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