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John Chuang 2
Network Competition
Design for Choice Design for Competition
Loci of Competition- Who, what, and where
Models of Competition- Quantify benefits of competition
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Loci of CompetitionA 2x2 Network Model
Edge Core
Logical/ Service
Internet Service Providers (ISPs)
Internet Backbone Operators
Physical
Last-mile access networks
Wide-area transit networks
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Models of Competition
Monopoly Perfect Competition Oligopoly
Many other models to capture “messiness” of the real-world, e.g., incomplete information, asymmetric information, bounded rationality, transactional costs, externalities, …
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Preliminaries
Agents: e.g., buyers and sellers Commodity: goods, services Market: to facilitate trade Utility: measure of satisfaction derived from trade
Equilibrium: predicted outcome
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Utility
Seller’s utility = profit () = revenue - cost- revenue = price * quantity- cost includes fixed and marginal costs
Buyer’s utility = valuation - price- Valuation aka willingness-to-pay (WTP)
Utility maximization- Seller i sets Pi and/or Qi to maximize profit- Buyer j decides which product, if any, to purchase
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Demand
w
q
Willingness to pay (WTP)
Marginal WTP: w(q)
…
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w
q
Amount paid (producer’s revenue)
q
p
Consumer surplus
w(q)
Consumer Surplus
Not every consumer may be served, even if their WTP > 0 Results in dead-weight loss (DWL)
DWL
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Supply
c(q)
q
Production cost function: c(q) Fixed cost = c(0) = F
F
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Marginal Cost
m(q)
q
Total cost (excluding fixed cost)
q
Marginal cost: m(q) = c’(q)
Marginal cost curve
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Producer Surplus
$
q
Marginal cost
q
Profit = revenue - cost = p·q - c(q) Producer surplus excludes fixed cost Example: for constant marginal cost function:
- Profit = (p-m)·q - c(0)- Producer surplus = (p-m)·q
Marginal WTP
m
pPS
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Social Surplus
w
q
Marginal cost
q
Also known as social welfare or total surplus SS = CS + PS
Marginal WTP
m
pCS
PS
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Monopoly v. Competition
What are the tradeoffs?
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Monopoly
Single producer -- free to set prices to maximize profit (usually at the expense of social welfare)
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Monopoly Example
Cost: c(q) = c- Zero marginal cost
Linear Demand: p(q) = 1 - q
Profit: = p·q - c Producer surplus: PS = p·q Profit maximization:
- Solve the equation d/dq = 0- q* = 1/2; p* = 1/2 = 1/4 - c
Consumer surplus, CS = 1/8 Social welfare = CS + PS = 3/8 Q: when will monopolist choose not to produce?
q
p
1
1
p(q) = 1 - q
q*
p*
Dead Weight Loss (DWL)
Consumer Surplus
Producer Revenue
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Perfect Competition
No dominant supplier- Price determined by the market, i.e., all suppliers are price takers
Competition drives price down to marginal cost- In example: p* = MC = 0 --> q* = 1- Profit, = -c- Producer surplus = 0- Consumer surplus, CS = 1/2- Social welfare = 1/2
Perfect competition maximizes social welfare, but suppliers cannot recover fixed cost
q
p
1
D
q*=1p* = 0
Consumer Surplus
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Monopoly v. Competition
What are the tradeoffs?
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Oligopoly
Competitive market with small number of suppliers- Duopoly is special case, though common in many telecommunication sectors
Common oligopoly models, analyzed as games:- Bertrand competition: price competition- Cournot competition: quantity competition- Stackelberg competition: leader follower game
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Stackelberg Game
Duopoly game played in two steps:- Supplier 1 (leader) first choose
quantity q1
- Given q1, supplier 2 (follower) choose q2 as best response
Game solved backwards, starting with supplier 2 Example: qi in [0,1], p = 1-q, ci = 0
- Supplier 2: max 2 = q2(1-q1-q2) --> q2 = (1-q1)/2
- Supplier 1: max 1 = q1(1-q1-q2) --> q1 = 1/2
- (q1,q2) = (1/2, 1/4) is Nash equilibrium
Q: how does this compare with the cases of monopoly and perfect competition?
q
p
1
1
p(q) = 1 - q
q*
p*
Dead Weight Loss (DWL)
Consumer Surplus
Producer Revenue
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Summary: Monopoly,Duopoly, andPerfect Competition
Q* P* Producer Surplus
Consumer Surplus
Total Surplus
Dead Weight Loss
Monopoly 0.5 0.5 0.25 0.125 0.375 0.125
Duopoly (Stackelberg)
0.75 0.25 0.1875 0.28125 0.46875 0.03125
Perfect Competition
1 0 0 0.5 0.5 0
q
p
1
1
p(q) = 1 - q
q*
p*
Dead Weight Loss (DWL)
Consumer Surplus
Producer Revenue
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Summary
Degree of competition matters! Whereas perfect competition can be ruinous to industries with low marginal cost (strong economies of scale)…
Oligopolistic competition can allow providers a path to cost recovery and profitability, while also avoiding the pitfalls of a monopoly
Actual social welfare realization depends on the actual shapes of the demand and supply curves
