Business Strategy

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• Business Strategy
• in Oligopoly Markets

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(No Transcript)
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Introduction

• In the majority of markets firms interact with
  few competitors
• In determining strategy each firm has to consider
  rivals reactions
• strategic interaction in prices, outputs,
  advertising
• This kind of interaction is analyzed using game
  theory
• assumes that players are rational
• Distinguish cooperative and noncooperative games
• focus on noncooperative games
• Also consider timing
• simultaneous versus sequential games

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What is Game Theory?

• No man is an island
• Study of rational behavior in interactive or
  interdependent situations
• Bad news
• Knowing game theory does not guarantee winning
• Good news
• Framework for thinking about strategic
  interaction

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Why Study Game Theory?

• Because we can formulate effective strategy
• Because we can predict the outcome of strategic
  situations
• Because we can select or design the best game for
  us to be playing

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Definition of a Game

• Must consider the strategic environment
• Who are the PLAYERS? (Decision makers)
• What STRATEGIES are available? (Feasible
  actions)
• What are the PAYOFFS? (Objectives)
• Rules of the game
• What is the time-frame for decisions? Sequential
  or simultaneous?
• What is the nature of the conflict?
• What is the nature of interaction?
• What information is available?

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Oligopoly Theory

• No single theory
• employ game theoretic tools that are appropriate
• outcome depends upon information available
• Need a concept of equilibrium
• players (firms?) choose strategies, one for each
  player
• combination of strategies determines outcome
• outcome determines pay-offs (profits?)
• Equilibrium first formalized by Nash No firm
  wants to change its current strategy given that
  no other firm changes its current strategy

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Nash Equilibrium

• Equilibrium need not be nice
• firms might do better by coordinating but such
  coordination may not be possible (or legal)
• Some strategies can be eliminated on occasions
• they are never good strategies no matter what the
  rivals do
• These are dominated strategies
• they are never employed and so can be eliminated
• elimination of a dominated strategy may result in
  another being dominated it also can be
  eliminated
• One strategy might always be chosen no matter
  what the rivals do dominant strategy

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An Example

• Two airlines
• Prices set compete in departure times
• 70 of consumers prefer evening departure, 30
  prefer morning departure
• If the airlines choose the same departure times
  they share the market equally
• Pay-offs to the airlines are determined by market
  shares
• Represent the pay-offs in a pay-off matrix

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The example (cont.)
What is the equilibrium for this game?
The Pay-Off Matrix
The left-hand number is the pay-off to Delta
American
Morning
Evening
Morning
(15, 15)
(30, 70)
The right-hand number is the pay-off to American
Delta
Evening
(70, 30)
(35, 35)
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The example (cont.)
The morning departure is also a dominated
strategy for American and again can be eliminated
The morning departure is a dominated strategy
for Delta and so can be eliminated.
If American chooses a morning departure,
Delta will choose evening
If American chooses an evening departure,
Delta will still choose evening
The Pay-Off Matrix
American
The Nash Equilibrium must therefore be one in
which both airlines choose an evening departure
Morning
Evening
Morning
(15, 15)
(30, 70)
Delta
(35, 35)
Evening
(70, 30)
(35, 35)
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Dominant Strategy

• A strategy that outperforms all other choices
  
• no matter what opposing players do
• COMMANDMENT
• If you have a dominant strategy, use it.
• Expect your opponent to use her dominant strategy
  if she has one.

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The example (cont.)

• Now suppose that Delta has a frequent flier
  program
• When both airline choose the same departure times
  Delta gets 60 of the travelers
• This changes the pay-off matrix

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The example (cont.)
However, a morning departure is still a
dominated strategy for Delta (Evening is still a
dominant strategy.
If Delta chooses a morning departure,
American will choose evening
The Pay-Off Matrix
American has no dominated strategy
But if Delta chooses an evening departure,
American will choose morning
American
American knows this and so chooses a
morning departure
Morning
Evening
Morning
(18, 12)
(30, 70)
Delta
(70, 30)
Evening
(70, 30)
(42, 28)
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Successive Deletion of Dominated Strategies

• Rational players
• Should play dominant strategies
• Should not play dominated strategies
• Should not expect others to play dominated
  strategies
• ? Thus, dominated strategies may be eliminated
  from consideration
• This may be done iteratively

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Example Tourists Natives

• Two bars (bar 1, bar 2) compete
• Can charge price of 2, 4, or 5
• 6000 tourists pick a bar randomly
• 4000 natives select the lowest price bar
• Example 1 Both charge 2
• each gets 5,000 customers
• Example 2 Bar 1 charges 4,
• Bar 2 charges 5
• Bar 1 gets 300040007,000 customers
• Bar 2 gets 3000 customers

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Tourists Natives

Bar 2
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Successive Elimination of Dominated Strategies

• Does any player have a dominant strategy?
• Does any player have a dominated strategy?
• Eliminate the dominated strategies
• Reduce the normal-form game
• Iterate the above procedure
• What is the equilibrium?

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Successive Elimination of Dominated Strategies
Bar 2
5
4
2
2
14
,
15
14
,
12
10
,
10
,
,
,
4
Bar 1
Bar 1
28
,
15
20
,
20
12
,
14
,
,
,
5
25
,
25
15
,
28
15
,
14
,
,
,
Bar 2
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Nash Equilibrium

• What if there are no dominated or dominant
  strategies?
• The Nash equilibrium concept can still help us in
  eliminating at least some outcomes
• Nash Equilibrium
• A set of strategies, one for each player, such
  that each players strategy is best for her given
  that all other players are playing their
  equilibrium strategies
• Best Response
• The best strategy I can play given the strategy
  choices of all other players
• Nash equilibrium Everybody is playing a best
  response
• No incentive to unilaterally change my strategy

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Example

• Change the airline game to a pricing game
• 60 potential passengers with a reservation price
  of 500
• 120 additional passengers with a reservation
  price of 220
• price discrimination is not possible (perhaps for
  regulatory reasons or because the airlines dont
  know the passenger types)
• costs are 200 per passenger no matter when the
  plane leaves
• the airlines must choose between a price of 500
  and a price of 220
• if equal prices are charged the passengers are
  evenly shared
• Otherwise the low-price airline gets all the
  passengers
• The pay-off matrix is now

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The example (cont.)
If Delta prices high and American low then
American gets all 180 passengers. Profit per
passenger is 20
The Pay-Off Matrix
If both price high then both get 30 passengers.
Profit per passenger is 300
If Delta prices low and American high then Delta
gets all 180 passengers. Profit per passenger is
20
American
If both price low they each get
90 passengers. Profit per passenger is 20
PH 500
PL 220
(9000,9000)
(0, 3600)
PH 500
Delta
(3600, 0)
(1800, 1800)
PL 220
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Nash Equilibrium (cont.)
There is no simple way to choose between these
equilibria. But even so, the Nash concept has
eliminated half of the outcomes as equilibria
(PH, PH) is a Nash equilibrium. If both are
pricing high then neither wants to change
(PH, PL) cannot be a Nash equilibrium. If
American prices low then Delta should also price
low
The Pay-Off Matrix
(PL, PL) is a Nash equilibrium. If both are
pricing low then neither wants to change
Custom and familiarity might lead both to price
high
American
(PL, PH) cannot be a Nash equilibrium. If
American prices high then Delta should also price
high
There are two Nash equilibria to this
version of the game
PH 500
PL 220
(0, 3600)
(9000, 9000)
Regret might cause both to price low
(9000,9000)
(0, 3600)
PH 500
Delta
(3600, 0)
(1800, 1800)
(3600, 0)
(1800, 1800)
PL 220
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Nash Equilibrium (cont.)
There is no simple way to choose between these
equilibria, but at least we have eliminated half
of the outcomes as possible equilibria
(PH, PH) is a Nash equilibrium. If both are
pricing high then neither wants to change
There are two Nash equilibria to this
version of the game
(PH, PL) cannot be a Nash equilibrium. If
American prices low then Delta wouldwant to
price low, too.
The Pay-Off Matrix
(PL, PL) is a Nash equilibrium. If both are
pricing low then neither wants to change
American
(PL, PH) cannot be a Nash equilibrium. If
American prices high then Delta should also price
high
PH 500
PL 220
(0, 3600)
(9000, 9000)
(9000,9000)
(0, 3600)
PH 500
Delta
(3600, 0)
(1800, 1800)
(3600, 0)
(1800, 1800)
PL 220
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Nash Equilibrium (cont.)
The only sensible choice for Delta is PH
knowing that American will follow with PH and
each will earn 9000. So, the Nash equilibria
now is (PH, PH)
Suppose that Delta can set its price first
Sometimes, consideration of the timing of moves
can help us find the equilibrium
The Pay-Off Matrix
Delta can see that if it sets a high price, then
American will do best by also pricing high.
Delta earns 9000
This means that PH, PL cannot be an equilibrium
outcome
American
This means that PL,PH cannot be an equilibrium
PH 500
PL 220
Delta can also see that if it sets a low price,
American will do best by pricing low. Delta
will then earn 1800
(0, 3600)
(3,000, 3,000)
(9000,9000)
(0, 3600)
PH 500
Delta
(3600, 0)
(1800, 1800)
(1800, 1800)
(3600, 0)
(1800, 1800)
PL 220