Investment and market structure in industries with congestion Ramesh Johari November 7, 2005 (Joint...

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