This paper was written as a part of a course assignment for the Business Policy and Strategy course taught by Prof. Avinash Nene at SICSR. The material has been adapted from the COURSERA MOOC for Competitive Strategy taught by Prof. Tobias Kretschmer at LMU Munich and a few other sources. I have tried to build relevant examples by myself.
In
this paper I will try to explore the different strategies for 2 player matrix
form games. 2 player matrix form games are those games that can be expressed in
the form of 2 competitors having 2 alternative strategies. This would typically
be 2 competitors having identical or similar products which could be priced low
or high.
Consider
2 toothpaste brands in the market, Colgate and Dabur. Both of these could price
their product low or high. Assuming infinite price elasticity of demand, the
brand with the lower price would get all the demand in the market. If both charge
a high price they split the market equally. Similarly if they both charge a low
price, they split the market equally and in this case their profits are lower.
|
|
Colgate
(high)
|
Colgate
(low)
|
|
Dabur
(high)
|
15/15
|
0/20
|
|
Dabur
(low)
|
20/0
|
10/10
|
The
above matrix indicates the 2 strategies for each player and the possible pay
offs for each. If Colgate and Dabur both charge a high price, they share the
market and get payoffs of 10 each. If they both charge a low price, they again
share the market and get payoffs of 5 each. If either one charges a low price
and the other high, the one charging low price gets the entire market. If the 2
firms co-operate, they both charge a high price and each gets a payoff of 15. However,
in this situation they are both incentivized to deviate and charge a low price
since they can improve their pay offs to 20 in this case.
If
Dabur alone charges a low price, Dabur gets the entire market with a payoff of
20. In this situation, Colgate is incentivized to charge a low price as well.
They both end up charging a low a price and split the market equally with pay
off of 10 each. Once they both charge the low price, they are not incentivized
to deviate from this position. This situation is called the “Nash Equilibrium”,
named after the mathematician John Nash.
In a Nash Equilibrium, none of the
2 competitors are incentivized to deviate from their market positions. A pure-strategy Nash equilibrium is an
action profile with the property that no single player can obtain a higher pay off
by deviating unilaterally from this profile.
Similar situation arises during the
pricing of telecom spectra where in the telecom operators could co-operate and
bid low to lower their costs and increase their payoffs. However, this does not
happen and they deviate to bid high to win the spectrum and end up with high
costs and lower pay offs than if they would have co-operated.
In this form of game, both the
competitors act selfishly to lead the game to an outcome which is not mutually
beneficial. Consider the game below: If none of the competitors advertise,
their payoffs split equally at 10 each. If any one competitor advertises, they
get the entire market (20) and their pay offs are 15 (less the cost of
advertising). However, if any one advertises, the other competitor is also incentivized
to advertise and they both end up advertising and making a lower payoff of 5
each. This situation is known as the “Prisoner’s Dilemma”, where in they could
get higher payoffs if they co-operate but instead they choose to act selfishly
and this lowers their pay offs. The Prisoner’s Dilemma is also a form of Nash
Equilibrium.
|
|
Colgate
(advertise)
|
Colgate
(not advertise)
|
|
Dabur
(advertise)
|
5/5
|
15/0
|
|
Dabur
(not advertise)
|
0/15
|
10/10
|
Here in a simultaneous game is
plotted as a sequential game with one of the players taking the lead. Often,
who takes the lead decides the outcome of the game. Consider a product
placement offer made by the James Bond movie producer to Sony, where in they showcase
James Bond using Sony Vaio laptops. This could boost their sales by $0.5 million
and would cost them a million dollars. If Sony refuse the product placement
offer, James Bond movie producer goes to Apple with the same offer. If Apple
accepts the offer, they stand to gain $1.5 million dollars and Sony would lose
$0.7 million. The costs are the same. In this case, Sony would be incentivized
to go ahead with the product placement even though they would incur a loss in
this process. This is evident from backward induction given full knowledge of
the game in advance.
Decision trees can be plotted to
analyze and aid the understanding of this game. Such a sequential analysis
could be used to analyze a simultaneous game and arrive the possible future
outcomes if are not sure of the competitors strategy.
The above figure
depicts the game tree for the case of the movie ET approaching Mars and Hershey
for product placement. The slide is from the MOOC course on Competitive
Strategy available on Coursera.
Simultaneous games described before
could be converted to sequential games described here by aggressive commitment or early mover strategies. These could
potentially alter the outcome in favor of the first mover.
Consider the case of Boeing and
Airbus. They both make jumbo jets. It is found that the market for air travel
could sustain the development of one new airliner. If both make a new airliner,
none of them is able to break even. What Airbus did was moved first and set up
a massive manufacturing capacity in Toulouse, France before the product
development was complete. They were able to start taking orders earlier and got
a significant market share from that. This is a form of an aggressive
commitment strategy that converts a simultaneous game into sequential game in
favor of the first mover. Aggressive commitment is called the hawk-dove strategy where in the
aggressive mover is the hawk and tries to recover an investment in spite of
higher costs.
In this section, we analyze the
impact of game repetitions to the strategy of a 2 player matrix form game. If
the game has a finite number of repetitions, we expect the players to
co-operate till the final repetition. In the final repetition, they will not co-operate
and they could misbehave without getting punished for the same. Consider the
game of soccer. A player is allowed 2 yellow cards before he or she gets a red
card. As a result, you see more yellow cards towards the end of the game then
during the early stages of the game. This is also known as the End Game Effect.
This usually becomes prominent
during the bankruptcy proceedings of a company. When a company is on the verge
of bankruptcy and requires significant debt restructuring, there are more
incentives to misbehave then to co-operate.
When GM was on the
verge of bankruptcy and asked for debt restructuring in 2008, the government
bought a controlling stake in GM. The US Government sold off its stake for a
handsome profit after GM was back in the black a few years later.
Greece could ask
for a similar debt restructuring from EU to extend its 30 year loans to 50 year
loans and reduce the debt payments. In return, EU could get a controlling stake
in Greece through a majority vote in Greek Parliament. This could avoid the End
Game Effect that has produced the stale mate in present debt negotiations.
In this case, the game can be
repeated a multiple number of times and the number of repetitions is not known.
For example, you have a burger stand at the IPL stadium and set the price of
your burgers everyday with new offers given out to cricket fans every day.
An important application of such
games is in the diamond industry where the diamond businesses such as De Beers
and its competitors have to set a price for the diamonds knowing that the
resources are finite but not going to end in the near term. Here the players
set a high price which is profitable to all to begin with. But as soon as one
player deviates and sets a low price, they set a low price for all the
subsequent periods and this wipes out all the industry profits. This is akin to
a penalty clause in the agreement.
The incentives to co-operate are
high if there are a few competitors and the interest rates are low. If there
are more competitors and the interest rates are high, there are more incentives
to deviate.
Consider a probability of co-operation
as p and a payoff for co-operation as X for each. If the game is repeated a
number of times, and the payoff for deviation is 2X in one term and 0 for the rest
we get a probability of co-operation as
X*(p+p*p+p*p*p+…) > 2X
=> X/ (1-p) > 2X
=> 1/ (1-p)>2
=> 1-p < 1/2
p>1/2 – here the probability of
co-operation is more than 50% since the payoffs are very even.
If the value of p is close to 0,
indicating that there is not going to be a market next year, the chances of
co-operation are going to be very low. If p is closer to 1, indicating that
there will be a market next year with a high certainty, the chances of co-operation
are going to be very high.
This highlights the tradeoff of
giving up long term profits for short term gains.
Consider the case of OPEC oil pricing and shale oil prices. OPEC used to charge $100 per barrel for crude oil till the American and Canadian shale oil producers started selling shale oil in USA and reduced the oil imports significantly. OPEC responded by cutting the price of oil and started a price war by pricing the oil at $40 per barrel. Shale oil business has a high non recoverable expense of setting up the well and the well life is typically a year. The costs however are lower. If the oil price drops, the cost of setting up new wells becomes infeasible. As a result, shale oil output will get reduced eventually and that is when OPEC will raise the price of oil most probably.
4 important entry strategies:
Commitment
Strategy: A credible commitment of the
entrant to stay in the market may stop incumbents retaliating.
Types of commitment:
·
High
sunk cost investments Eg. Production
Capacity
·
R&D
for a particular market
·
Advertising
into 1 brand that cannot be re-directed to another market
·
Exit
from other strategic markets
Eg. Market entry of Deutsche BA in
German airline industry: If it enters then Lufthansa can choose to retaliate or
not. If Lufthansa chooses to retaliate, Deutsche BA can choose to stay in the
market or exit. This can be solved using a game tree as shown below:
This game tree is solved using backwards induction. If
Lufthansa has chosen to retaliate, Deutsche BA can chose to stay or exit. If
Deutsche BA chooses to exit, its losses are -3 and if it chooses to stay, its
losses are -4. In this case, it is beneficial for Deutsche BA to exit.
Now Lufhtansa has the choice to retaliate or not given
Deutsche BA has entered. Deutsche BA knows that Lufhtansa is going to retaliate
if it enters and in this case, Deutsche BA will have to exit.
What Deutsche BA can do now is invest in a commitment
strategy by investing in additional airplanes. The more planes to fly is a sunk
cost investment. This changes the exit payoffs for Deutsche BA from -3 to -5. Now
it is optimal for Deutsche BA to stay and is better for Lufthansa not to
retaliate. The outcome of this game now with the commitment strategy will be
that Deutsche BA will enter and Lufthansa will not retaliate, with both making
a profit of 4. The outcome of the game was thus changed by committing.
Entrants will enter with a cheaper
product that will appeal to the more price sensitive buyers. For the
incumbents, this is not a particularly threatening move. Over time, this firm will improve their
products and take large chunks of the market from the market leaders. The
market leaders will not be able to replicate the low cost business model of the
entrant.
Eg. Bloomberg started in 1981 by
providing basic financial data. They served only the small investment analysts
and brokers who could not offer the services of the main stay firms. Over time
they started improving their data offerings and analysis and started eating
into the market share of Dow Jones and Reuters.
The art of Judo is about taking the
strength of your rival and using it to your advantage. It works with an entrant
whose size is small against the incumbent whose size is large. While charging a
lower price, the entrant will also limit his market size by limiting their
capacity. This will make it less profitable for the incumbent to cut prices as
we will see below:
Pl = entrants price
Ph = incumbents price
Xe = size of market addressed by
entrant
Xh= total size of the market
The entrant also signals they are
not going to increase market share in the near future.
How does the incumbent react to
this? The incumbent will see the entrant coming in and lose market share equal
to xe to the entrant. One option would be to fight back and drive the entrant
out of the market. This would require charging prices lower than those of
entrant. So his prices go down from ph to pl, leading to lower profits.
The incumbent will not attack if
the losses from accepting the entrant are less than the losses from attacking
the entrant.
Ph*xe <
(ph-pl)*(xe+xh)
Ph*xe
is what incumbent loses since the entrant charges the lower price pl. If you
lower the price from ph to pl, the loss is equal to this price difference times
market size.
The
factors that determine this are:
1.
Market Size: If the market size is
large, there are less chances of retaliation because it is more expensive to
retaliate
2. Capacity or market share of
entrant: The smaller xe is, lower are the chances of retaliation
3. Price difference (ph-pl): If pl is
much smaller, it is going to be much more difficult for incumbent to retaliate.
These
3 factors influence the success of the entrant in the Judo Economics strategy
Eg.
Amazon and Barnes and Noble: When Amazon entered online retail in 1994, Barnes
and Noble did not retaliate. Barnes and Noble feared that an online book store
competition would trigger a price war and cannibalize the sales of the
classical book stores. Amazon started gradually dragging customers away from
the brick and mortar book stores.
The
entrant here focusses on a niche market that makes it very difficult for the
incumbent to retaliate. This is very similar to Judo Economics.
Eg.
Local phone services offered by NetCologne just in Cologne. Deutsche Telecom
was then the incumbent. Deutsche Telecom was not able to reduce prices just for
one city and so NetCologne was able to carve out a niche for themselves in
Cologne.
Eg.
Unsuccessful niche market strategy: Deutsche BA entered the German market to
offer flights on only certain pair routes in Germany. However, Lufthansa can
retaliate on particular routes. Lufthansa was able to reduce prices on the
Munich-Dusseldorf route where Deutsche BA reduced its prices. It was fairly
cheap for Lufthansa to retaliate as they were able to focus on the niche market
very easily.
Blocking
entry by reducing costs may be cost effective if the overall profits from
reduced costs are still higher than what you would achieve if you do not reduce
the costs and the competitor does (We are assuming infinite price elasticity of
demand here.)
Blocking
entry will amount to doing something that is costly to you to deter entry. If
you accommodate entry, your profits will be lower due to the lost market share
(duopoly profits). We compare the net
present value of blocking to the net present value of accommodating. Which of those 2 is larger is going to
determine whether you are going to deter entry or accommodate entry.
First
of all incumbent could simply raise entry barriers. Eg. If a diamond producer
secures access to all the diamonds that can be mined, it is going to be
difficult for a new entrant to enter. These are structural entry barriers where
in you acquire more resources than is required to meet the demand.
Taking
advantages of economies of scale and scope could help raise entry barriers. If
you could produce more or at a larger scale, your marginal costs would be lower
and you will be able to charge a lower price. This lower market price will make
the market unattractive to the new entrant.
Leverage
experience advantages: You can get better and cheaper at doing things based on
your experience. The closer you are to the technology frontier, the more
difficult it is for others to come in.
Marketing
advantages such as brand loyalty could also act as an entry barrier. Eg.
Kleenex was the first brand to enter market of paper towels and built a brand
that became synonymous with paper towels. Kleenex became the dominant player
with much larger market share than competitors due to this brand building.
Raising
switching costs by selling complementary products or signing people up for long
term contracts, it is going to be difficult for new entrants to get a critical
mass of consumers.
Aggressive
pricing before entry has happened (ex ante) where as predatory pricing happens
after the entry has happened.
Limit
pricing: Keep prices low in spite of the fact that you have a monopoly
position. This could send a signal to the potential entrant that there is low
demand so don’t bother coming in. Another signal you could send is that you are
a low cost incumbent and so the entrant should expect a steep price war.
This
only works if we have incomplete information. Eg. There is uncertainty of the
cost structure.
Eg.
There used to be ferries across the English Channel taking commuters from
England to France. When the plans to build the Channel Tunnel were announced,
these ferry operators lowered their prices indicating that the market demand is
low and the prices won’t pay off for the cost of building the tunnel. However,
after the tunnel was built, they raised their prices back again to the original
levels.
Predatory
pricing definition applies if you have a competitor and that competitor will be
driven out of the market by low prices that you charge. This can be used to
induce exit and also deter future entry. This is widely used in the
semiconductor industry by memory makers where the prices of memory modules have
dropped precipitously over the last 5-10 years and many memory makers have had
to close their shops or merge with others due to this. This has been
investigate by anti-trust authorities in USA.
Predatory
pricing by The Times and The Independent in UK. As you can see, The Times ended
up gaining the full market share after this price war.
Here
you over invest to produce very cheaply and reduce your cost of production to a
point where it becomes unfeasible for potential entrants to stay profitable.
Another
method of pre-emption is go for horizontal differentiation and produce many
variants of the same product. This leaves less space in the market for new
entrants.
You
can choose outlets more densely than would be optimal.
Reference:
1. Coursera MOOC: Competitive Strategy
taught by Prof. Tobias Kretschmer at LMU Munich
2. MIT 14.11 Pure Strategy Matrix Form
Games and Nash Equilibria (MIT OCW)
3.
