at below cost so as to survive at least in the short run; a strategy that far from solving the problem further accentuates as well as perpetuates the problem.

The issues that emerges from the above is that though the airline industry is a competitive market it does not produce an equilibrium price and therefore is inefficient and incapable of optimising social welfare. Economists have for long advocated in favour of intervention by the government where market based solution is not efficient. Thus the policy implications are the following:

1. Should the airline industry in India be treated as natural monopoly and allowed the concomitant benefits?
2. Should there be direct intervention by the government to neutralise the instability, which is inherent in the nature of the airline industry?
3. Should airlines be allowed ‘fare agreement’ in the line of Conferences in the shipping industry?  

References

Antoniou, Andreas, The Status of the Core in the Airline Industry: The Case of the European Market. Managerial and Decision Economics. 19(1), 1998, 43-54

Button, Kenneth, Liberalising European Aviation: Is there an Empty Core Problem? Journal of Air Transport Economics, 30(3), 1996, 275-291.

Nyshadham, Easwar A., and Raghavan, Sunder, The Failure of Electronic Markets in the Air Cargo Industry: A Core Theory Explanation. Electronic Markets, 11(4), 2001, 246-249

Pirrong, Stephen C., An Application of Core Theory to the Analysis of Ocean Shipping Markets. Journal of Law & Economics XXXV, 1992, 89-131

Sjostrom, William, Collusion in Ocean Shipping: A test of Monopoly and Empty Core Models. Journal of Political Economy, 97(5), 1989, 1160-1179

Telser, Lester G., The Usefulness of Core Theory in Economics. Journal of Economic Perspectives, 8(2), 1994, 151-164

 

    

Annexure 1

Annual Earnings – World Airlines

YEAR	Operating Results	YEAR	Operating Results
	Profit		Profit
	($-mils)		($-mils)
1947	-120	1978	3,100
1948	-49	1979	736
1949	-9	1980	-635
1950	41	1981	-692
1951	24	1982	-160
1952	-13	1983	2,100
1953	-3	1984	5,100
1954	32	1985	4,100
1955	78	1986	4,600
1956	84	1987	7,200
1957	-41	1988	10,200
1958	15	1989	7,600
1959	105	1990	-1,500
1960	32	1991	-500
1961	-118	1992	-1,800
1962	97	1993	2,300
1963	329	1994	7,700
1964	619	1995	13,500
1965	887	1996	12,300
1966	1,025	1997	16,300
1967	913	1998	15,900
1968	734	1999	12,300
1969	874	2000	10,700
1970	450	2001	-11,800
1971	609	2002	-4,900
1972	806	2003	-1,500
1973	1,195	2004	3,300
1974	792	2005	4,300
1975	730	2006	14,960
1976	2,156	2007	19,650
1977	2,629

Source: Air Transport Association (http://www.airlines.org/economics/finance/World+Airline+Finance.htm, accessed on 26.02.09)

Note: The data above reflects the system wide activity of scheduled passenger and cargo airlines operating worldwide, as recorded by ICAO. Domestic operations within the former USSR are excluded prior to 1998.

Annexure 2

Annual Earnings – World Airlines

YEAR	Operating Results	YEAR	Operating Results
	Margin		Margin
	(%)		(%)
1947	-11.4	1978	5.3
1948	-3.6	1979	1
1949	-0.6	1980	-0.7
1950	2.7	1981	-0.7
1951	1.3	1982	-0.2
1952	-0.6	1983	2.1
1953	-0.1	1984	4.8
1954	1.3	1985	3.7
1955	2.6	1986	3.7
1956	2.4	1987	4.9
1957	-1	1988	6.1
1958	0.4	1989	4.3
1959	2.2	1990	-0.8
1960	0.6	1991	-0.2
1961	-2	1992	-0.8
1962	1.5	1993	1
1963	4.6	1994	3.1
1964	7.6	1995	5.1
1965	9.5	1996	4.4
1966	9.5	1997	5.6
1967	7.3	1998	5.4
1968	5.1	1999	4
1969	5.3	2000	3.3
1970	2.5	2001	-3.8
1971	3	2002	-1.6
1972	3.5	2003	-0.5
1973	4.4	2004	0.9
1974	2.4	2005	1
1975	1.9	2006	3.2
1976	5	2007	3.9
1977	5.2

Source: Air Transport Association (http://www.airlines.org/economics/finance/World+Airline+Finance.htm, accessed on 26.02.09)

Note: The data above reflects the system wide activity of scheduled passenger and cargo airlines operating worldwide, as recorded by ICAO. Domestic operations within the former USSR are excluded prior to 1998.

Annexure 3

Annual Earnings – World Airlines

YEAR	Net Results	YEAR	Net Results
	Profit		Profit
	($-mils)		($-mils)
1947	-135	1978	2,412
1948	-74	1979	588
1949	-42	1980	-919
1950	-10	1981	-1,150
1951	-21	1982	-1,300
1952	-45	1983	-700
1953	-52	1984	2,000
1954	-33	1985	2,100
1955	-11	1986	1,500
1956	15	1987	2,500
1957	-66	1988	5,000
1958	-46	1989	3,500
1959	-25	1990	-4,500
1960	-97	1991	-3,500
1961	-133	1992	-7,900
1962	-27	1993	-4,400
1963	106	1994	-200
1964	366	1995	4,500
1965	534	1996	5,300
1966	661	1997	8,550
1967	609	1998	8,200
1968	446	1999	8,500
1969	409	2000	3,700
1970	-10	2001	-13,000
1971	138	2002	-11,300
1972	234	2003	-7,560
1973	434	2004	-5,570
1974	41	2005	-4,100
1975	-67	2006	4,990
1976	825	2007	14,530
1977	1,656

Source: Air Transport Association (http://www.airlines.org/economics/finance/World+Airline+Finance.htm, accessed on 26.02.09)

Note: The data above reflects the system wide activity of scheduled passenger and cargo airlines operating worldwide, as recorded by ICAO. Domestic operations within the former USSR are excluded prior to 1998.

Annexure 4

Annual Earnings – World Airlines

YEAR	Net Results	YEAR	Net Results
	Margin		Margin
	(%)		(%)
1947	-11.4	1978	4.1
1948	-3.6	1979	0.8
1949	-0.6	1980	-1
1950	2.7	1981	-1.2
1951	1.3	1982	-1.4
1952	-0.6	1983	-0.7
1953	-0.1	1984	1.9
1954	1.3	1985	1.9
1955	2.6	1986	1.2
1956	2.4	1987	1.7
1957	-1	1988	3
1958	0.4	1989	2
1959	2.2	1990	-2.3
1960	0.6	1991	-1.7
1961	-2	1992	-3.6
1962	1.5	1993	-1.9
1963	4.6	1994	-0.1
1964	7.6	1995	1.7
1965	9.5	1996	1.9
1966	9.5	1997	2.9
1967	7.3	1998	2.8
1968	5.1	1999	2.8
1969	5.3	2000	1.1
1970	2.5	2001	-4.2
1971	3	2002	-3.7
1972	3.5	2003	-2.3
1973	4.4	2004	-1.5
1974	2.4	2005	-1
1975	1.9	2006	1.1
1976	5	2007	2.9
1977	5.2

Source: Air Transport Association (http://www.airlines.org/economics/finance/World+Airline+Finance.htm, accessed on 26.02.09)

Note: The data above reflects the system wide activity of scheduled passenger and cargo airlines operating worldwide, as recorded by ICAO. Domestic operations within the former USSR are excluded prior to 1998.

Annexure 5

What is Core Theory

 

Core Theory concepts are closely related to many standard economics concepts and are rooted in Game Theory. To keep the exposition simple, we do not discus these issues. The following definitions are necessary for understanding Core Theory. A numerical illustration and industry examples are included with the definitions.

Terminology And Definitions

Allocation: As individual buyers and sellers participate in a market they seek gains from their trading activities. The gains, each of the market participants receive from their individual trading activity is considered their allocation. In effect, the allocation is their pay-off for participating in the market.

Avoidable cost: The firm in the industry has the option of avoiding this cost. For example in the shipping industry the ship can decide to sail or not to sail and hence can avoid the cost associated with sailing (this decision is separate from cost of purchasing the ship). Similarly in the airline industry the aircraft may decide not to fly and can avoid fuel and other costs associated with flying (this decision is separate from the decision to acquire the aircraft).

Sunk cost: Expenditure, which cannot be recovered. The cost of purchasing a ship or an aircraft can be considered sunk cost.

Divisible vs. Indivisible demand: Divisible demand refers to situations where demand can be broken down into separate units. For example in ocean liner shipping where small packets are shipped or as in the case of airlines where each seat on the aircraft can be considered a separate unit which can be sold at different prices. Whereas in the case of indivisible demand it is not possible to divide demand into different units as in the case of bulk shipping.

Empty core: Situation where there is no stable equilibrium. In some industries, competition leads to an empty core problem.

In general the essential theoretical ideas of core theory can be set forth in this way.

1. There are a group of n individuals (or firms) in a market; some of who are buyers and others are sellers. They can all trade with each other in a single market, or in sub markets, or may decide not to trade at all.

2. The buyers and sellers can measure the gains from trade. For the buyer it is the maximum amount the buyer is willing to pay for the quantities purchased less the amount actually paid. For the seller, it is the amount actually received less the amount the seller would have been willing to accept.

Following Telser (1994), assume that there are three individuals; the first two are potential buyers of a widget, and the third is a seller. The seller S has a valuation of $10 for the widget. Buyer1 (B1) has a reservation price of $12 for the widget and buyer2 (B2) has a reservation price of $15. Let x denote the return to the seller and y1 and y2 denote the returns to the buyers, respectively. In case the seller sells the widget, he would settle for no less than $10 which is his option value, so that x 11 10. For the potential buyers y1 [mu] 0 and y2 [mu] 0, since each can refuse to make a purchase and thereby ensure a net gain of zero.

3. The buyers and sellers can contract with each other and form groups called coalitions to maximize their gains, or allocations, from trade. Such a process of contracting can be either unrestricted or restricted depending on the nature of the Industry.

With three members, there are a total of [2.sup.3] -1 = 7 possible coalitions, excluding the coalition with no members. These are {S}, {B1}, {B2}, {S, B1}, {S, B2}, {B1, B2}, {S, B1, B2}. Coalitions with single members are called singletons and coalition with all members is called the grand coalition.

4. An allocation is dominated if some members of the coalitions can do better for themselves by leaving one coalition and joining another coalition. If the members cannot do better by leaving their existing coalition then the allocation is undominated.

5. A buyer or a seller would be a member of a coalition as along as they can do at least as well as they could in any other coalition (it is important to point out that deciding not to trade or being alone is also a possible coalition). The approach is to consider all possible coalitions of traders; recognizing that any coalition of traders will only participate in the market as a whole if and only if they can do at least as well as they could in another coalition. In the decision of a member as to which coalition to join, the maximum payoff available in all other coalitions provides the lower bound.

Core theory considers all possible coalitions, including singleton coalitions. An implication is that, if a coalition forms instead of singletons, we can surmise that all the members believed that they were better off than they were being alone (pareto-optimal).

6. If we have a coalition with all the buyers and sellers in it (called the grand coalition) then it means that the each buyer and seller feels that this is the coalition which would maximize their gains otherwise they would not be in the coalition.

7. The grand coalition should therefore offer to each buyer and seller at least as much as they could get in any other coalition they can form i.e., it should be a undominated allocation. The allocation from each possible coalition therefore imposes a lower bound on the payoff for each member, which must be satisfied for the grand coalition to exist. Since we include all possible grouping--i.e., singletons, 2-person, 3-person etc. till n-person coalitions, the grand coalition should satisfy the constraints imposed by all coalitions.

8. If there exists no other coalition, which can make at least one person better off without making another person worse off, then economists call such a situation "Pareto Optimum". An allocation is an efficient allocation if it is a Pareto optimal allocation. It follows that any coalition, which survives all the restrictions imposed, by all the coalitions is a pareto-optimal solution.

9. If such a "grand coalition" exists which is an efficient allocation for all concerned, then we say that a core exists. The core therefore consists of all the undominated allocations. A grand coalition is a market in which all buyers and sellers are present. If a grand coalition is the core, then all members choose to be in the market-like many-to-many relationship rather than forming sub-markets or groups.

10. The core may sometimes have either one allocation or many allocations. It is also possible that there may not be any allocation in the core. This is called an empty core. The empty core implies that there is no stable coalition. Whatever coalition can be formed, there is always an incentive for some subgroup to benefit by leaving it. When the core is empty, there is no pareto-optimal situation. In the specific context, it means that members may switch among multiple coalitions opportunistically. Telser (1987) uses the word "chaos" to describe this situation.

In formal terms, the notion of the core stems from the theories of cooperative games. There are various version of these, of which the Nash cooperative solution (Nash, 1950; 1953) has been attracting the most attention recently, although the number of those who have read the salient papers probably do not constitute enough to be depicted in a three dimensional diagram. Nash focused on situations where coalitions may be formed of actors in a market but where side payments are not allowed. In other words, situations where the pay-offs of forming any coalition are not transferable between the parties involved. The literature on the core has been of the variety where side payments are possible. This means that one is not looking at a coalition where there is a Pareto improvement but rather one where there is a potential Pareto gain in the Hicks-Kaldor tradition. It is assumed that every coalition exercises the same degree of rationality as an individual, so that the imputation (P) allocates to each coalition at least as much as could be obtained by independent action. Imputations are vectors in Euclidean n-space summarizing the pay-offs to each player. Hence Pn in a three player game could be (0.2, 0.7. 0.1) where player 1 receives 0.2, player 2 receives 0.7, and player 3 receives 0.1. With all players and pay-offs accounted for, the total pay-off equals the pay-off of the grand coalition of players.

To illustrate the conditions for a core to exist we assume that there are three players in the market (1, 2, 3) with a

three game characteristic function form:

v(f) = 0

v(1) = 0, v(2) = 0, v(3) = 0

v(1, 2) = 0.1, v(1, 3) = 0.3, v(2, 3) = 0.3

v(1, 2, 3) = v(N) = 1

where N is the set of players {1, 2,…,n}.

 

The core is the set of all undominated imputations. It is that set of imputations (Π = Π1, Π2,…,, Πn) that satisfies:

 

∑Πi ≥ v(S)for every subset S of N where N is the number of players.

 

Source: Raghavan & Raghavan and Burton

19

 

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[1] Why Air Travel Does’nt Work, Fortune, April 3, 1995

[2] The Usefulness of Core Theory in Economics, Lester G. Telser; Journal of Economic Perspectives, 8(2), 1994. (http://docs.google.com/fileview?id=F.c37ca0ec-e410-49bb-9afe-8b8d9696768c&hl=en; accessed on 22.02.09)

[3] See Annexure 5 for a detailed exposition

[4] Telser; opcit

[5] Avoidable cost is defined as the cost that a firm has the option to avoid. For example, in the airline industry an airline has the option not to fly an aircraft and avoid fuel and other costs associated with flying. Also see Annexure 5.

[6] Sunk cost is expenditure that cannot be recovered. For example, the cost of purchase of an aircraft. Also see Annexure 5