Investment and market structure in industries with congestion Ramesh Johari November 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)l1(x1) l2(x2)l2(x2) l3(x3)l3(x3) Congestion cost seen by a consumer

Model 1: “selfish routing” Consumers split so l 1 ( x 1 ) = l 2 ( x 2 ) = l 3 ( x 3 ) ) Wardrop equilibrium Consumers Destination l1(x1)l1(x1) l2(x2)l2(x2) l3(x3)l3(x3)

Model 2: Selfish routing + pricing Providers charge price per unit flow Consumers Destination p 1 + l 1 (x 1 ) p 2 + l 2 (x 2 ) p 3 + l 3 (x 3 ) Prices

Model 2: Selfish routing + pricing Assumes the networks are given Timing: First: Providers choose prices Next: Consumers split so: p 1 + l 1 ( x 1 ) = p 2 + l 2 ( x 2 ) = p 3 + l 3 ( x 3 ) [Recent work on equilibria, efficiency, etc., by Ozdaglar and Acemoglu, Tardos et al., etc.]

Model 3: Our work Providers invest and price Consumers Destination p 1 + l(x 1, I 1 ) p 2 + l(x 2, I 2 ) p 3 + l(x 3, I 3 )

Model 3: Our work Providers invest and price Consumers Destination p 1 + l(x 1, I 1 ) p 2 + l(x 2, I 2 ) p 3 + l(x 3, I 3 ) 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 p i and investments I i customers split so that: p i + l ( x i, I i ) = p j + l ( x j, I j ) for all i, j Profit of firm i : p i x i - C ( I i )

Costs Two sources of “cost”: disutility to consumers: congestion cost provisioning cost of providers: investment cost

Model details: Efficiency Efficiency = minimize total cost:  i [ x i l ( x i, I i ) + C ( I i ) ] Total congestion cost in provider i’s network Provider i’s investment cost

Model details: Efficiency Efficiency = minimize total cost:  i [ x i l ( x i, I i ) + C ( I i ) ] 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 investment K (  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 are short 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 ) = x q / 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 ) = x q / I and C ( I ) = I, then Nash equilibrium exists iff N ¸ 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 cost of 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 informs investment cost structure Performance objectives inform congestion cost structure Both impact market efficiency

Open issues Future directions: Ignored contracting between providers Peering relationships Transit relationships Ignored heterogeneity of consumers