Platform Competition in Two-Sided Markets

Abstract

Many if not most markets with network externalities are two-sided. To succeed, platforms in industries such as software, portals and media, payment systems and the Internet, must “get both sides of the market on board”. Accordingly, platforms devote much attention to their business model, that is to how they court each side while making money overall. The paper builds a model of platform competition with two-sided markets. It unveils the determinants of price allocation and end- user surplus for different governance structures (profit-maximizing platforms and not-for-profit joint undertakings), and compares the outcomes with those under an integrated monopolist and a Ramsey planner.

Question

The paper asks a question that the textbook theory of multiproduct pricing cannot pose: in a market where two distinct groups of users must be brought together through a common [[platform]], how should the platform divide the total price it charges between the two sides — and not merely what total price it should set?

A market with [[network-effect|network externalities]] is two-sided when the volume of transactions and the platform’s profit depend not only on the total price levied on the parties to a transaction, but also on its decomposition between them . Videogame consoles court gamers as a loss leader while charging developers; PC operating systems do the reverse . The central question — which side to subsidise and which to milk — is precisely what the trade press calls the [[business-model]] of a platform, and what Rochet and Tirole set out to derive rather than assert.

Methods

The paper is a theoretical contribution: it builds and solves a microeconomic model of platform pricing, with no econometric estimation (the authors offer only “casual empiricism” in seven mini case studies ).

Primitive. A (buyer, seller) pair corresponds to one potential transaction. Buyers’ and sellers’ per-transaction benefits bᴮ, bˢ are drawn independently; quasi-demands Dᴮ(pᴮ) = Pr(bᴮ ≥ pᴮ) and Dˢ(pˢ) depend only on the price charged to that side . The volume of realised transactions is the product Dᴮ(pᴮ)·Dˢ(pˢ) .
Benchmarks. The model is solved in turn for (a) a profit-maximising private monopoly, (b) a Ramsey planner maximising welfare under budget balance, (c) competing for-profit (“proprietary”) platforms, and (d) competing not-for-profit associations (e.g. payment-card cooperatives).
Extensions. Section 6 generalises to fixed usage costs and nonlinear pricing; comparative statics (multihoming, marquee buyers, captive buyers) yield testable implications.
Key constructs. Multihoming (a user connecting to several platforms), the singlehoming index σ (the share of “unique customers”), and steering (using low prices to pull a user into an exclusive relationship).

The mathematics is Lerner-style first-order conditions on log-concave demands; all results take the form of closed-form pricing formulae.

Findings

F1 — The total price obeys the classical Lerner formula. A monopoly platform’s total price p = pᴮ + pˢ satisfies (p − c)/p = 1/η where η = ηᴮ + ηˢ is the sum of the two sides’ elasticities [rochetTirole2003, p. 10, eq. (2)]. The level of price is therefore conventional; the novelty is entirely in its split.

F2 — The price structure is set by the ratio of elasticities, not inverse elasticities. The optimal allocation across sides satisfies pᴮ/ηᴮ = pˢ/ηˢ [rochetTirole2003, p. 10, eq. (5), Prop. 1(ii)]. The side with the higher elasticity bears the lower relative markup — the platform subsidises the side that is harder to attract. This is the formal content of “getting both sides on board”.

F3 — Ramsey (socially optimal) prices embody the surplus each side creates for the other. Under budget balance pᴮ + pˢ = c, welfare-optimal prices satisfy a cost-allocation condition in which each side’s price is weighted by the average net surplus Vᴮ, Vˢ it generates on the opposite side [rochetTirole2003, p. 12, Prop. 2, eq. (7)]. Crucially, the Ramsey structure does not correspond to a “fair cost allocation”; like a private business model it aims at getting both sides on board .

F4 — Competition replaces demand elasticities with own-brand elasticities. In a symmetric equilibrium between proprietary platforms the pricing formula is identical to the monopoly one, except ηᴮ becomes the higher own-brand elasticity ηₒᴮ and ηˢ becomes ηˢ/σ [rochetTirole2003, p. 19, Prop. 3]. When all buyers singlehome (σ = 1) the two coincide ; as multihoming spreads (σ falls), steering raises the effective elasticity and competition bites harder on that side.

F5 — Comparative-statics implications for the business model. From the §7 summary [rochetTirole2003, p. 29]: - More multihoming on the buyer side facilitates steering on the seller side and tilts the price structure in favour of sellers. - Marquee buyers (buyers generating high surplus for sellers) raise the seller price and lower the buyer price. - Captive buyers tilt the structure to the benefit of sellers.

F6 — Neutrality is the knife-edge where two-sidedness vanishes. If end users can costlessly pass charges through to each other (as first-year students are taught for a value-added tax), the decomposition is undone and the market collapses to a one-sided one . Two-sidedness is therefore created by frictions — transaction costs, volume-insensitive costs, and the impossibility of monitoring the interaction — that block pass-through .

F7 — Illustration: payment cards. Visa and MasterCard are not-for-profit associations owned by over 6,000 bank and nonbank members [rochetTirole2003, p. 30]; they set interchange fees that subsidise cardholders at merchants’ expense, while American Express — a for-profit closed system — historically charged a higher merchant discount because its clientele was a marquee side, a gap that narrowed as cardholders multihomed .

Relation to the course’s central question

The Rayna thesis asks: qu’est-ce qu’un business model, et en quoi la valeur est-elle un impact incarné chez un stakeholder ? This paper is one of the foundational formalisations behind that question, and it informs it sharply.

First, it gives “business model” a precise, non-rhetorical meaning. Rochet and Tirole repeatedly equate a platform’s business model with its price-allocation decision — “how it courts each side while making money overall” . A business model, in this reading, is not a narrative but a choice of price structure: which stakeholder is the profit centre and which is the subsidised side. This is a stricter, mechanism-level definition than the strategy-literature notion (cf. [[teece-2010-business-models-strategy-innovation|Teece 2010]], [[chesbrough-2002-business-model-capturing-value|Chesbrough & Rosenbloom 2002]]), and it usefully bounds what the more managerial accounts leave loose.

Second, it operationalises “value as an impact incarnated in a stakeholder”. The whole engine of the model is that a buyer does not internalise the surplus his participation creates for sellers (unlike the consumer who buys both razor and blade) . Value is literally an impact one side has on another side’s surplus (Vᴮ, Vˢ), and the optimal — and the socially efficient — price structure is the one that prices that cross-side impact [rochetTirole2003, p. 12, Prop. 2]. This is a remarkably faithful mathematical image of “value = impact incarnated in a stakeholder”: the value a platform captures from a stakeholder is governed not by that stakeholder’s own willingness to pay alone, but by the impact that stakeholder has on the surplus of the other stakeholder.

Third, it explains [[value-capture]] versus [[value-creation]] in [[ecosystem|ecosystems]]. The result that a side may be priced below cost — even free — precisely because it creates large surplus for the other side is the canonical justification for [[freemium]], advertising-funded media, and marketplace subsidy wars; it is the economic substrate of the [[prosumption]] / [[co-creation]] and [[multi-sided-platform]] discourse the course builds on. The paper does not, however, address [[business-model-innovation|business-model innovation]] as a dynamic capability, nor [[open-innovation]] or [[disruption]] — it is a static equilibrium theory. Its contribution to the Rayna thesis is definitional and mechanistic, not processual.

Open questions

The testable implications (insights 3–6) are offered with only “casual empiricism”; the authors explicitly defer econometric validation to future work . Which of the four comparative-statics predictions actually survives data?
The model takes the matching process between buyers and sellers as given; it does not model search or matching quality. How does endogenous match quality alter the optimal price structure?
Welfare is evaluated under budget balance and a Ramsey benchmark, but distributional consequences across the two stakeholder groups are not ranked. Who should be subsidised when the two sides differ in social weight?
Two-sidedness here is a knife-edge defined by the failure of pass-through. How robust is the whole apparatus to partial, stochastic pass-through?
The model is static. How do these structures map onto business-model innovation over a platform’s life-cycle (the dynamic question the course foregrounds)?

References

rochetTirole2003 rochetTirole2006 schmalensee2002 rohlfs1974 katzShapiro1985 farrellSaloner1985 caillaudJullien2003 bayeMorgan2001 rochetTirole2002 laffontEtAl2001 parkerVanAlstyne2000 armstrong2006

claims:
  - id: lerner-total-price
    text: "Total monopoly price obeys the Lerner formula (p-c)/p = 1/eta with eta = etaB + etaS"
    citekey: rochetTirole2003
    page: 10
    locus: "eq. (2), Prop. 1(i)"
  - id: price-structure-ratio-elasticities
    text: "Optimal price structure equates pB/etaB = pS/etaS (ratio, not inverse, of elasticities)"
    citekey: rochetTirole2003
    page: 10
    locus: "eq. (5), Prop. 1(ii)"
  - id: ramsey-other-side-surplus
    text: "Ramsey prices embody the average net surplus each side creates on the other side"
    citekey: rochetTirole2003
    page: 12
    locus: "Prop. 2, eq. (7)"
  - id: competition-ownbrand-elasticity
    text: "Under proprietary competition etaS is replaced by etaS/sigma (singlehoming index sigma)"
    citekey: rochetTirole2003
    page: 19
    locus: "Prop. 3"
  - id: multihoming-favours-sellers
    text: "More buyer-side multihoming tilts the price structure in favour of sellers"
    citekey: rochetTirole2003
    page: 29
    locus: "§7 insight 4"
  - id: marquee-buyers
    text: "Marquee buyers raise the seller price and lower the buyer price"
    citekey: rochetTirole2003
    page: 29
    locus: "§7 insight 5"
  - id: visa-mastercard-members
    text: "Visa and MasterCard are not-for-profit associations owned by over 6,000 bank/nonbank members"
    citekey: rochetTirole2003
    page: 30
    locus: "§7.1"
  - id: two-sided-definition
    text: "A network-externality market is two-sided iff the platform can cross-subsidise between sides (decomposition matters, not just total price)"
    citekey: rochetTirole2003
    page: 36
    locus: "§8"
unsourced: []