Journal of Revenue and Pricing Management - DalleMule 20081a

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Implications and effectiveness of iterated

pricing games in the Brazilian retail market

Leandro L. DalleMuleÃ

Received (in revised form): 12th December, 2007

Ã

95-34 Intervale Rd, Stamford, CT 06905, USATel: þ 1 203 979 3981; Fax: þ 1 212 655 8291; E-mail: [email protected]

Leandro L. DalleMule holds a master’s in

business administration in managerial eco-

nomics and decision sciences from the Kellogg

School of Management at Northwestern Uni-

versity, a bachelor’s degree in mechanical engineering from University of Sao Paulo,

Brazil and is currently pursuing an advanced

graduate degree in applied mathematics from

Columbia University. He has several years of

experience in pricing, marketing, and risk

management for the oil and gas and financial

services industries. He currently works in the

Pricing and Revenue Management practice in

the New York office of Deloitte & Touche USA

LLP, a major consultancy firm.

ABSTRACT

KEYWORDS: game theory, tit for tat, retail,

pricing, gasoline

Retail pricing is often a complex non-zero sum,

iterated game played by both analytically sophisti-

cated businesses and strategically primitive ones.

Game theory can help retailers avoid, survive, and

win pricing wars — but it is undoubtedly not a

trivial endeavour. This paper analyses how a tit for

tat pricing strategy can be successfully utilised against multiple opponents through an example drawn from

the Brazilian gasoline retail market. Although

ultimately successful, the pricing strategy adopted by

oil companies cost them approximately $15m per

year in forgone profits or $214,000 per gas station.

A relatively high price to pay in a small countryside

city in Brazil.

Journal of Revenue and Pricing Management

advance online publication, 7 March 2008;

doi:10.1057/rpm.2008.1

INTRODUCTIONBig box retailers or hypermarkets, such as Wal-

Mart and Carrefour, discovered that selling

low-priced gasoline can generate incremental

traffic into their stores. This trend began in

France and England about 14 years ago. In

1997, it expanded into Latin America through

Carrefour and Wal-Mart, with 11 stores in

Brazil and 15 in Argentina. All those markets

experienced a dramatic reduction in margins

following hypermarkets’ entry.

Major oil companies in the United States

also experienced significant decreases in profit

due to hypermarkets’ move into the retail

gasoline market. The 2003 OPIS Retail Year in

Review also showed that in these new

hypermarket areas, gasoline was often sold near

cost. Gasoline margins in the US averaged just

6.7 cents per gallon during first quarter of

2002, down substantially from 10.8 cents/

gallon in 2001. But markets where big retailers

offered gasoline fared even worse, with margins

ranging from 1.6 to 3.1 cents per gallon.

What is the best strategy for the oilcompanies to retain their profits and compete

effectively with hypermarkets’ gasoline sta-

tions? The purpose of this paper is to analyse

how game theory strategies can be applied to

retail pricing through a case study of a major

oil company that successfully reacted to a

hypermarket in Brazil.

www.palgrave-journals.com/rpm

&2008 Palgrave Macmillan Ltd, 1476-6930 $30.00 1–10 Journal of Revenue and Pricing Management 1



AN OVERVIEW OF THE PRISONER’S

DILEMMA AND TIT FOR TAT STRATEGY

In game theory, the prisoner’s dilemma is a

variation of a non-zero sum game in which

two players may each ‘cooperate’ with or

‘defect’ (ie cheat or betray) the other player.

In the prisoner’s dilemma game the only

concern of each individual player is maximising

his own payoff, without any concern for the

other player’s payoff. In the traditional form of

this game, the cooperating strategy is generally

dominated by the defecting strategy, so that the

only possible equilibrium for the game is for all

players to defect. In other words, rational

choice leads the two players to both play defect

even though each player’s individual reward

would be greater if they both played cooperate,thus the dilemma.

In the classical prisoner’s dilemma, two

suspects, A and B, are arrested by the police.

The police have insufficient evidence for

convicting any. The police officer isolated both

suspects in separate rooms, offering both the

same deal: ‘if you testify for the prosecution

against your partner and he remains silent, you

will walk free and your silent accomplice will

receive the full 10-year sentence’. If both

suspects stay silent, both are sentenced to only

six months in jail for a minor charge. If each

suspect betrays the other, each receives a five-

year sentence. Each suspect must make the

choice of whether to betray the other or to

remain silent. However, neither one knows for

sure what choice the other will make.

In the iterated prisoner’s dilemma the game

is played repeatedly. Thus each player has an

opportunity to ‘punish’ the other player for

previous noncooperative play. Then, coopera-

tion may then arise as an equilibrium outcome

(ie a Nash-equilibrium). The incentive todefect can be overcome by the threat of

punishment, leading to the possibility of a

cooperative outcome.

Tit for tat is one of the simplest, easiest, and

most effective strategies for the iterated prison-

er’s dilemma. It is the strategy of starting with

cooperation and then, in the subsequent moves,

doing whatever the other player did on the

previous move. For instance, if one player cheats

on the fourth move, the other cheats on the

fifth. Tit for tat is founded on reciprocity and is

dependent on four conditions:

(1) unless provoked, the agent will always

cooperate

(2) if provoked, the agent will retaliate in the

next iteration

(3) the agent is quick to forgive (ie next

iteration)

(4) the agent must have a good chance of compet-

ing against the opponent more than once.

The key dependency of tit for tat is that the

competition continues long enough for re-

peated punishment and forgiveness to generatepositive payoffs for both players in the long

term, offsetting potential losses caused by

initially attempting cooperation.

The effectiveness of tit for tat can be seen in

biology, politics, war, and business, among

other fields. Its surprisingly simple proprieties

make it difficult to believe that it can

succeed over more complex and ‘intelligent’

strategies.

Critics of prisoner’s dilemma and tit for tat

often cite the collusive behaviour that such

strategies can incite in economics and indeed

there is a fine line between cooperation risen

from tit for tat pricing strategies and cartel price

fixing. This study aims at analysing the effects

of tit for tat pricing strategies in the retail

market, not debating whether the legal in-

tricacies of oligopoly pricing. Other strong

criticism to the prisoners’ dilemma is that it is

too simple to characterise complicated eco-

nomic relationships. However, even the com-

plexities of large and subtle situations can also

be expressed mathematically through gametheory frameworks such as the prisoner’s

dilemma (May et al., 1995).

THE BRAZILIAN RETAIL GASOLINE

MARKET

Gasoline prices in Brazil were fully controlled

by the government until 1995. Until then, the

Journal of Revenue and Pricing Management 1–10&

2008 Palgrave Macmillan Ltd, 1476-6930 $30.002

Implications and effectiveness of iterated pricing games in the Brazilian retail market



country had experienced frequent and long

periods of hyperinflation, sometimes momen-

tarily interrupted by unsuccessful economic

plans. As a consequence, consumers were not

aware of gasoline prices and gas stations did not

know how to compete on prices — service was

the sole differentiator.

After the oil and gas market deregulation in

1995, the gasoline retail market enjoyed a brief

period of tranquility and, with only five major

companies operating in the country, oligopoly

competition was an achievable, profitable way

to do business. Nevertheless, as any economist

would expect, from 1997 onwards high profits

were threatened by several new entrants.

Among these new entrants, big-box retailers

started looking at the gasoline retail marketwith greater interest.

The first big-box retailer to enter the market

was the French Carrefour. With large grocery

stores established in high-traffic locations in

Brazil, Carrefour could easily execute the same

business plan hypermarkets had successfully

implemented in France and England in the

mid-1980s. Their plan was to build gas stations

on the parking lot of their stores and offer the

lowest-priced gasoline, either through their

own or a white-label brand.

For hypermarkets, gasoline was not viewed

as a product itself, but as a means to increase

store traffic. As long as the marginal cost of fuel

equalled its marginal revenue, such investment

would quickly pay off. There were also

additional benefits from offering the lowest-

price gasoline such as a reinforced everyday

low-price brand image and extra revenue

from car-washing, lubricants, and convenience

products.

THE CASE STUDY OF A MAJOR OILCOMPANY’S PRICING REACTION TO A

HYPERMARKET

The case study takes place in the countryside of

the state of Sao Paulo, Brazil between 1996 and

2000. Test and control markets were established

based on statistically equivalent historical sales

and pricing patterns. The test market had

approximately 70 service stations of traditional

multinational and national oil companies

(Exxon, Shell, Texaco, BR, etc). The control

group is an average of several small markets in

Brazil, with comparable gasoline sales and

population size.

In 1996 a major international hypermarket

chain built a gasoline station on its parking lot,

hereto described as the ‘hypermarket gas

station’. In a matter of weeks after its opening,

the hypermarket gas station was offering the

lowest price in that market, 10–15 per cent

below the traditional companies, what drove

sales to approximately 1 million litres a month

(264,000 gallons), 4–5 times more than the

average traditional gas station.

In order to inhibit hypermarkets’ growthand avoid repeating what had happened in

Europe, a major international oil company,

‘company A’, adopted an aggressive pricing

strategy in Brazil. Including the studied market,

in each of the 11 cities where the hypermarket

gas stations were practicing the lowest-price

strategy, oil company A responded by matching

prices to the last decimal place. If hypermarket

gas station prices went up, so did company A’s,

usually in a matter of hours.

Such pricing strategy was followed by an

equally aggressive communication material —

‘We Match Hypermarket Gas Station Prices’

— and a quick feedback system. In other

words, the oil company A was able to change

prices 3 or 4 times a day if necessary, in all of its

stations for a given market to match hyper-

market’s prices as quickly as possible. Such

strategy fits very well in the tit for tat framework

described earlier, which is used as the basis for

this analysis.

In the studied market, approximately three

months into the hypermarket reaction pro-gramme, oil company A experienced volume

increases of more than 300 per cent, motivating

other traditional oil companies to react by

adopting a similar pricing strategy. Such

abnormal volume increase came from company

A’s traditional competitors, not the hypermar-

ket gas station itself. Consequently, other oil


DalleMule



companies had to choose either entering the

fight or going bankrupt.

Nearly all 70 traditional gas stations entered

the game nine months after the price war had

begun, hence pushing the average sales per

station back to historical levels. Volumes went

down and so did prices. The return to market

equilibrium at lower prices consumed all

incremental, volume-driven profit realised by

first comers’ matching hypermarket gas station

prices. Gasoline prices remained significantly

below comparable markets without hypermar-

ket gas stations, driving profitability for the

entire test market near zero or into negative

territory in a few cases.

Although the events that took place during

the price war are certainly interesting toanalyse, even more intriguing is what happened

to prices after the war ended. In markets where

a tit for tat pricing strategy was adopted, prices

not only returned to the national market level

but also continued to go up, outperforming

markets without hypermarket gas stations

shortly after the war was over (Figure 1).

How would cooperation emerge spontaneously

among fierce competitors without collusion?

What drove the price gradient observed in the

test market?

Generally, if markets are well integrated,

prices will tend to move up and down together.

Therefore, changes in relative prices indicate a

change in market structure, technology, regula-

tion, or some other factor. The retail gasoline

market in Brazil is relatively small and well

integrated. During the period analysed, there

were no significant differences in technology or

regulation among the test and control markets

studied. Moreover, refineries were controlled

by the government’s oil company (Petrobras),

what to a great extent equalised gasoline rack

prices across markets and distributors. There-

fore, as the following analyses will attempt to

explain, some other factor was responsible for

the price differential seen in hypermarket

markets.

ANALYSIS OF A TWO-STAGE PRICING

GAME USING TIT FOR TAT

In the case study described above, despite oil

company A’s best efforts to impact the

hypermarket gas station profits and discourage

other hypermarkets from entering the market,

the actual impact on the big-box retailer

profitability was initially negligible. As ex-

plained earlier, the soar in volume experienced

by company A after it matched hypermarket

* Data from IBGE (Brazilian Institute if Statistics) based on pump-prices in all major cities. Prices were adjusted to inflation and

governmental price increase.

0.4

0.45

0.5

0.55

0.6

1 11 21 31 41 51 61 71 81 91

Control Group (National Price Level, No War) Test Group (Hypermarket Pesent, Tit for tat Employed)

Months

Average Gasoline Monthly Prices in USD/Liter for Test and Control(1994-2002)*

Tit for tat pricing strategy

Figure 1: During the period when tit for tat pricing strategy was executed, prices in the test group exhibited a

significantly different behaviour when compared to the control group






gas station prices occurred mainly because it

captured existing demand from the other

traditional 70 stations, not necessarily from

the hypermarket gas station itself.

Had this game ended before the other oil

companies reacted to company A or had

company A withdrawn after a few iterations,

this would have been a classic always defect

strategy that would have never achieved

cooperation. Likely, market prices would have

returned to national average level soon after

company A’s pull back and the hypermarket gas

station would have continued its lowest-price

strategy intact. Under a short-lived game with

limited iterations, oil company A would have

gained a few extra dollars from the temporary

volume gain but would have failed to hinder hypermarkets’ expansion in Brazil.

Oil company A, however, did not withdraw,

‘forcing’ the other traditional oil companies to

adopt the same pricing strategy in order to

contain their revenue leakage to company A’s

stations. This marks the beginning of a second

game that will ultimately affect hypermarket

gas station’s results and lead to cooperation in

the marketplace — although interestingly enough,

company A’s end goal was always to deter

hypermarkets’ growth into the Brazilian gasoline

retail market, not to achieve cooperation.

Based on this rationale, the analysis of the

pricing game against the hypermarket gas

station can be separated in two different, yet

connected, stages. The first stage being played

between oil company A versus other traditional

oil companies, with little or no participation of

the hypermarket gas station. The second stage

being played by all traditional oil companies

against the hypermarket gas station. Players,

results, and strategies are very different in each

stage.In the first stage of the game (Figure 2),

company A’s gas stations alone did not

represent a credible threat to hypermarket gas

station profits and volumes and therefore, the

reciprocity aspect of tit for tat strategy was never

triggered. Although the original plan devised

by company A’s management was to execute tit

for tat against the hypermarket gas station, it did

not happen at first, the main reason being that

the hypermarket gas station payoffs were not

directly dependent upon Company A’s prices.

In order to meaningfully impact the sales

volume of the hypermarket gas station, the

majority of all other 70 traditional gas stations

had to join the game. Thus, initially company

A was playing an always defect strategy with all

other stations. In fact, during stage I owners

and managers of other traditional stations did

not understand what company A was doing and

why it had suddenly become so aggressive.

Company A’s pricing actions were not a

function of how other stations were playing,

even though they were directly competing for

volume. Consequently, the other gas stationsdid not react immediately to the new prices

implemented by company A’s stations and

underwent a steep sales and profit decline.

The game played between company A and

its traditional competitors was as important as

the game played between Company A and the

hypermarket gas station because it fostered the

Shell

Elf

Texaco

Exxon

BP

Company

A

Hypermarket

Always Defect

T i t

f o r T

a t

D e f e

c t

D e f e c t

D e

f e c t

D e f e c

t

D e f e c t

Shell

Elf

Texaco

Exxon

BP

Company

A

Hypermarket

Always Defect

T i t

f o r T

a t

D e f e

c t

D e f e c t

D e

f e c t

D e f e c

t

D e f e c t

Shell

Elf

Texaco

Exxon

BP

Company

A

Hypermarket

Always Defect

T i t

f o r T

a t

D e f e

c t

D e f e c t

D e

f e c t

D e f e c

t

D e f e c t

Shell

Elf

Texaco

Exxon

BP

Company

A

Hypermarket

Always Defect

T i t

f o r T

a t

D e f e

c t

D e f e c t

D e

f e c t

D e f e c

t

D e f e c t

Stage One Game

The other players viewed game as the scheme above. In spite of

company A playing tit for tat against the hyperma rket, effectively

to the other oil companies, company A was playing ‘always

defect’ strategy.

Figure 2: In the first stage of the pricing game,

company A’s strategy represented a threat to all

other gasoline brands, not only the hypermarket gas

station as originally designed


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environment to impact hypermarket’s beha-

viour, which ultimately led to cooperation.

The second stage of the game (Figure 3)

began when all traditional oil company stations

jointly, yet independently, moved against the

hypermarket gas station. Then the new players

were the group of traditional oil companies and

the hypermarket gas station. The game still

fitted nicely into the iterated prisoner’s dilem-

ma framework, utilised to analyse the results.

In the second stage of the game, the

combined retaliatory power of the 70 tradi-

tional oil stations did impact hypermarket gas

station results, compelling it to react. Only in

stage 2 is that tit for tat pricing strategy started

being effectively executed by all players.

Multiple-stage pricing games can take long-

er to achieve cooperation than a straightfor-ward tit for tat , hurting players’ profitability to a

greater extent. The initial noncooperative

behaviour (always defect strategy) causes extended

periods of losses, making it more difficult for

participants to understand the rules of the game

and what it takes to achieve cooperation.

Conversely, empirical evidence from this case

showed that once cooperation is established, it

is resistant to external influences to cheat or

defect or to invasions of other strategies.

The prevalence of cooperation, however,

depended greatly on players’ confidence that

they were engaged in a long-term relationship.

The recently stabilized Brazilian economy

supported the foundation of sustained coopera-

tion in the case analysed. Players were able to

focus not only on short-term profitability, but

also on long-term results. During periods of

economic uncertainty or high inflation, it is

more difficult to achieve cooperation through

tit for tat pricing strategy. In these cases, a more

aggressive strategy based on frequent defects

appears to be more commonly adopted than

cooperative ones.

QUANTITATIVE ANALYSIS OF CASE

STUDY RESULTS

Two statistical analyses were conducted with

the intention of verifying whether the price

behaviour observed in the test group was

significantly different than the control group.

Shell

Elf

Texaco

Exxon

BP

CompanyA

Shell

Elf

Texaco

Exxon

BP

Shell

Elf

Texaco

Exxon

BP

Stage Two Game

Shell

Elf

Texaco

Exxon

BP

CompanyA

HypermarketAlways Defect

& TFT

During the second stage of the game all players have a commonopponent: the hypermarket. Then, under this perspective, the strategy

becomes effectively as tit for tat.

T i t f o

r T

a t

T i t

f o r T

a t

T i t f

o r T a t

T i t f o

r T a t

T i t f o r T a t

T i t f o r T a t

Figure 3: In the second stage of the pricing game, all major gasoline brands compete against the

hypermarket gas station, creating the basis for future cooperation






Prices were adjusted for inflation and uniform

governmental increases prior to the deregulation.

Initially, hypothesis testing analysis was

performed on monthly gasoline prices for both

test and control markets. The alternative

hypothesis was framed based on the premise

that prices in the study market (test) are different

from the market (control) prices. Until oil company

A began to execute tit for tat , gasoline prices in

the test market were not statistically different

from the average market prices or control

group, except for a couple of randomly sparse

months. After company A began reacting to the

hypermarket gas station, gasoline prices in the

test market differed significantly and consis-

tently from the control group.

Subsequently, so as to quantify the pricedifferences between test and control markets, an

ordinary least squares regression model was built.

During the war, prices fell on average US$0.10

per gallon or approximately 5 per cent in the test

versus control market. While the average price

reduction for the test market may seem low, it

did mean that all 70 stations in that market

reduced their prices by 5 per cent on average

during approximately two and half years.

This represents approximately $15m per

year in forgone profits or $214,000 lost per

gas station due to the price war. Nonetheless,

post-war prices increased on average by

approximately 4 per cent versus prices before

the war.

SIMULATION OF NON-ZERO SUM

PRICING GAMES IN RETAIL GASOLINE

In the case study, the execution of a tit for tat

pricing strategy ultimately resulted in coopera-

tive behaviour from both players. Nonetheless,

a thorough understanding of the implications

of tit for tat in pricing demands that alternativescenarios be studied as well. To achieve that, a

two-player tit for tat simulation program was

developed based on economical and beha-

vioural characteristics found in the case study.

In the simulation program, player 1 always

plays tit for tat and player 2 can play multiple

strategies depending on market conditions.

Initially, player 2 always plays a random,

unconditional, and uninformed strategy, that

is, it has no preference for defecting or

cooperating and is completely independent of

player 1’s actions. The total market in the

simulation is formed by the two players only.

In each iteration, defection or cooperation

affects prices in increments of $0.01 per litre.

The starting gasoline margin is assumed to be

$0.10 per litre — analogous to the case study

environment. Based also on empirical results,

neither player can sustain margins equal or less

than zero for more than consecutive three

months. If the program finds such pattern, it

changes player 2’s behaviour from a random to

a tit for tat strategy. Player 1 will at all times play

tit for tat independently of its profit margins or player 2’s actions.

Lastly, price thresholds were incorporated

into the program so that prices can neither

increase nor decrease indefinitely. Threshold

values were based on the retail gasoline market

equilibrium and estimated demand curve at the

time of the case study. The lower limit is set

when the program detects a pattern of infinite

losses (or multiple defections). The starting

reference price is the average pump price in

1994. A total of 500 simulations were run.

SIMULATION RESULTS

Even though player 2 would begin playing tit

for tat after a maximum of three months of

negative or zero margins, player 2’s initial

irrational pricing strategy still led to non-

cooperative final results. After 115 iterations,

more than 90 per cent of the 500 simulations

(Figure 4) ended in a noncooperative outcome.

On the short run, tit for tat always lost against

any other aggressive or irrational strategy, driving

negative payoffs for all players until marginsbecame zero. What is somewhat unexpected is

that even when all players played tit for tat ,

cooperation did not emerge often enough to

offset the profitability damage caused during the

noncooperative part of the game.

If a player chooses to use tit for tat against an

unconditional and uninformed opponent, it


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must be aware of the elevated likelihood of

incurring high costs and still not achieving

cooperation. Only approximately 10 per cent

of the simulation output showed that coopera-tion was achieved (Figure 5). Nonetheless,

expected additional profitability from coopera-

tion was not enough to offset the expected

losses incurred during the noncooperative phase

even during the five-year period analysed.

A further drill down on the causes of

extended noncooperative behaviour showed

that it often occurred when player 2 defected

just after it had switched strategies — from

random to tit for tat . The outcome is an

unending echo of alternating defections fromboth players, resulting in a sustained, self-

reinforcing, noncooperative behaviour, even

though both players had adopted tit for tat .

It is key to understand that tit for tat is not

forgiving enough to revert the self-destruction

behaviour observed in the simulation model. In

other words, one player will have to give up

Figure 4: The probability map generated by the model shows that, after the tit for tat strategy started in month

42, prices have a strong tendency to drop, stabilising in month 72, 18 per cent below where they were before

the price war

0.4

0.45

0.5

0.55

0.6

1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1

Simulation Cooperative

Average Gasoline Montlhy Prices - Actual vs. SimulationCooperative Behavior Frequency of Price Results in Cooperative Outcomes

P r i c e I n d e x ( 1 0 0 = P r e - G a m e )

Actual Prices from 1994-2002 Study Market

Σ

Figure 5: While the tit for tat strategy can potentially lead to a cooperative outcome, the model shows that the

frequency of such results is approximately only 10 per cent






and be ‘more’ forgiving than the other. A

potential solution when two retaliatory strate-

gies continuously defect against each other is

called a tit for two tats. A tit for two tats player will

let the first defection go unchallenged as a

means to avoid the ‘death spiral’ of the previous

example. Only if the opponent defects twice in

a row, the tit for two tats player will respond by

defecting.

Employing tit for two tats against an irra-

tional, unconditional opponent can be the

solution to avoid the high likelihood of

noncooperative results seen in the tit for tat

simulation model (Figure 6). By changing

player 1’s strategy to tit for two tats and keeping

all other assumptions and rules constant, theprobability of cooperative behaviour increased

to close to 100 per cent.

CONCLUSION

As in biology, warfare, and politics, tit for tat

seems to be a great strategy to help businesses

achieve a hard-to-invade state of cooperation.

Cooperation in this case means that players will

act individually but still achieve the best

collective outcome for the group, not engaging

themselves in a competitive ‘death spiral’ that

can lead to mutual extinction.

The application of tit for tat strategies,

particularly in retail pricing, must be carefully

examined and executed, from strategic, opera-

tional, and regulatory points of view. The

analyses undertaken on this paper focused on

the strategic aspects of achieving a cooperative

Nash equilibrium in retail pricing. Further

analyses are required on the legal, regulatory,

and operational realms to assess the complete

implications of game theory in retail pricing.

Nonetheless, the paper supports a few strategickey takeaways to achieving cooperation

through tit for tat retail pricing:

1. Clearly communicate your actions, showing the

reciprocity nature of your strategy as well as your

retaliatory power. Make the strategy credible

and establish a visible pattern for your moves.

2. Expect short-term economic losses. If

playing against aggressive or irrational

opponents, consider adopting alternative

strategies such as tit for two tats to foster

cooperation and prevent mutual destruction

from tit for tat’s more retaliatory nature.

3. Ensure to have enough economic power

before entering the game. When the

opponent executes an unconditional, unin-

formed strategy the game is likely to have

two stages, taking longer and making it

more difficult to achieve cooperation.

4. Employ the tit for tat strategy in small

markets with less than 100 players, so all

can converge to a common strategy sooner

and increase the resistance to invasive andmore aggressive strategies.

5. Retaliate quickly to defection and reward

quickly to cooperation. By reacting to every

single move in a short period of time, two

things happen: the retaliatory nature of tit for

tat is clearly communicated and the period

of losses (or low profitability) is reduced.

Figure 6: The probability map generated by the model shows that after the tit for two tats strategy

started in month 42, prices have a strong

tendency to drop initially; however, after 50

months into the pricing war, cooperation is

achieved and prices stabilise 10 per cent higher

than where they were before the price war


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6. Intelligence and emotion play a fundamental

role in pricing games and can affect positively

or negatively the outcome. A pure logical

and rational approach to the problem is likely

to lead both competitors to destruction.

7. High likelihood of future relationship be-

tween players is fundamental to achieving

cooperation. As shown, cooperation can

emerge between self-centred egoist players if

they are likely to do business in the long term.

8. The higher the sunk costs, the higher the

willingness to cooperate. When retailers

have an unrecoverable high stake in the

business, they tend to increase their efforts

to achieve cooperation.

REFERENCES

2003 OPIS Retail Year in Review, published by

OPIS Retail Fuel Watch, a division of the Oil Price

Information Service (OPIS ).

May, R. M., Nowak, M. and Sigmund, K. (1995)

‘The arithmetic of mutual help’, Scientific Amer-

ican, 272, 676–81.

Stigler, G. J. (1964) ‘A theory of oligopoly’, Journal

of Political Economy, 72, 1, 44–61.

APPENDIX

The ordinary least model utilised in thequantitative analysis above aimed at quantifying

the differences in prices during three indepen-

dent periods: before price war, during war, and

post-war. Although the model lacks variables

needed to understand causality, it confirms the

hypothesis testing results described before.

OLS Model Functional Form:

f ðTestPricesÞ ¼ c þ bÃ1Price Before War

þ bÃ2Price During War

þ bÃ3Price Post War þ e

Results:

Variables Coefficient

(USD/

Litre)

Relevance

at a o5%

Description

Before

war

Dropped N /A Categorical

dummy variable

for period before

price war

During

war

À0.026 High Categor ical

dummy variablefor

noncooperative

behaviour

Post

war

+0.021 High Categor ical

dummy variable

for period when

cooperative

behaviour was

achieved

Month À0.00003 Not

significant

Month

Constant 0.523 High Cents per litre

The overall model is highly significant F = 45.21,

but as expected due to lack of variables, adjusted R 2

is relatively low at 58 per cent. Alpha values smaller

than 5 per cent were assumed in this analysis,

supporting the elevated confidence in the results

given the relative small size of the population

J l f R d P i i M m t 1 10&

2008 P l M ill Ltd 1476 6930 $30 0010


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