Investment and market structurein industries with congestion
Ramesh JohariNovember 7, 2005
(Joint work with Gabriel Weintraub and Ben Van Roy)
Big picture
Consider industries where:• customer experience
degrades with congestion• providers invest to
mitigate congestion effects
Basic question: What should we expect?
The current situation
Current answer: don’t know!• Trauma in the backbone industry• Unbundling, then bundling of DSL• Municipal provision of WiFi access
How do engineering facets impact industry structure?
Outline
• Background and model• Returns to investment• The timing of pricing and investment• Key results• Future work and conclusions
Basic model
Consumers Destination
Basic model
Consumers Destination
Total mass = X ; assumed “infinitely divisible”
Basic model
Consumers Destination
Providers
Model 1: “selfish routing”
Only considers congestion cost
Consumers Destination
l1(x1)
l2(x2)
l3(x3)
Congestion cost seen by a consumer
Model 1: “selfish routing”
Consumers split so l1(x1) = l2(x2) = l3(x3)) Wardrop equilibrium
Consumers Destination
l1(x1)
l2(x2)
l3(x3)
Model 2: Selfish routing + pricing
Providers charge price per unit flow
Consumers Destination
p1 + l1(x1)
p2 + l2(x2)
p3 + l3(x3)
Prices
Model 2: Selfish routing + pricing
Assumes the networks are given
Timing:First: Providers choose pricesNext: Consumers split so:
p1 + l1(x1) = p2 + l2(x2) = p3 + l3(x3)
[Recent work on equilibria, efficiency, etc., byOzdaglar and Acemoglu, Tardos et al., etc.]
Model 3: Our work
Providers invest and price
Consumers Destination
p1 + l(x1, I1)
p2 + l(x2, I2)
p3 + l(x3, I3)
Model 3: Our work
Providers invest and price
Consumers Destination
p1 + l(x1, I1)
p2 + l(x2, I2)
p3 + l(x3, I3)
Investment levels
Model details
• Cost of investment: C(I)• Congestion cost: l(x, I)
• Given “total traffic” x and investment I• Increasing in x, decreasing in I
• Given prices pi and investments Ii customers split so that:
pi + l(xi, Ii) = pj + l(xj, Ij) for all i, j
Profit of firm i: pi xi - C(Ii)
Costs
Two sources of “cost”:• disutility to consumers:
congestion cost• provisioning cost of providers:
investment cost
Model details: Efficiency
Efficiency = minimize total cost:
i [ xi l(xi , Ii) + C(Ii) ]
Total congestion costin provider i’s network
Provider i’sinvestment cost
Model details: Efficiency
Efficiency = minimize total cost:
i [ xi l(xi , Ii) + C(Ii) ]
Central question:When do we need regulation
to achieve efficiency?
Returns to investment
A key role is played by:K(x, I) = x l(x, C-1(I) )
Idea: measure investment in $$$.Fix > 1.K( x, I) < K(x, I):
increasing returns to investmentK( x, I) > K(x, I):
decreasing returns to investment
Returns to investment
Increasing returns to investment occur if:• one large link has lower congestion
than many small links(e.g. statistical multiplexing)
• marginal cost of investment is decreasing
Example:Fiber optic backbone (?)
Returns to investment
Decreasing returns to investment occur if:• splitting up investments is beneficial
(e.g. many “small” base stations vs.one “large” base station (?) )
• marginal cost of investment is increasing
Increasing returns and monopoly
Important (basic) insight:increasing returns to investment )natural monopoly is efficient )some regulation needed
For the rest of the talk:Assume decreasing returns to investment.
Timing: pricing and investment
When do providers price and invest?
• Long term investment,then short term pricing?
• Or, short term investment,and short term pricing?
Timing: pricing and investment
Long term investment +short term pricing:
Can be arbitrarily inefficient.
(Under-investment first,then price gouging later.)
Timing: pricing and investment
What about simultaneous pricing and investment?i.e., investment decisions areshort term and relatively reversible
Remarkable fact:Competition is efficient!(in a wide variety of cases…)
Summary of results
• In a wide range of models,if a (Nash) equilibrium exists,it is unique, symmetric, and efficient.
• Sufficient competition is needed to ensure equilibrium exists.
• With fixed entry cost:competition is asymptotically efficient.
Efficiency of equilibrium
If C(I) is convex and:• l(x, I) = l(x)/I, and l(x, I) is convex; OR• l(x, I) = l(x/I), and l(¢) is convex; OR• l(x, I) = xq / I , for q ¸ 1
Then:At most one Nash equilibrium exists,and it is symmetric and efficient.
Efficiency of equilibrium
Included:l(x, I) = x/I :
x = total # of bits to transfer
I = capacity (in bits/sec)l(x, I) = time to completion
Not included:M/M/1 delay: l(x, I) = 1/(I - x)
Existence of equilibrium
If l(x, I) = xq/I and C(I) = I,
then Nash equilibrium exists iffN ¸ q + 1
(N = # of providers)
Entry
Suppose:To enter the market, providers pay a
fixed startup cost.
Then:As the customer base grows, the
number of entrants becomes efficient.
Application: Wi-Fi
In Wi-Fi broadband access provision,we see:
• constant marginal costof capacity expansion
• low prices for upstream bandwidth• short term investment decisions
Would competition be efficient?
Application: source routing
Common argument:Source routing would give providers
the right investment incentives
Our answer:• depends on cost structure• depends on timing of pricing and
investment
Back to Clean Slate
What is the value of this research?
• Technology informsinvestment cost structure
• Performance objectives informcongestion cost structure
• Both impact market efficiency
Open issues
Future directions:
• Ignored contracting between providers• Peering relationships• Transit relationships
• Ignored heterogeneity of consumers
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