Competition, bargaining power and pricing in two-sided markets

Competition, bargaining power and pricing in two-sided markets

Kimmo SoramäkiHelsinki University of Technology

www.soramaki.net

Wilko BoltDe Nederlandsche Bank

Norges Bank Oslo, 24 February 2008

Two-sided markets

• Rochet-Tirole (2006) define two-sided markets roughly as

• Examples: software platforms, newspapers, shopping malls, payment cards, etc.

“markets where one or several platforms enable interactions between end-users, and try to get the two (or multiple) sides “on board” by appropriately pricing each side”

Two-sided Platform vs Merchant

• Merchant purchases from sellers and resells to consumers• Platform enables interactions between sellers and consumers

source: Hagiu, A. 2007, Review of Network Economics 6, 115-133

Related literature

• Surge in literature on 2sms models– Rochet-Tirole (JEEA 03, RJE 06), Armstrong (RJE 06), Caillaud-Jullien

(RJE 03), Chakravorti-Roson (RNE 06), etc

• Models/markets– membership: buyers and sellers pay a fixed “membership” fee for an

uncertain number of future transactions

– usage: buyers and sellers pay a per-transaction fee

– Combination

• Questions…– Does competition in 2sms lead to lower prices for both sides?

– What is the optimal price structure?

– Does competition lead to convergence to marginal cost level?

This paper

• We develop a usage model of two-sided markets with perfect multi-homing. Bargaining plays a role when market sides prefer different platforms.

• We are interested in the profit-maximising usage fees set by homogeneous duopolistic platforms.

• We find that for sufficiently low cost level, in Nash-equilibrium all costs are borne by the side without bargaining power. The equilibrium price allows excess profits for both platforms.

• We argue that skewed pricing found empirically in many two sided markets, can perhaps be explained by which side chooses the platform when both sides are willing to transact on multiple platforms.

• Rochet & Tirole (2003) show optimal pricing for monopolistic platform with only usage fees:

– Optimal price level (total price)– Optimal price structure (price ratio)

• Optimal prices

– total price: (p-c)/p=1/ε– price structure: p1/p2=ε1/ε2

where p=p1+p2 and ε=ε1+ε2.

Recall: Monopolistic Platform

Role of bargaining power

• When buyers and sellers are willing to transact on several platforms, how is the platform chosen? Both sides may have opposing preferences, depending on the prices

• We investigate the situation where one side chooses the platform– example: choosing payment instrument at a store -> generally buyer

chooses an instrument accepted by the merchant.– both sides have an order of preference, but are willing to transact on a

less preferred platform, instead of foregoing the transaction

• Similar to “routing rules”– Hermalin-Katz (RJE 06) consider a strategic game of routing rules– “if you choose the network and I know you multi-home, I will strategically

single-home on my preferred network”

The model

platform 1

buyers sellers

platform 2

1. buyers are willing to transact on a platform if ub≥pb

2. if ub≥pb1 and ub≥pb

2, buyers prefer platform with lower price

3. if ub≥ pb1=pb

2, half prefer platform 1, and half prefer platform 2

4. the same holds for sellers

5. if buyers and sellers are willing to transact on both platforms, but prefer a different one – choice is determined by bargaining power characterized by τ

• Let’s start where platforms 1 and 2 have the same prices

Demand - example

initially 1 and 2 split this market

,

,

=

=

• platform 1 reduces buyer´s price and increases seller´s price

Demand - example

served by 1 if buyer chooses the platform, by 2 if seller chooses the platform

served by 2 alone

served by 1 alone

,

,

Demand and profit

Profit (c=marginal cost):

Platforms need to evaluate 9 price regions. Demand:

45º

Best-reply dynamics

starting point: zero profits price

demand is split by the two platforms

45º

45º

Best-reply dynamics

Monopolistic best reply

- platform gets monopolistic demand and profits

- competitor gets demand only from sellers with ps

0 < us< psM

45º

Best-reply dynamics

hε

Undercutting phaseundercutting by εoptimal overpricing by h

- undercutting other platform’s buyer price will get all eligible buyers on board

- this allows the platform to increase seller price to a point where the increased margin offsets lost demand

45º

Best-reply dynamics

hε

Corner price

Undercutting and overpricing continues until corner price is reached.

Here platforms split the demand

45º

Best-reply dynamics

Two Nash-equilibria

"Grab the dollar" - game

One of the platforms sets its seller price below ps

C. Its margin is lower but it has additional demand from sellers with ps

C<us<psC. The best

response to this is pC.

The platform with lower seller price has higher profits -> "first mover advantage"

c < c*

45º

Best-reply dynamics

Best reply to corner price in case of high marginal cost

Increase in buyer’s price, but decrease in seller’s price to level where the platform gets demand from sellers with ps

BR<us<psC, i.e.

seller’s that are not willing to transact on the other platform

c > c*

Out-of carrier pricing

Undercutting continues below carrier

Nash equilibrium exists if a price control exists to the right of the intersection

Without price controls undercutting continues until a "flip" in prices is better : no equilibrium

c-us

pH

pLpM

Summary

• Competition is more complex in two sided markets

• Unequal "bargaining power" can lead to highly skewed prices

• Generally Nash-equilibrium prices allow excess profits for the platforms

• The results are robust to alternative utility specifications

• Future research on the model will include inter alia

– higher number of platforms– social welfare considerations – control of platforms– membership decision, fixed costs and variable costs– endogenous bargaining and multi-homing

Policy implications for card payments?

• Perhaps too early, but …

• Highly skewed prices may be an outcome of competition when one side of the market chooses platform when both sides multi-home

• Restricting end-user prices (e.g. not allowing negative prices) may lead to excess profits to schemes

• Duopolistic competition does not necessarily reduce prices to cost level

• With SEPA and more competition among schemes, prices for retailers should go up… according to the model.

… and for interchange fees

• In competitive markets 4-party schemes should use the interchange fee to achieve the desired price structure (whatever they tell about cost based interchange fees)

• Highly skewed prices can only be achieved in 4-party schemes by a high interchange fee

• Restricting interchange fees can give a competitive advantage to 3-party schemes (they can undercut more on the buyer side, and compensate it on the seller side).

Takk

contact me at: [email protected]