professor: c. courcoubetis
TRANSCRIPT
Professor: C. Courcoubetis
Network Economics - 2
Networks Throughout history, networks have served as the foundation
for connecting humans to one another and their activities Networks provide the fabric for our societies and economies
and the infrastructure for commerce, science and technology social systems, and education
Examples of networks: transportation, communication, energy, financial, social
A computer network is a collection of hardware components and computers interconnected by communication channels that allow sharing of resources and information
Economic issues for networks: sharing of resources control of strategic functions efficient competition of stakeholders
Network Economics - 3
Types of networks Network system nodes links flows
Transportation Urban
Air Rail
intersections, homes, offices airports railroads
roads
airline routes railroad track
autos
planes trains
Manufacturing and logistics
distribution points, processing points
routes assembly lines
parts, products
Communication computers, satellites, routers and switches
fiber, wireless, microwave
packets, bits
Energy production plants, loads pumping stations
transmission lines pipelines
electricity water gas oil
Network Economics - 4
Economic networks An economic network: A combination of individuals, groups
or countries interacting to benefit the whole community uses the various competitive advantages and resources of
each member to increase the production and wealth of all the members
could be static where members do not change, or dynamic where the network is constantly changing as members are added or leave
Economic networks are more general than physical networks Physical networks (Internet) are the basis for the formation of
many economic networks defined at various layers (network-application)
Network Economics - 5
What exactly is network economics? For a computer scientist: the internet is unique among
engineered systems because it is federated Different actors own different parts of the system Behavior depends as much on human interests as it does
on protocols Many technologies can’t even reach users unless network
operators are motivated to deploy them in their network equipment
For an economist: there are strong externalities Negative externalities: the internet can be congested by
too much traffic Positive externalities: Internet technologies become more
valuable to each user as more people use them
Network Economics - 6
Economic competition: users and providers Ref: J. Walrand, Pricing of Bandwidth and Communication On Demand
Services, BoD 2008
Network Economics - 7
Users and providers are strategic Users
Exploit the network as much as possible for the given charge (selfish behaviour)
Use new applications and protocols if best for them Modify technology is possible (boost TCP, etc.) Over-consume, free-ride
Providers (network) Price to maximize revenue Invest in capacity only if competition forces them Love to control content and sell their own Decide on deploying new technologies (WiMax, metro WiFi, 4G,
QoS, …) Under-invest
Content Free-ride on networks
Network Economics - 8
Economics = incentives
The taxi tariff
The “all-you can eat” restaurants: flat vs usage-based
The Internet café tariff: dynamic pricing
Low Extra Delay Background Transport (ledbat) (BitTorrent clients)
Routing economics: the Braess paradox
Better traffic multiplexing
Network Economics - 9
Braess paradox
4000 cars
2000 2000
t=20
t=20 ttot= 65
t=0 4000
ttot= 80
Network Economics - 10
Traffic multiplexing in the Internet Traffic shaping:
traffic = real-time + non real-time delay increase => smaller peak rate small delay in non real-time => big difference for the
network! Incentives for traffic shaping! But how? The right pricing combined with the appropriate
transport protocols
Real-time traffic Non real-time traffic
With shifted non real-time Required bandwidth for specific QoS
Network Economics - 11
New economic environment Networks not any more state monopolies Decisions are profit-oriented No central decision making in the Internet (federated) How will distributed computing evolve? the Internet? the
NGN? Network technologies define the environment for “tussles”:
network service providers, application service providers, customers, equipment vendors, content providers
Who from the above stakeholders will make the necessary investments?
Who will be more in control? Is regulation needed?
Network Economics - 12
Questions that require economics Simple over-dimensioned networks or more complex control for QoS? How should network connectivity be priced? How should congestion be handled by new protocols? Should eyeball ISPs tax content providers and provide differential
treatment to content (Network Neutrality)? Interconnection for more than best-effort? How will the Internet evolve? Single Internet or multiple specialized
networks? who will invest? What is the effect of cheap storage in content distribution? What are the correct design principles for network protocols ? How can the future Internet be business model neutral? Power of position in the value chain? (Google vs T1, T2, T3 networks) New business models for network operators? What is the impact of cloud computing, p2p,…? Business models for Google, Amazon, …?
Network Economics - 13
Course outline Basic economic concepts Pricing Game theory
Economics of flow control
Interconnection economics
Access network economics
Network Neutrality
The telecommunications market and the evolution of the Internet
New Internet applications
Basic Economics
Network Economics - 15
Basic Economics - Outline The consumer The producer The social planner Market mechanisms and
competitive equilibria Marginal cost pricing and
cost recovery Externalities and
congestion pricing Market competition Lock-in
Networks and positive externalities
Game theory The information economy Pricing in communication
networks
Network Economics - 16
The context
Communication services are economic commodities Demand factors: amounts of services purchased by users
utility of using a service, demand elasticity Supply factors: amounts of services produced
technology of network elements, service control architecture, cost of production
Market model: models interaction and competition Prices: control mechanism
control demand and production, deter new entry provide income to cover costs structure and value depends on underlying model
Network Economics - 17
Economic models and tariffs Prices result from the solution of economic models Possibly different contexts for deriving optimal prices
surplus maximization: standard market models with actual competition: monopoly, oligopoly, perfect competition
stability under competition and fairness: sustainability against potential entry, recovering costs, fairness w.r.t. cost causation, no subsidization
asymmetric information models: principal-agent models, hidden action and hidden information
Network Economics - 18
Terminology
Terminology: price: correlated with service unit tariff: charge structure
– more general form of charging (i.e., a+px) – control mechanism
charge: total amount that must be paid
The consumer, producer, social planner
Network Economics - 20
The consumer’s problem Consumers:
utility function increasing, concave
consumer surplus (net benefit):
solve optimisation problem (linear prices):
at optimum
u(x)
x p x(p)
$ �
u(x) − charge(x)
CS
Network Economics - 21
The demand curve: single customer
$
The demand curve: D(p) = x
1(p ) =
CS (p) =
quantity demanded at price p
consumer surplus at price p
= value of consuming x
x
1(p ) := argmax
x{u
1(x ) − px }
CS (p)
p
x1(p )
u1'(x )
D(p) u1(x ) = CS (p) + px
px1
x
Network Economics - 22
The demand curve: 2 customers
$
The demand curve:
D(p) = x1(p ) + x
2(p ) p
x1(p )
U '(x )
x2(p )
x1(p )
x2(p )
x1(p ) + x
2(p ) x
CS (p)
Network Economics - 23
Elasticity of demand
Elasticity of demand:
Cross-elasticity:
-> Complements, substitutes �
px(p)
|i |= ∞
|i |= 1
|i |= 0
Network Economics - 24
Endowment effects
• The consumer has a fixed amount to spend • Market prices are given =
Network Economics - 25
Producer: profit function (producer surplus):
The producer’s problem
Monopoly:
�
maxy∈Y[py − c(y)], for given pPerfect competition:
�
maxy∈Y[p(y + z)y − c(y)]Oligopoly:
Regulation: fixed p, produce y =y( p )
�
π(y) = revenue(y) − c(y), y ∈Y
Demand curve price maker
price taker
Network Economics - 26
The producer in a competitive market
Competitive market with price :
�
maxy
py − c(y) for p = p Producer solves:
$
�
c'(y*) = p
Network Economics - 27
The Cournot game
∂πj(x
1, x
2)
∂xj
= 1 − xi− 2x
j
Network Economics - 28
The social planner’s problem
control
Note that this is equivalent to
�
maxxu(x) − c(x)⇔
�
∂u(x*)∂xi
=∂c(x*)∂xi
= MC
$
Social Welfare
Network Economics - 29
Constant marginal cost
$
x
Cost of
x
MC
Net social gain
MC
MC = marginal cost of x
Set prices = marginal cost
Simple case: constant marginal cost
Network Economics - 30
Setting prices equal to marginal cost The social planner sets prices equal to marginal cost at the
level of production that satisfies demand Prices (may) converge to SW optimum
How does the social planner know the true marginal cost?
$
= D(p)
Network Economics - 31
SW maximization Social planner solves P1:
There exist a positive for which the solution of P1 is the free maximization of
Hence at the optimum
minλ≥0
max{xi ,y j }
{ ui(x
i) − c
j(y
j)
j∑
i∑ + λ( y
jj∑ − x
ii∑ )}
Observe that λ behaves like a price!
Network Economics - 32
Mathematics background
Lagrangian methods: constraint optimization
Network Economics - 33
Lagrangian sufficiency and shadow prices
= optimum as a function of b
Network Economics - 34
Lagrangian methods
P : maximize f (x ), s.t. g(x ) = b and x ∈X
Example : maximizexi ≥0
wil
i =1
n
∑ og(xi) subject to x
ii =1
n
∑ = b
Lagrangian: L(x ,λ) = f (x ) + λ(b − g(x ))x (λ) = argmax
x L(x ,λ) = argmax
x [f (x ) + λ(b − g(x ))]
"Find" λ * s.t. g(x (λ*)) = b. Then x* = x (λ*)
L(x ,λ) =i =1
n
∑wilogx
i+ λ(b − x
ii =1
n
∑ )
wi
xi
= λ, w
i
λi =1
n
∑ = b ⇒ λ* =w
i
bi =1
n
∑ , xi* =
wi
wi
bi =1
n
∑
Network Economics - 35
Duality
= dual problem = min
λ h(λ)
If no “duality gap”, then φ(b ) = min
λ h(λ) = h(λ*)
example:
If f concave, g convex and X is a convex set, thenmax
x:g (x )=bx∈X
f (x ) = minλ
maxx∈X
[f (x ) + λ(b − g(x ))]
Network Economics - 36
Summary of necessary conditions
max f (x ) : x * : ∂f (x *)∂x
i
= 0 ( + check 2nd derivative)
maxf (x ) s.t. g1(x ) = b
1, g
2(x ) = b
2 (any f , g )
x*,λ* : (i) x * maximizes f (x ) + λ1*(b
1− g
1(x )) + λ
2*(b
2− g
2(x ))
(ii) g1(x*) = b
1, g
2(x*) = b
2
max f (x ) s.t. g1(x ) ≤ b
1, g
2(x ) ≤ b
2 (any f , g )
x*,λ* ≥ 0 : (i) x * maximizes f (x ) + λ1*(b
1− g
1(x )) + λ
2*(b
2− g
2(x ))
(ii) g1(x*) ≤ b
1, g
2(x*) ≤ b
2
(iii) λ1*(b
1− g
1(x*)) = 0, λ
2*(b
2− g
2(x*)) = 0 : slackness conditions
⇔ gi(x *) < b
i⇒ λ
i* = 0 and λ
i* > 0 ⇒ g
i(x*) = b
i
Market mechanisms and competitive equilibria
Network Economics - 38
Competitive equilibrium • Market mechanism using prices • Every participant in the market is small, can not affect prices • Equilibrium: stable point where production = demand, price p
consumers producers
Market clearance:
=> Social welfare optimum! => Tatonnement
Network Economics - 39
Single link with capacity constraints Total amount of resource available = , zero cost Maximization problem:
Mathematical solution: minmax the Lagrangian
Problem solution with market mechanism: use price
Each user solves:
= shadow cost of capacity
The optimal point of (1) is characterized by for which:
Note: although cost = 0, optimal price is not!
Network Economics - 40
Solving the dual
But this is done by each customer solving CUM using as a price
But this exactly how prices are updated in a market!
Network Economics - 41
Stability
�
where ˙ λ (t) = k(C − xi(t)i∑ ) for a small k
and xi(t) maximizes Ui(xi) − λ(t)xi at each t
�
Then ˙ V (t) = ui' ˙ x i(t) + ˙ λ (t)(C − xi(t)
i∑
i∑ ) − λ(t) ˙ x i(t)
i∑
= (u'i −i∑ λ(t)) ˙ x i(t) + ˙ λ (t)(C − xi(t)
i∑ )
= ˙ λ (t)(C − xi(t)i∑ )
= −k(C − xi(t)i∑ )2 < 0 But if there are delays??
Network Economics - 42
Market mechanisms
Under general conditions,
where is the Lagrange multiplier in (1)
Observe: - The optimum of (1) is achieved by a decentralized mechanism - The network does not need to know the utilities of the users
Network Economics - 43
Strategy issues Why should users respond truthfully their ? it may be profitable to cheat! In a case of 2 unequal users, the large user may pretend
he is small $
net benefit of user 1 if truthful
net benefit of user 1 if he pretends he is like user 2
Network Economics - 44
A possible analysis of a user charge In general we can analyze the total charge the user is
paying as S = F+U+G+Q, where F= covers fixed cost, U= covers usage cost, G= “congestion” part, Q= quality part
Quality 1
Quality 2
0
w= real cost/byte (into the network) F= real connection cost (with the network)
U G Q
varia
ble
part
rate
volume during T
variable part of price
when demand > capacity
Marginal cost pricing
Cost recovery
Network Economics - 46
Marginal cost prices Strong points:
welfare maximisation under appropriate conditions firmly based on costs easy to understand
Weak points: do not cover total cost (need for subsidisation) must be defined w.r.t. time frame of output expansion?
– short run marginal cost = 0 or – use long-run marginal cost (planned permanent
expansion) difficult to predict demand and to dimension the network difficult to relate cost changes to marginal output changes
Network Economics - 47
Marginal cost pricing problems Marginal cost = covers all sacrifices, present or future,
external or internal to the company, for which production is at the margin causally responsible
Problem1: specifying the time perspective should we use long-run MC rather than short-run MC? MC includes present and future causally attributed costs problem: total cost coverage
Problem2: specifying the incremental block of output incremental cost depends on size of increment charge the shortest run MC for the smallest output
increment? Problem3: large proportions of common costs
Network Economics - 48
Recovering network cost
Pricing at marginal cost maximises efficiency but does not necessarily recover network cost example: assume Then under marginal cost pricing, and the network revenue is , hence we are short of
Ways out: Ramsey prices (linear prices) add fixed fee (two-part tariffs) general non-linear tariffs
– –
�
p = β
�
α
Network Economics - 49
Two-part tariffs
Cost = $
AC (average cost)
�
MC
Under MC pricing, network needs to recover an additional amount
Use tariff
Customer benefit = < 0 ?
N customers
user demand at price
(marginal cost)
Marginal cost pricing
Sharing common marginal costs
Network Economics - 51
Objective Most services are not produced stand-alone There is common marginal cost How should this cost be shared if SW is to be maximized? We show that
sharing is not a priori fixed but depends on demand not trivial to compute cost-based pricing is not just a function of the cost
function examples: peak-load pricing, priority queues
Network Economics - 52
The case of common marginal cost Consider two products that are jointly produced using the
same facility. How to attribute the joint marginal cost a?
a b1
b2
�
amax{x1,x2}+ b1x1 + b2x2cost =
Network Economics - 53
The case of common marginal cost
L = u1(x1)+ u2 (x2 )− az − b1x1 − b2x2 + λ1(z − x1)+ λ2 (z − x2 )Find λ1,λ2 ≥ 0, x1, x2, z, s.tu '1(x1) = λ1 + b1, u '2 (x2 ) = λ2 + b2, a = λ1 + λ2
x1 ≤ z, x2 ≤ z,λ1(z − x1) = 0, λ2 (z − x2 ) = 0 ⇔z − xi > 0 ⇒λi = 0, λi > 0 ⇒ z − xi = 0
maxx1,x2 ,z
u1(x1)+ u2 (x2 )− az − b1x1 − b2x2
s.t. x1 ≤ z, x2 ≤ z
Economic interpretation: p1 = b1 + λ1, p2 = b2 + λ2, λ1 + λ2 = a
Network Economics - 54
A graphical calculation of prices Assume
The joint MC cost a is provided only by the high demand product
Case 1 D1>>D2
Case 2 D1 ≈ D2
Here both products share the joint MC cost a
Network Economics - 55
Special case: Peak load pricing
L = u(x1,…, xT )− b xt
T∑ − az + λ1(z − x1)+ ...+ λT (z − xT )
4 3 4
Network Economics - 56
Priority queues Real-time and best effort traffic share the same server C Real-time traffic is assigned priority, needs Best-effort uses the left-over capacity How to split the capacity marginal cost a?
x1 ≤C / ρ, ρ = 3
QoS constraint stability constraint p1
p2
Network Economics - 57
Priority queues: analysis maxx1,x2 ,C
u1(x1)+ u2 (x2 )− aC
s.t. 3x1 ≤C, x1 + x2 ≤C
maxx1,x2 ,C
u1(x1)+ u2 (x2 )− aC + λ1(C − 3x1)+ λ2 (C − x1 − x2 )
Find x1, x2,C, and λ1,λ2 ≥ 0 s.t.u '1(x1) = 3λ1 + λ2, u '2 (x2 ) = λ2, λ1 + λ2 = aC − 3x1 ≥ 0, C − x1 − x2 ≥ 0λ1(C − 3x1) = 0, λ2 (C − x1 − x2 ) = 0
Equivalently: p1 = 3λ1 + λ2, p2 = λ2, λ1 + λ2 = a⇔λ1 =p1 − p2
3, λ2 = p2, p1 + p2 = 3a
Case B: C − 3x1 < 0, x1 + x2 = C⇔ x2 > 2x1, λ1 = 0 (⇒ p1 = p2 = a)
Case A: C − 3x1 = 0, x1 + x2 <C⇔ x2 < 2x1, λ2 = 0 (⇒ p1 = 3a, p2 = 0)
Case C: C − 3x1 = 0, x1 + x2 = C⇔ x2 = 2x1, λ1,λ2 ≥ 0 (⇒ p1 + 2p1 = 3a)
2x1 < x2 2x1 = x2
2x1 > x2
Network Economics - 58
Priority queues Case A: low demand for best-effort
p2 = λ2 = 0!!
2x1 < x2 2x1 = x2
2x1 > x2
No need to move! we are at the optimum!
Network Economics - 59
Priority queues Case B: low demand for real-time
2x1 < x2 2x1 = x2
2x1 > x2
No need to move! we are at the optimum! p1 = p2 = a!!
Network Economics - 60
Priority queues
Methodology: construct to intersect
Case C: balanced demand p20 = 0Methodology: start with and increase
until p2 s.t. p1 = 3a − 2p2
2x1 = x2x1(p1) = A1 − b1p1 ⇔2x1(p1) = 2A1 − 2b1p1 ⇔2x1(p2 ) = 2A1 − 2b1(3a − 2p2 ) = 2x1
0 + 4b1p2
x2 (p2 )
Network Economics - 61
Conclusions Marginal cost pricing is hard to implement in practice When joint costs, it is hard to attribute to individual
services, depends on demand Same problem if joint facility must be configured to
accommodate maximum service provisioned In communication networks, services may share joint
facilities like in priority queues
Lock-in
Reference: “Information Rules” by Carl Shapiro and Hal R. Varian
Network Economics - 63
Recognizing lock-In Durable investments in complementary assets
Hardware Software
Supplier wants to lock-in customer Customer wants to avoid lock-in Basic principle: Look ahead and reason back Examples:
Bell Atlantic and AT&T – 5ESS digital switch used proprietary operating system – Large switching costs to change switches
Computer Associates User behavior in the Web
Network Economics - 64
Small switching costs matter Small switching cost per customer but large customer
bases Phone number portability Email addresses
– Hotmail (advertising, portability) – ACM, CalTech
Look at lock-in costs on a per customer basis
Network Economics - 65
Profits & switching costs in general: Profits from a customer = total switching costs + quality/cost
advantages Customer C switches from A to "same position" w/ B: Total
switching costs = customer costs + B's costs In commodity market like telephony, profit per customer = total
switching costs per customer Example: ILECs vs CLECs: ILEC profits = customer + CLEC
switching costs Can answer these questions:
How much to invest to get locked-in base Evaluate a target acquisition (e.g., Hotmail) Product and design decisions that affect switching costs
Network Economics - 66
�
p
new entrant price =p, offers discount d to switching customer
customer indifferent to switch
new entrant balances costs
A model of switching cost
switching cost s
q = equilibrium market price
Network Economics - 67
Classification of lock-In
Durable purchases and replacement: declines with time
Brand-specific training: rises with time
Information and data: rises with time
Specialized suppliers: may rise
Search costs: learn about alternatives
Loyalty programs: rebuild cumulative usage
Contractual commitments: damages
Externalities
Network Economics - 69
Externalities Externalities: the actions of one agent affect the utility of
an other agent: Positive (network effects), negative (congestion)
No externality:
Externality:
SW optimal prices can not be determined by the market alone: need special price mechanism that takes account of the externalities
Network Economics - 70
Example n identical users, user i consumes , marginal cost =2 (a) Positive externalities (network effects)
(b) Negative externalities (congestion)
Price = MC = 2. User i maximizes over
Social planner maximizes:
�
xi
�
ui(x) =U(xi) + [x1,…,xn ]
�
ui(x) =U(xi) − [x1,…,xn ]
positive effect of other users participating
negative effect (disutility) because of other users participating
�
(a)U(xi) + [x1,…,xn ] − 2xi =U(xi) − xi(b)U(xi) − [x1,…,xn ] − 2xi =U(xi) − 3xi
�
xi
�
(a)∀i :U(xi) + nxi − 2xi =U(xi) + (n − 2)xi(b)∀i :U(xi) − nxi − 2xi =U(xi) − (n + 2)xi
>>0
Network Economics - 71
Externalities
�
x
�
3x
�
(n + 2)x
�
xpu
�
xpSW = xmax
�
xnSW
�
xnu
�
U(x)
�
U(x)
Congestion Network effects
�
User :U(xi) − xi − 2xi =U(xi) − 3xiSW :U(xi) − nxi − 2xi =U(xi) − (n + 2)xi
�
User :U(xi) + xi − 2xi =U(xi) − xiSW :U(xi) + nxi − 2xi =U(xi) + (n − 2)xi
Networks and Positive Externalities
From “Information Rules” by Carl Shapiro and Hal R. Varian
Network Economics - 73
Positive externalities: positive market feedback
Positive feedback: strong get stronger, weak get weaker Negative feedback: stabilizing effect Makes a market “tippy” Examples: VHS v. Beta, Wintel v. Apple “Winner take all markets”
Mar
ket s
hare
Time
50%
0
100%
Valu
e fo
r the
use
r Number of compatible users
winner
looser
battle zone
Time
Num
ber o
f use
rs
launch
takeoff
saturation
Network Economics - 74
Sources of positive feedback
Supply side economies of scale Declining average cost Marginal cost less than average cost Example: information goods
Demand side economies of scale Network effects: virtual networks
– Network externalities: one market participant affects others without compensation being paid.
Examples: fax, email, Web, Sony v. Beta, Wintel v. Apple
Network Economics - 75
Network effects (1)
100
500
1000
1500
2000
2500 price
0 100
A B
1 N-n N
n
Network Economics - 76
Network effects (2)
Network Economics - 77
Key observations Number of users is important
Metcalfe’s Law: Value of network of size n proportional to n2
More likely nlogn Importance of expectations Network effects lead to substantial collective switching
costs: even worse than individual lock-in (due to coordination costs). Example: QWERTY
Evolution vs revolution, openness vs. control (standards setting)
Network externalities don’t always apply ISPs (but watch out for QoS) PC production
Pricing with (positive) externalities
Two sided markets
Network Economics - 79
Definition Two-sided markets (two-sided networks) are economic platforms
having two distinct user groups that provide each other with network benefits
Examples: credit cards (cardholders and merchants); operating systems (end-users and developers), yellow pages (advertisers and consumers); video game consoles (gamers and game developers); communication networks, such as the Internet (end users, content providers)
Members of each group exhibit a preference regarding the number of users in the other group; these are called cross-side network effects
Explain many free pricing strategies where one user group gets free use of the platform in order to attract the other user group
1-sided: volume of interaction
Network Economics - 80
Pricing in two-sided markets Pricing each group in a two-sided network must consider
network effects
Rule 1: subsidize the more price sensitive side, and charge the side whose demand increased more strongly in response to growth on the other side
Case of Adobe
Network Economics - 81
Pricing in two-sided markets Rule 2: subsidize those who add platform value
Case of Microsoft vs Apple
Pricing
Price discrimination
Network Economics - 83
Monopoly: linear+uniform prices • Goal: maximize profits • Advantage: economies of scale (small MC) • Disadvantage: inefficiency, small consumer surplus Combine with regulation
$
q
MC
Demand
Marginal revenue
Welfare loss
Network Economics - 84
Oligopoly • Firms are not price takers • Individual decisions can influence prices • Game theory provides appropriate models • Many models of competition, results sensitive to assumptions
- Cournot, Bertrand, Stackelberg, etc.
A “rule-of-thumb” result: -Assume n identical competing firms -Market demand function =
Prices:
Network Economics - 85
Price discrimination: an example
Sell a product to different customer types
$
3
1
1 2 3 4
$
3
1
1 2 3 4
$
3
1
1 2 3 4
Profit=3 Profit=4 Profit=6
Price discrimination: personalized pricing, versioning, group pricing
Network Economics - 86
Personalized pricing (1) First-degree price discrimination: • extracts maximum profit from customer • addresses each customer separately • “take it or leave it” offer “amount x for m dollars” • Pareto efficient operation
$
q
MC=0 A
Network Economics - 87
Two part tariff Optimal strategy: use a single volume price to maximize social welfare, then take it all customer surplus back using subscription fees
Example: a customer with utility , cost
If is the price at which social welfare is maximized, then use tariff
subscription fee = constant, independent of consumption
usage charge
A
Network Economics - 88
Two-part tariff example Achieve first-degree price discrimination
Tariff: <f,p>=<$4500,10c>
Network Economics - 89
Personalized pricing (2) examples: mail orders, airlines, travel agencies information: depends on the kind of enterprise price sensitivity of customers is key
do market research (promotional pricing) use discount coupons
Internet: more individualized and interactive price offer depends on what your buying (dynamic) remember customer history inexpensive market research (via promotions) overstock sales
from: Varian and Shapiro: Information Rules
Network Economics - 90
Group pricing (1) Third-degree price discrimination: • customer type pricing, no self-selection • social welfare increases -> increase of output
$
q
Small market is also served!
Network Economics - 91
Group pricing (2) why sell to groups rather than to end users:
price sensitivity: members of different groups differ systematically in price sensitivity
network effects: value increases with group ownership lock-in: become ubiquitous in an organization sharing arrangements: pricing for sharing
– items that are used infrequently by a single user are provided by info intermediaries (libraries, video stores
– transaction costs determine whether it is better to sell or rent information
– do even better: offer prices for both sale and rental from: Varian and Shapiro: Information Rules
Network Economics - 92
Versioning
Second-degree price discrimination: market segmentation • set of offers available to all customers • customers self select (incentive compatibility) • examples: quantity discounts, versioning
$
q
$
q MC=0
A
B
C A D
B
C
making self selection work improving revenue
0
Network Economics - 93
Non-linear tariffs
$
q
MC G
TL :A + p1x TH :G +MCx
A
Gp1
x2
A
Given the two tariffs TH and TL, the customers choose the same quantities they would choose using the optimal “take it or leave it” offers
Network Economics - 94
Versioning and pricing Make prices depend on value to customers Don’t need to price by customer identity Offer product line, and watch choices Design menu of different versions
Target different market segments Price accordingly (self selection)
Traditional information goods: Hardback/paperback Movie/video
from: Varian and Shapiro: Information Rules
Network Economics - 95
Dimensions to use for versions
Delay
User Interface
Image Resolution
Speed of operation
Format
Capability
Features
Comprehensiveness
from: Varian and Shapiro: Information Rules
Network Economics - 96
Example
40 type As: $100 for speed, $40 for slow
60 type Bs: $50 for speed, $30 for slow
Identity-based pricing: $7000 revenues
Offer only speedy: $50 is best price, revenues=$5,000
Offer only slow: not as profitable
from: Varian and Shapiro: Information Rules
Network Economics - 97
Versioning solution
Try speedy for $100, slow for $30
Will this work? Compare benefits and costs
100-100=0, but 40-30=10 > 0
Discount the fast version: 100-p=40-30
So, p=90
Revenues = $5,400 = 90x40 + 30x60
from: Varian and Shapiro: Information Rules
Network Economics - 98
Making self-selection work
May need to cut price of high end
May need to cut quality at low end
Value-subtracted versions
May cost more to produce the low-quality version
In design, make sure you can turn features off!
from: Varian and Shapiro: Information Rules
Network Economics - 99
How many versions? One is too few Ten is (probably) too many Two things to do
Analyze market Analyze product
Analyze your market: does it naturally subdivide into different categories? are behaviors sufficiently different?
Analyze your product: design for high-end, reduce quality for low-end
Default choice: 3 versions Extremeness aversion from: Varian and Shapiro: Information Rules
Network Economics - 100
Damaged good example
Profit=100(19-2)+100(8-2-1)=2200$
From “How to Price” Oz Shy
$2
2
$10
Network Economics - 101
Two-part tariffs Same as versioning
Price: determines quantity consumed Fixed part: lump sum of money requested
Network Economics - 102
Multipart tariffs Multipart tariffs are equivalent to multiple 2-part tariffs
Network Economics - 103
Tying (Bundling) Offer many goods as a package Example: Microsoft Office Added benefit: they work together Price of bundle < sum of component prices
buy one product, then other is priced less than standalone price
Reduce dispersion in customer value Example: price separate or together Mark: $120 for WP, $100 for spreadsheet Noah: $100 for WP, $120 for spreadsheet Profits
– Without tying: $400 – With tying: $440
from: Varian and Shapiro: Information Rules
Network Economics - 104
Tying Consumer choices under no tying, pure tying and mixed
tying
Negative externalities Congestion pricing
Network Economics - 106
Defining a congestion price Define:
The maximization problem including choosing capacity
�
B = amount of resource (bandwidth)
X = total traffic = xrr∑
D = packet delay = for M/M/1: 1/(B − X)c(B) = cost of resource
�
max{xi },B
ui(xi,D(X,B)) − c(B)i=1
n
∑
Network Economics - 107
Analysis The first-order optimality conditions (for fixed B) are
which suggest a congestion price
Lets check: user i solves �
∂ui(xi,D)∂xi
+∂D∂xi
∂u j (x j ,D)∂Dj
∑ = 0, i = 1,...,n (i)
�
pE = −∂D∂X
∂ui(xi,D)∂Di
∑
�
maxxi{ui(xi,D) − pE xi}
�
⇔∂ui∂xi
+∂D∂xi
∂ui∂D
− pE =∂ui∂xi
+∂D∂xi
∂ui∂D
+∂D∂xi
∂u j (x j*,D)
∂Dj∑ = 0
which is the same as (i) when n is large
Network Economics - 108
Remarks Note that
is the marginal increase of the negative externality for a
marginal increase of
Or the willingness of the users to pay for not increasing
the total rate
To compute it we need to know the utility functions of the
participants (which is not the case in a competitive
market without externalities)
�
pE = −∂D∂xi
∂ui(xi,D)∂Di
∑
Network Economics - 109
Capacity expansion Do the maximization including the choice of B: maximize
First order conditions:
�
W (B) = ui(xi*,D*) − c(B)
i∑
dW (B)dB
= ∂W∂xi
*i∑ ∂xi
*
∂B+ ∂W∂D
∂D∂B
− c '(B)
= ∂ui∂Di
∑ ∂D∂B
− c '(B)=(*)− ∂ui
∂Di∑ ∂D
∂ XΔXΔB
− c '(B) = ΔXΔB
pE − c '(B)
⇔ expand if pEc '
> ΔBΔX
( = 1 for M/M/1)
ΔX,ΔB :D(X,B) = d⇔ ∂D∂X
ΔX + ∂D∂B
ΔB = 0⇔ ∂D∂B
= − ∂D∂X
ΔXΔB
(*)
�
DM/M/1(X,B) =1
B − x jj∑
⇔ ΔXΔB
= 1
Network Economics - 110
Example: delay cost at a single link
�
B
�
D(X,B) =1
B − x jj∑
�
Max SW : maxx1 ,…,xn
[u j (x j ) −j∑ γ j x jD( xk )
k∑ ]
⇔ ′ u i −γ iD −γ ixi ′ D − ′ D γ j x jj≠ i∑ = 0 (1)
Free market equilibrium: User i: maxxi
[ui (xi )−γ i xiD( xk )k∑ ]
⇔ ′ui −γ iD −γ i xi ′D = 0 (2) the system is more congested!
�
Ui(xi,D) = ui(xi) −γ ixiD
Network Economics - 111
Delay cost at a single link
�
B
�
D(X,B) =1
B − x jj∑
Max SW: maxx1,…xn
[uj (x j )−j∑ γ j x jD( xk )k∑ ]
⇔ ′ui −γ iD −γ i xi ′D − ′D γ j x jj≠i∑ = 0 (1)�
User i : ui(xi) −γ ixiD
To maximize SW: charge xi with price pic = ′D γ j x jj∑
User i: maxxi
[ui (xi )−γ i xiD( xk )− pic
k∑ xi ]
⇔ ′ui −γ iD −γ i xi ′D − pic = 0 (3)
same conditions
For n large use uniform price pc = ′D γ j x jj∑ = 1(B − x jj∑ )2
γ j x jj∑
Network Economics - 112
Congestion prices on sample paths Two practical problems to compute congestion prices
to take derivatives we need the form of the utilities need to compute average performance measures in
network (slow, inaccurate) Instead of constructing deterministic prices that reflect
derivatives of some average quantity, construct fluctuating prices that capture temporal congestion effects -> result in same average price
Charge each packet individually for the cost it imposes to other packets
How do we learn the delay cost of individual packets if not uniform?
Network Economics - 113
Computing congestion prices 1. Congestion charge rate px is computed on an average basis
pc x
x = average flow g = average congestion cost
2. Each packet is charged the cost increment that it causes
Packet a is charged the extra cost it causes (sender of a receives one congestion mark = 1c)
a b
• The rate of charge px is averaged on the particular sample path
• In many systems marking prob p ≈ = pc
p x $/s
x p/s
p = marking probability
Assume: cost unit = extra cost caused by a single packet when loss occurs
x
�
pc =∂g∂x
loss
loss, delay
p/s
$/s
Network Economics - 114
Sample path congestion prices
time
capacity
sample path congestion price: 1 0
arriving load
Example: Server that serves up to 10 packets in each time slot
Network Economics - 115
How to reveal true congestion cost Need to design a mechanism
n equal length packets queue at a router, incur delays
Schedule packets to minimize weighted delay cost
How do we learn the costs ?
Mechanism Design paradigm!
Serve in decreasing order of declared
Charge each packet the cost it causes to the other
packets behind it
=> Incentive compatible and optimal!
cii∑ Di
ci
ci
Di
Network Economics - 116
Smart markets (Vickrey auction) Which k packets to serve in a time slot? Use a bandwidth auction in each time slot Packets declare maximum price they are willing to pay (bids) System accepts the k packets with the highest bids Packets pay a uniform price = highest bid of not accepted
packet Type of congestion charge (why?) Incentive compatible
Information issues A market of lemons
Network Economics - 118
Information
Economic agents that interact make decisions based on information available regarding the other agents
Less information available leads to decrease of efficiency Adverse selection occurs when some type of agent
finds it profitable to choose an offer intended for another type. As a result, the seller obtains less profit than anticipated There may be no prices for the firm to recover costs no equilibrium (inefficient market: market failure) Beneficial for both seller and buyers to signal
information
Network Economics - 119
Adverse selection and ISPs (1) potential customers, each requiring units of Internet
use, uniformly distributed on [0,1] Provider charges A customer of type has a utility He won’t buy service if his surplus is negative The network exhibits economies of scale. The unit cost
when using total bandwidth for its customers is includes a discount factor that varies linearly
from to 1 with the total amount of bandwidth purchased
�
p(b) = αbn /2
+1 1− bn /2
⎛ ⎝ ⎜
⎞ ⎠ ⎟
�
u(x) = x
�
x − w(x)
�
n /2
�
w(x)
Network Economics - 120
Adverse selection and ISPs (2) Complete information:
customer of type is charged
All customers subscribe, provider and customers have positive profits
for small enough
Network Economics - 121
Adverse selection and ISPs (3) Incomplete information: price is same for all customers Adverse selection: price targeted to recover costs for
average customer, heavy customers profit and increase average cost => no stable market
Assume that provider charges heaviest customers subscribe, Typical (average) customer
Profit from typical customer =
�
π = w −12p(b)(1+ w) = w −
12[1− (1−α)(1− w2)] 1+ w( )
�
n(1− w)
�
x =1+ w2
�
b = n(1− w) (1+ w)2
if for all values of
General network flow pricing
Network Economics - 123
Fairness in flow allocations Fairness: How should the bandwidth be shared among
competing flows? Economics: Pareto efficiency, max some form of SW Network engineering: Max throughput, max-min,
proportional fairness,… Can we relate the two?
Network Economics - 124
SW max. with capacity constraints
Generalize the single link case: flow identity defined by a
route r (set of links it traverses), = bit rate of flow r
Assume a utility function for flow , solve
NUM:
Network Economics - 125
Example: weighted prop. fairness
w-Proportional Fairness (WPF): Network problem:
Network Economics - 126
Nash bargaining solution -> WPF Two players bargain to share profit Alternate in rounds making proposals -counterproposals
…. Stationary strategy =>
u11/n1u2
1/n2 = v11/n1v2
1/n2 = e− s
W-proportional fairness
Game theory
Network Economics - 128
What is game theory? Traditional optimization: theory of optimal decision
making of a single agent Game theory: study of interacting decision makers Games: models of interactive decision making
strategic form: a player chooses his plan of action once and for all covering all possible contingencies
extensive form: explicit description of sequential structure of the decision problems
different solution concepts one-shot, repeated games
Network Economics - 129
The prisoner's dilemma
Example of strategic game Description: game matrix (common knowledge) Nash equilibrium: each player’s strategy choice is a best reply to the strategy choices of the other players
3,3 1,1 0,4
4,0 Player A
Player B
cooperate
defect
cooperate defect
Nash equilibrium = (defect,defect)
strategies
= dominant strategy equilibrium
Network Economics - 130
Other concepts Nash equilibria may involve mixed (randomized) strategies Nash equilibria always exist, but may be many! Which one is reasonable to expect?
dominant strategy equilibrium: simplify the game by eliminating dominated strategies
concept of subgame perfect equilibrium
2,1 1,2 0,0
0,0 Bach
Stravinsky
Bach Stravinsky
1,-1 1,-1 -1,1
-1,1 head
tail
head tail
Network Economics - 131
Subgame-perfect equilibrium The ultimatum game Some NEs are not rational in the actual game setup
0 1
0 0
II
Y N
x
1-x
0 0
II
Y N
1 0
0 0
II
Y N
II II
I
0$ x$
1$
0 1
0 0
II
Y N
x
1-x
0 0
II
Y N
1 0
0 0
II
Y N
II II
I
0$ x$
1$
NE1: player 2 gets all: not SGP! NE2: player 1 gets all .99
.01 0
0
II
Y N
1 0
0 0
II Y N
I
.99$ 1$
II
Y N
If problem is discrete, then 2 SGP NEs!
Network Economics - 132
Multiple equilibria Which one to select?
Network Economics - 133
Repeated games Larger strategy space: take account of history long-run interest different than short-run interest Can enforce cooperation by using punishment strategies Cartels
3,3 1,1 0,4
4,0 Player A
Player B
cooperate
defect
cooperate defect Strategy Grim: cooperate in the current move unless the other player defected in the previous move, in which case defect forever
Payoff with discount r =
Network Economics - 134
An example of strategic voting Boris, Horace and Maurice: membership committee vote: a new member is considered for admission, Alice is in the agenda, but there also a new proposal for Bob to replace Alice
Alice or Bob
Alice or
Nobody
Bob or
Nobody
Alice
Bob
Alice
Nobody
Nobody
Bob
Alice Nobody
Bob
Nobody Alice Bob
Bob Alice
Nobody
Boris Horace Maurice
Preferences
1 2
3
Strategic voting: guess other’s strategy
from: Ken Binmore, “Fun and Games”
Network Economics - 135
An auction example Bidder A: Bidder B:
Auction 1: highest bid wins, pay your bid Auction 2: highest bid wins, pay loosing bid
Auction2: strategy = tell the truth, always B gets the good Auction1: strategy = shade bids, sometimes A gets the good!
0 2 1 Auction 1 is not achieving max SW!
Network Economics - 136
Public goods Non-excludable and non-rival goods Incentive problem in provisioning: the free-rider problem
Example: provision a common facility of size = 1,2
1,1 0,0 -1,2
2,-1 Player A
Player B
provision 1
provision 0
provision 1 provision 0
Free-riding: player i prefers the other player to contribute Free-market fails to provision optimum amount of public goods
Network Economics - 137
Strictly competitive games Strategic and extensive forms
Zermelo’s algorithm: work backwards on subgames first
Theorem: Any finite strictly competitive game with perfect Information has a value