Transcript on pricing information.

Information, economics, and
game theory
Bundling
• Bundling is also a nice way to deal with
heterogeneous consumer preferences.
• Example: two items: i1 and i2, two consumers c1
and c2
• c1 values i1 at $5 and i2 at $3
• c2 values i2 at $5 and i1 at $3
• Assigning separate prices to each item, the best a
seller can do is charge $3 and make $12 total.
• If a seller can bundle the two items together, he
can charge $8 and make $16 total.
– (there are similar examples in which consumers do
better with bundling)
Value-added bundling
• Bundling can be used to add value to an existing
product.
• A seller filters, bundles and organizes existing
information goods.
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RedHat
AP news wire
Brokerages
Cable packages
• Helps consumers deal with the glut of information
• Takes advantage of complementarity (two things
are more valuable together than separately)
Price Schedules
• Bundling is just one of a number of price
schedules that are possible when marginal
cost is very low.
• This makes a number of new schemes
possible for the sale of information goods.
• Gives producers more flexibility to
distinguish themselves from each other.
– Specialists (searchers) often prefer single items
– Generalists (browsers) want larger quantities
Price Schedules
• Per-article pricing (linear pricing): Every
item costs $p.
– Example: mp3 sales, back-dated NYT articles
• Bundling: Consumers pay a fixed price $b
for access to all goods.
– Example: cable packages, Salon, Netflix (sort of)
• Two-part tariff (subscription + fee) – Consumers
pay an entry fee $f, plus a per-item price $p.
– Buying clubs, rebates (fee is negative), amusement
parks, shared computer resources
Price Schedules
• Mixed Bundling: Consumers are offered a
choice between a linear price and a bundle.
– Microsoft Office vs Word, Excel
• Block pricing (discount pricing):
Consumers pay a price $p1 for the first n
items, and $p2 for each additional item.
– Grain, electricity, bandwidth
Price Schedules
• Nonlinear pricing
– Consumer pays a different price for each item.
– Logical extension of block pricing.
– Power consumption, water usage
• Each of these schedules implements a form
of price discrimination.
Price Schedules
• More complex schedules are able to fit
consumer demand more exactly.
Price Discrimination
• Goal: Charge different prices to different
consumers.
– Extract more surplus (consumer $$)
– Make it possible for more consumers to buy.
• First-degree price discrimination: explicitly
charge different prices to different
consumers.
– Hard to do, potentially illegal
Price Discrimination
• Second-degree price discrimination
– Different prices are charged for different
quantities.
• Third-degree price discrimination
– Consumers are grouped into different classes,
which are charged different rates.
• Different versions of software
• Airlines
• Senior discounts
Issues with Schedule Complexity
• In theory, a more complex schedule is better for
the producer
– Allows him to match consumer demand more precisely.
• Problems
– Complex schedules are difficult and confsing for people
• Agents may help with this
– If producers must learn what prices to offer, a tradeoff
develops
• Extra profit from a more complex schedule vs the cost of
learning more parameters.
Fixed Price Schedules
Simpler schedules can be learned more easily,
but extract lower long-run profit
Summary
• Information goods have a number of
characteristics that differentiate them from
physical goods
– Nonrivalry, nontransparency, nonexcludability,
zero marginal cost
• Sellers of information goods need to
account for the fact that traditional market
rules may not apply.
Summary
• Information goods can be easily packaged
and bundled.
• More complex pricing schedules are also
available
– Trade off the ability to precisely meet consumer
demand against number of parameters needed.
Negotiation
• Once agents have discovered each other and
agreed that they are interested in buying/selling,
they must negotiate the terms of the deal.
• Might be simple (take it or leave it) or complex
(iterated bargaining)
• Might involve only price, or many other
dimensions (quality, service contract, warranty,
delivery, payment terms, etc.)
Mechanism Design
• By setting up the rules that agents use to negotiate,
we can ensure that particular sorts of behavior or
solutions occur.
–
–
–
–
–
–
Truth-telling
Maximize profit
Maximize social welfare
Maximize participation
Reach solutions quickly
Etc.
• Choosing rules that lead to a particular outcome is
known as mechanism design
Supply and Demand
• Supply and demand are the two parameters
that govern a market’s behavior
• Supply: quantity of product available
• Demand: amount of product wanted at a
particular price.
Demand
• We can visualize demand as a downwardsloping curve
Quantity
demanded
Price
Supply
• Similarly, supply can be visualized as an
upward-sloping curve.
Quantity
demanded
Quantity
supplied
Price
Equilibrium
• The point at which supply and demand
intersect is called the competitive equilibrium
Quantity
demanded
Quantity
supplied
Price
In a perfect world, prices will drive supply and demand
to the equilibrium
Equilibrium
• One of the central tenets of market
economies is the invisible hand
• If there is too much supply, prices will fall
due to competition – this increases demand.
• If there is too much demand, prices will
increase – this encourages supply.
• In equilibrium, the quantity supplied will
equal the quantity demanded.
Breaking an Equilibrium
• There are many things that can keep a
market from equilibrium
–
–
–
–
–
–
Lack of sellers (monopoly/oligopoly)
“Lock-in” among buyers
Incomplete or slow-moving information
Collusion among (usually) sellers or buyers
External price controls
Etc.
Properties of an Equilibrium
• Equilibria have some nice properties:
– Everyone who wants to buy/sell at this price
can.
– This sort of solution is called “efficient”
– Given this price, no one wants to change.
– The system is stable; given that you are at an
equilibrium you will stay there.
Rationality
• Rationality is the assumption that an agent
(human or software) will act so as to
maximize its happiness or advantage.
• We often try to measure this advantage
numerically using utility
• Money can sometimes serve as a substitute
for utility
Markets and Games
• Markets are useful for understanding interactions
among a large group of agents
– No need to speculate about individual actions
• In many e-commerce settings, negotiation takes
place in a one-on-one format
• In this case, game theory is a more useful
analytical tool.
– Also very useful for designing agents that operate in
open environments.
Game Theory
• Developed to explain the optimal strategy in
two-person interactions.
• Initially, von Neumann and Morganstern
– Zero-sum games
• John Nash
– Nonzero-sum games
• Harsanyi, Selten
– Incomplete information
An example:
Big Monkey and Little Monkey
• Monkeys usually eat ground-level fruit
• Occasionally climb a tree to get a coconut
(1 per tree)
• A Coconut yields 10 Calories
• Big Monkey expends 2 Calories climbing
the tree.
• Little Monkey expends 0 Calories climbing
the tree.
An example:
Big Monkey and Little Monkey
• If BM climbs the tree
– BM gets 6 C, LM gets 4 C
– LM eats some before BM gets down
• If LM climbs the tree
– BM gets 9 C, LM gets 1 C
– BM eats almost all before LM gets down
• If both climb the tree
– BM gets 7 C, LM gets 3 C
– BM hogs coconut
• How should the monkeys each act so as to
maximize their own calorie gain?
An example:
Big Monkey and Little Monkey
• Assume BM decides first
– Two choices: wait or climb
• LM has four choices:
– Always wait, always climb, same as BM,
opposite of BM.
• These choices are called actions
– A sequence of actions is called a strategy
An example:
Big Monkey and Little Monkey
Little monkey
c
w
Big monkey
w
c
w
c
0,0
9,1 6-2,4 7-2,3
What should Big Monkey do?
• If BM waits, LM will climb – BM gets 9
• If BM climbs, LM will wait – BM gets 4
• BM should wait.
• What about LM?
• Opposite of BM (even though we’ll never get to the right side
of the tree)
An example:
Big Monkey and Little Monkey
• These strategies (w and cw) are called best
responses.
– Given what the other guy is doing, this is the best thing
to do.
• A solution where everyone is playing a best
response is called a Nash equilibrium.
– No one can unilaterally change and improve things.
• This representation of a game is called extensive
form.
An example:
Big Monkey and Little Monkey
• What if the monkeys have to decide
simultaneously?
Little monkey
c
w
Big monkey
w
0,0
c
w
c
9,1 6-2,4 7-2,3
Now Little Monkey has to choose before he sees Big Monkey move
Two Nash equilibria (c,w), (w,c)
Also a third Nash equilibrium: Big Monkey chooses between c & w
with probability 0.5 (mixed strategy)
An example:
Big Monkey and Little Monkey
• It can often be easier to analyze a game
through a different representation, called
normal form
Little Monkey
Big Monkey
c
v
c
5,3
4,4
v
9,1
0,0
Choosing Strategies
• In the simultaneous game, it’s harder to see
what each monkey should do
– Mixed strategy is optimal.
• Trick: How can a monkey maximize its
payoff, given that it knows the other
monkeys will play a Nash strategy?
• Oftentimes, other techniques can be used to
prune the number of possible actions.
Eliminating Dominated Strategies
• The first step is to eliminate actions that are
worse than another action, no matter what.
Big monkey
c
w
w
Little monkey
0,0
Little Monkey will
Never choose this path.
c
w
c
9,1 6-2,4 7-2,3
Or this one
w
c
9,1
4,4
We can see that Big
Monkey will always choose
w.
So the tree reduces to:
9,1
Eliminating Dominated Strategies
• We can also use this technique in normalform games:
Column
a
b
a
9,1
4,4
b
5,3
0,0
Row
Eliminating Dominated Strategies
• We can also use this technique in normalform games:
a
b
a
9,1
4,4
b
5,3
0,0
For any column action, row will prefer a.
Eliminating Dominated Strategies
• We can also use this technique in normalform games:
a
b
a
9,1
4,4
b
5,3
0,0
Given that row will pick a, column will pick b.
(a,b) is the unique Nash equilibrium.
Prisoner’s Dilemma
• Each player can cooperate or defect
Column
cooperate
defect
cooperate
-1,-1
-10,0
defect
0,-10
-8,-8
Row
Prisoner’s Dilemma
• Each player can cooperate or defect
Column
cooperate
defect
cooperate
-1,-1
-10,0
defect
0,-10
-8,-8
Row
Defecting is a dominant strategy for row
Prisoner’s Dilemma
• Each player can cooperate or defect
Column
cooperate
defect
cooperate
-1,-1
-10,0
defect
0,-10
-8,-8
Row
Defecting is a dominant strategy for row,
And also for column
Prisoner’s Dilemma
• Each player can cooperate or defect
Column
cooperate
defect
cooperate
-1,-1
-10,0
defect
0,-10
-8,-8
Row
Frustration: even though mutual cooperation is a better
strategy for everyone, defection is the Nash equilibrium!
Prisoner’s Dilemma
• Relevant to:
–
–
–
–
Arms negotiations
Online Payment
Product descriptions
Workplace relations
• How do players escape this dilemma?
Game Theory
• Developed to explain the optimal strategy in
two-person interactions.
• Initially, von Neumann and Morganstern
– Zero-sum games
• John Nash
– Nonzero-sum games
• Harsanyi, Selten
– Incomplete information
An example:
Big Monkey and Little Monkey
• Monkeys usually eat ground-level fruit
• Occasionally climb a tree to get a coconut
(1 per tree)
• A Coconut yields 10 Calories
• Big Monkey expends 2 Calories climbing
the tree.
• Little Monkey expends 0 Calories climbing
the tree.
An example:
Big Monkey and Little Monkey
• If BM climbs the tree
– BM gets 6 C, LM gets 4 C
– LM eats some before BM gets down
• If LM climbs the tree
– BM gets 9 C, LM gets 1 C
– BM eats almost all before LM gets down
• If both climb the tree
– BM gets 7 C, LM gets 3 C
– BM hogs coconut
• How should the monkeys each act so as to
maximize their own calorie gain?
An example:
Big Monkey and Little Monkey
• Assume BM decides first
– Two choices: wait or climb
• LM has four choices:
– Always wait, always climb, same as BM,
opposite of BM.
• These choices are called actions
– A sequence of actions is called a strategy
An example:
Big Monkey and Little Monkey
Little monkey
c
w
Big monkey
w
c
w
c
0,0
9,1 6-2,4 7-2,3
What should Big Monkey do?
• If BM waits, LM will climb – BM gets 9
• If BM climbs, LM will wait – BM gets 4
• BM should wait.
• What about LM?
• Opposite of BM (even though we’ll never get to the right side
of the tree)
An example:
Big Monkey and Little Monkey
• These strategies (w and cw) are called best
responses.
– Given what the other guy is doing, this is the best thing
to do.
• A solution where everyone is playing a best
response is called a Nash equilibrium.
– No one can unilaterally change and improve things.
• This representation of a game is called extensive
form.
An example:
Big Monkey and Little Monkey
• What if the monkeys have to decide
simultaneously?
Little monkey
c
w
Big monkey
w
0,0
c
w
c
9,1 6-2,4 7-2,3
Now Little Monkey has to choose before he sees Big Monkey move
Two Nash equilibria (c,w), (w,c)
Also a third Nash equilibrium: Big Monkey chooses between c & w
with probability 0.5 (mixed strategy)
An example:
Big Monkey and Little Monkey
• It can often be easier to analyze a game
through a different representation, called
normal form
Little Monkey
Big Monkey
c
v
c
5,3
4,4
v
9,1
0,0
Choosing Strategies
• In the simultaneous game, it’s harder to see
what each monkey should do
– Mixed strategy is optimal.
• Trick: How can a monkey maximize its
payoff, given that it knows the other
monkeys will play a Nash strategy?
• Oftentimes, other techniques can be used to
prune the number of possible actions.
Eliminating Dominated Strategies
• The first step is to eliminate actions that are
worse than another action, no matter what.
Big monkey
c
w
w
Little monkey
0,0
Little Monkey will
Never choose this path.
c
w
c
9,1 6-2,4 7-2,3
Or this one
w
c
9,1
4,4
We can see that Big
Monkey will always choose
w.
So the tree reduces to:
9,1
Eliminating Dominated Strategies
• We can also use this technique in normalform games:
Column
a
b
a
9,1
4,4
b
5,3
0,0
Row
Eliminating Dominated Strategies
• We can also use this technique in normalform games:
a
b
a
9,1
4,4
b
5,3
0,0
For any column action, row will prefer a.
Eliminating Dominated Strategies
• We can also use this technique in normalform games:
a
b
a
9,1
4,4
b
5,3
0,0
Given that row will pick a, column will pick b.
(a,b) is the unique Nash equilibrium.
Prisoner’s Dilemma
• Each player can cooperate or defect
Column
cooperate
defect
cooperate
-1,-1
-10,0
defect
0,-10
-8,-8
Row
Prisoner’s Dilemma
• Each player can cooperate or defect
Column
cooperate
defect
cooperate
-1,-1
-10,0
defect
0,-10
-8,-8
Row
Defecting is a dominant strategy for row
Prisoner’s Dilemma
• Relevant to:
–
–
–
–
Arms negotiations
Online Payment
Product descriptions
Workplace relations
• How do players escape this dilemma?
Prisoner’s Dilemma
• Each player can cooperate or defect
Column
cooperate
defect
cooperate
-1,-1
-10,0
defect
0,-10
-8,-8
Row
Prisoner’s Dilemma
• Each player can cooperate or defect
Column
cooperate
defect
cooperate
-1,-1
-10,0
defect
0,-10
-8,-8
Row