3.1.3 Examples of Game Situations
Outline
3.1. What is a Game ?
3.1.1. The elements of a Game
3.1.2 The Rules of the Game: Example
3.1.3. Examples of Game Situations
3.2 Types of Games
3.3. Solution Concepts
3.3.1. Static Games of complete information: Dominant
Strategies and Nash Equilibrium in pure and mixed
strategies
3.3.2. Dynamic Games of complete information: Backward
Induction and Subgame perfection
Strategic Behavior in Business and Econ
Reminder
A game is a situation in which the final outcome depends
on the decisions of all the individuals involved.
It is always important to identify:
1. The environment of the game
Players
Strategies
Payoffs
1. The rules of the game
Timing of moves
Nature of conflict and interaction
Information conditions
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Examples of Game Situations
1.
2.
3.
4.
5.
6.
Cigarette Advertising on TV
The Battle for TV share
Summer pricing
Rock-Paper-Scissors Game
Market Entry
FCC spectrum auction
Strategic Behavior in Business and Econ
1. Cigarette Advertising on TV
All US tobacco companies advertised heavily on
TV
1964
Surgeon General issues official warning
Cigarette smoking may be hazardous
Cigarette companies fear lawsuits
Government may recover healthcare costs
1970
Companies strike agreement
Carry the warning label and cease TV advertising in
exchange for immunity from federal lawsuits.
5
Strategic Behavior in Business and Econ
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The environment of the game
Players:
Reynolds and Philip Morris
Strategies:
Advertise or Not Advertise
Payoffs:
Companies’ Profits
Each firm earns $50 million from its customers
Advertising costs a firm $20 million
Advertising captures $30 million from competitor
The Rules of the Game
Timing of moves
Nature of conflict and interaction
Share)
Information conditions
Simultaneous
Conflict (Market
Symmetric
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The game represented
Philip Morris (player 2)
Not advertise
Advertise
Not
advertise
50, 50
20, 60
Advertise
60, 20
30, 30
Reynolds
(player 1)
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This is a “Prisoners' Dilemma” game !
Prediction of Game Theory:
Both have a clear best
strategy
Philip Morris (player 2)
Not advertise
Advertise
Not
advertise
50, 50
20, 60
Advertise
60, 20
30, 30
Advertise no matter what
Reynolds
(player 1)
Strategic Behavior in Business and Econ
Prisoner’s Dilemma
If there is a clearly best strategy use it, and expect your opponent to
use it as well
The outcome is NOT efficient. They both realize that there is a better
outcome
Players must accept mutually bad outcomes
Bad to be playing a prisoner’s dilemma, but good to make others play
After the 1970 agreement:
Cigarette advertising decreased by $63 million
Industry Profits rose by $91 million
How did they escape from the Prisoners' Dilemma ?
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The government threat lowered the “expected”
payoff of Advertise
Philip Morris (player 2)
Not advertise
Advertise
Not
advertise
50, 50
20, ??
Advertise
??, 20
??, ??
Reynolds
(player 1)
?? = very low !
Strategic Behavior in Business and Econ
2. The Battle for TV share
In 1988 the Spanish government authorized, for the first time, the
launching of privately owned TV stations.
In 1990, Antena 3 and later Telecinco were the two first
private TV's to operate in Spain.
Competition for audience share was ferocious at the beginning, and TV
schedules were often changed from one day to the next, reacting to others
stations programming.
Strategic Behavior in Business and Econ
In a given day, at a given time slot, there were two alternative show options:
a Champions League match or a National Geographic documentary. The
estimated audience for the match is of 2 million people whereas the
documentary can be of interest for 1 million and a half.
If the two stations offer the same show then they share the audience. If they
program different shows then each gets all the audience that corresponds to
that show.
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The environment of the game
Players:
Antena 3 and Telecinco
Strategies:
Match or Documentary
Payoffs:
Audience
2 million if Match, 1.5 million if documentary
Share audience if program same show
The Rules of the Game
Timing of moves
Nature of conflict and interaction
share)
Information conditions
Simultaneous
Conflict (audience
(apparently)
Symmetric
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The game represented
Telecinco (player 2)
Match
Match
Documentary
1, 1
2, 1.5
Antena 3
(player 1)
Documentary
1.5, 2
0.75, 0.75
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This is a “coordination game”
Prediction of Game Theory:
The best strategy depends
on the other's strategy
Documentary if Match
Match if Documentary
Telecinco (player 2)
Match
Match
Documentary
1, 1
2, 1.5
Antena 3
(player 1)
Documentary
1.5, 2
0.75, 0.75
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This is a “coordination game”
Prediction of Game Theory:
NOTICE: The “coincidence” of
red circles points out stable
outcomes: no one wants to
change if the other doesn't
Telecinco (player 2)
Match
Match
Documentary
1, 1
2, 1.5
Antena 3
(player 1)
Documentary
1.5, 2
0.75, 0.75
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Coordination Game
The outcome is beneficial to all the players
They can avoid direct competition
The problem is where and how to coordinate (specialization, take
turns, etc)
The law prohibits explicit coordination
After some initial erratic movements, TV stations try to
differentiate . . .
Strategic Behavior in Business and Econ
3. Summer pricing
Summer in Spain is a very good opportunity for business in the tourism
sector. There are millions of tourist visiting and, very often, bars and
restaurants take advantage of them by raising prices.
The problem is that they might loose the local patrons !
Strategic Behavior in Business and Econ
Two bars (bar 1, bar 2) compete for thirsty patrons
They can charge price of $2, $4, or $5 for a drink
They can have tourists and natives as costumers
6,000 tourists pick a bar randomly
4,000 natives select the lowest price bar
(The cost of a drink for the bars is not important for the
decision)
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The environment of the game
Players:
Strategies:
Payoffs:
Bar 1 and Bar 2
$2, $4, or $5
Monetary Profit
The Rules of the Game
Timing of moves
Nature of conflict and interaction
competition)
Information conditions
Simultaneous
Conflict (price
Symmetric
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Example of Payoff Computation:
Since tourists pick a bar at random, each bar expects to get 3,000
tourists regardless of the price charged
Natives will go to the cheapest bar
Bar 1 charges $4, Bar 2 charges $5
Bar 1 gets (expected):
3,000 tourists + 4,000 natives = 7,000 customers x $4 = $28,000
Bar 2 gets (expected):
3,000 tourists + 0 natives = 3,000 customers x $5 = $15,000
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The game represented
Bar 2
$4
$2
Bar 1
$2
$4
$5
10 , 10
12 , 14
15 , 14
$5
14 , 12
20, 20
15 , 28
14 , 15
28 , 15
25, 25
(in thousands of dollars)
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This is a competition game
Prediction of Game Theory:
There is not a clearly best
strategy
Bar 2
$4
$2
Bar 1
$2
$4
$5
10 , 10
12 , 14
15 , 14
$5
14 , 12
20, 20
15 , 28
14 , 15
28 , 15
25, 25
(in thousands of dollars)
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This is a competition game
Prediction of Game Theory:
But there is a clearly bad
strategy: $2 is always worse
than $4 (or $5)
Bar 2
$4
$2
Bar 1
$2
$4
$5
10 , 10
12 , 14
15 , 14
$5
14 , 12
20, 20
15 , 28
14 , 15
28 , 15
25, 25
(in thousands of dollars)
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This is a competition game
Prediction of Game Theory:
If $2 is removed from the
game (it will never be used)
then the game is more clear
Bar 2
$4
$2
Bar 1
$2
$4
$5
10 , 10
12 , 14
15 , 14
$5
14 , 12
20, 20
15 , 28
14 , 15
28 , 15
25, 25
(in thousands of dollars)
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This is a competition game
Prediction of Game Theory:
Now $4 is clearly the best
strategy no matter what
my competitor does
Bar 1
$4
$5
Bar 2
$4
$5
20, 20
15 , 28
28 , 15
25, 25
(in thousands of dollars)
Strategic Behavior in Business and Econ
This is a competition game
Prediction of Game Theory:
NOTICE: The “coincidence” of
red circles is (again) the stable
outcome
Bar 1
$4
$5
Bar 2
$4
$5
20, 20
15 , 28
28 , 15
25, 25
(in thousands of dollars)
Strategic Behavior in Business and Econ
When there are many strategies available, try to see if some of them
are clearly outperformed by other strategies
Do not use “bad” strategies, and don't expect your competitor to use
them either
Price competition not always leads to the lowest price, nor to the
highest price
Market behavior must be clearly understood
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4. Rock-Paper-Scissors Game
THE WORLD RPS SOCIETY
OFFICIAL ABRIDGED RULES OF PLAY
1. The Game is played where two players substitute the three elements of Rock,
Paper and Scissors with representative hand signals.
2. These hand signals are delivered simultaneously by the players
3. The Outcome of play is determined by the following
Rock wins against Scissors,
Scissors wins against Paper
Paper wins against Rock
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The player showing the winning
“strategy” wins the play (+1) and the
other looses (-1). If they both show
the same figure, then the game ends
with a tie, there is no winner and no
looser.
The game is played repeatedly, but,
for simplicity, we will show the
one-shot version
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The environment of the game
Players:
Strategies:
Payoffs:
Player 1 and Player 2
Rock, Scissors or Paper
+1 if winning, -1 when loosing, 0 if tie
The Rules of the Game
Timing of moves
Nature of conflict and interaction
(both can't win)
Information conditions
Simultaneous
Conflict
Symmetric
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The game represented
Player 2
Rock
Player 1
Rock
Paper
Scissors
0, 0
+1, -1
-1, +1
Paper
-1, +1
0, 0
+1, -1
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Scissors
+1, -1
-1, +1
0, 0
This is a zero-sum game
(one player's earnings are other player's losses)
Player 2
Rock
Player 1
Rock
Paper
Scissors
0, 0
+1, -1
-1, +1
Paper
-1, +1
0, 0
+1, -1
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Scissors
+1, -1
-1, +1
0, 0
This is a zero-sum game
(one player's earnings are other player's losses)
Prediction of Game Theory:
There are not “always good”
nor “always bad” strategies
Player 2
Rock
Player 1
Rock
Paper
Scissors
0, 0
+1, -1
-1, +1
Paper
-1, +1
0, 0
+1, -1
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Scissors
+1, -1
-1, +1
0, 0
This is a zero-sum game
(one player's earnings are other player's losses)
Prediction of Game Theory:
There is no “coincidence” of
red circles
Player 2
Rock
Player 1
Rock
Paper
Scissors
0, 0
+1, -1
-1, +1
Paper
-1, +1
0, 0
+1, -1
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Scissors
+1, -1
-1, +1
0, 0
There are games that don't have “always winning” strategies
and can not be simplified by discarding “always bad” strategies
Also, there are games that have no “coincidence” of “red
circles” (best replies)
In real plays, the RSP game is played “at random”.
If you opponent detects a “pattern of behavior” she will
react accordingly
But things can become more complex . . .
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The Master's Guide to Rock, Paper & Scissors defines the term gambit as:
"A series of three successive moves made with strategic
intention."
The use of Gambits in competitive RPS has been one of the greatest and most
enduring breakthroughs in RPS strategy. Selecting throws in advance helps prevent
unconscious patterns from forming and can sometimes reduce the subconscious
signals that give away the next throw, often called “tells”. Gambits are the focal point
of beginner strategy and form the basis of many advanced strategies.
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5. Market Entry
A firm wants to enter a new market, and its main concern
is about the reaction of an incumbent company that currently
is making a profit $100,000
If the reaction is aggressive, the challenger will suffer a loss
of $10,000, and the incumbent's profits will be reduced to
only $20,000 (because of the costs of the fight). On the
other hand, if the incumbent chooses to accommodate to the
new market scenario, then the two companies will share the
$100,000 profit ($50,000 each)
Obviously, the challenger can always choose to stay out if that
seems to be the best choice (with a profit of $0)
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The environment of the game
Players:
Strategies:
Payoffs:
Firm 1 (challenger) and Firm 2 (incumbent)
Firm 1: Enter or Stay out
Firm 2: Aggressive or Accommodate
as described
The Rules of the Game
Timing of moves
Nature of conflict and interaction
Information conditions
Sequential: Firm 1 first, then Firm 2
Conflict (market)
Symmetric
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The game represented
(- 10,000 , 20,000)
Firm 2
(50,000 , 50,000)
Firm 1
(0, 100,000)
Since the game is sequential, the representation must
incorporate the sequence of moves
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This is a credibility (reputation) game
Prediction of Game Theory:
Firm 2, if called to play, will
choose to Accommodate
(- 10,000 , 20,000)
Firm 2
(50,000 , 50,000)
Firm 1
(0, 100,000)
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This is a credibility (reputation) game
Prediction of Game Theory:
Firm 2, if called to play, will
choose to Accommodate
(- 10,000 , 20,000)
Firm 2
(50,000 , 50,000)
Firm 1
(0, 100,000)
Being Aggressive is not a “rational” choice as it would
harm itself
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This is a credibility (reputation) game
Prediction of Game Theory:
Firm 1, foreseeing the choice
of Firm 2, will Enter
(- 10,000 , 20,000)
Firm 2
(50,000 , 50,000)
Firm 1
(0, 100,000)
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This is a credibility (reputation) game
Prediction of Game Theory:
Firm 1, foreseeing the choice
of Firm 2, will Enter
(- 10,000 , 20,000)
Firm 2
(50,000 , 50,000)
Firm 1
(0, 100,000)
The final outcome is that the two firms share the market
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Scenarios that consist of a sequence of moves must
be represented accordingly: a tree instead of a table
Game trees are solved by Backward Induction
Credibility games show that “incredible threats” are not
rational (The same goes for “incredible promises”)
The timing of moves is very important (preventive
wars)
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6. FCC Spectrum auctions
The FCC used comparative hearings to allocate spectrum licenses prior to 1982 and used
lotteries starting in 1982. The Commission was given auction authority in 1993 and held
its first auction in 1994. Comparative hearings allowed regulators to decide which
applicant would put the spectrum to its best use. The lotteries of small licenses
contributed to the geographic fragmentation of the cellular industry, delaying the
introduction of nationwide mobile telephone services in the United States. Auctions were
identified as the mechanism best able to assign the licenses to the highest valuing users
and to return a part of the value to the taxpayer. The basic simultaneous multiple round
auction format that was adopted in 1994 remains the mainstay of FCC auctions today,
although it has evolved over time.
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The environment of the game
Players:
Strategies:
Payoffs:
Any cell phone company (Verizon, AT&T, . . .)
Submit a bid (pay the government for the
right to use the spectrum)
monetary profits
The Rules of the Game
Timing of moves
Nature of conflict and interaction
Information conditions
mixture of simultaneous and sequential
Conflict (market share)
Asymmetric
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The game represented
An auction is a game because the outcome of your strategy
(your bid) depends on the strategies (bids) of other players
Auctions are very complicated games.
They can be represented by trees, but they are too complex
to be useful.
Typically, mathematical instruments are necessary
There are different types of auctions
FCC auctions are of the type “Common Value”
The item has a single though unknown value
Bidders differ in their estimates of the true value
of the object
Bidders differ in their cost structure, which is unknown to
each other
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Auctions are very good “money raisers”
Money raised by auctions in the cellular spectrum:
Germany
United Kingdom
France
84 billion
62 billion
33 billion
U.S. 2008 (700Mhz auction)
(From January 24th to March 18th )
20 billion
(101 bidders, 1019 licenses)
Spain
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???
No Auction in Spain !!
The government issued licenses based on public
examination/contest (comparative hearings)
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No Auction in Spain !!
The government issued licenses based on public
examination/contest (comparative hearings)
The Spanish government raised
880 million
( 35 times less than France !! )
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Summary
Different game scenarios may have different features
and hence different representation
It is important to recognize the type of game we want
to study
The goal is always to find a prediction of what seems to
be the more logical or stable outcome (equilibrium) of
the game
Strategic Behavior in Business and Econ