Competition, bargaining power and pricing in two-sided markets
Kimmo SoramäkiHelsinki University of Technology / ECB
Wilko BoltDe Nederlandsche Bank
The Economics of Payment Systems Paris, 25 October 2007
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”
Related literature
• Surge in literature on 2sms models– Rochet-Tirole (JEEA 03, RJE 06), Armstrong (RJE 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
• Consider part of 1’s strategy space , i.e. and
Demand - example
initially 1 and 2 split this market
,
,
,
,
• i.e. platform 1 reduces buyer price and increases seller 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
staring point: zero profits price
45º
45º
Best-reply dynamics
monopolistic price
staring point: zero profits price
monopolistic best reply
- platform gets monopolistic demand and profits
- competitor gets demand only from sellers with ps
2 < us< ps
M
45º
Best-reply dynamics
monopolistic price
hε
staring point: zero profits price
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
monopolistic price
“corner” price
hε
staring point: zero profits price
Nash-equilibrium
undercutting and overpricing continues until corner price is reached.
here platforms split the demand
45º
Best-reply dynamics
monopolistic price
“corner” price
“best reply” to “corner” price
staring point: zero profits price
best reply to corner price
increase in buyer’s price, but decrease in seller’s price to level where the platform gets demand from sellers with ps
1<us<psC, i.e. seller’s that
are not willing to transact on the other platform
Illustration of profits
buyers have bargaining power
buyers’ utility range
sellers’ utility range
marginal cost for platform
Platform 1's profits given that platform 2 plays p0=(3/8, 3/8). Monopoly price pM=(0.25, 1.25) is the best reply
Platform 1's profits given that platform 2 plays pC=(0,1.375). Best reply to is pC as well.
45º
Negative prices
Assumption:demand 1 when p<0
Price cutting takes place until p* at which profits equal those of pBR
p*
Summary
• Generally the Nash-equilibrium prices allow excess profits for the platforms, prices to the two sides are highly skewed.
• The results are robust to alternative utility specifications– left support needed for convergence, i.e. ai>-∞
• Future research on the model will include inter alia
– higher number of platforms– heterogeneous platforms– social welfare considerations – control of platforms– membership decision, fixed costs and variable costs– endogenous bargaining
Interpretation:Analogue of Bertrand Competition
• Homogeneous competition between 2 identical firms– Bertrand price undercutting leads to p=c (unique equilibrium).
• Homogeneous competition between 2 identical platforms– price undercutting on one side, price compensation on the other– one side gets service “for free”, the other side pays– excess profits remain, i.e. total price > c (unique equil. for low c)
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
• Highly skewed prices can only be achieved in 4-party schemes by a high interchange fee– Restricting interchange fee can give a competitive advantage to 3-
party schemes (they can undercut more on the buyer side)
• Restricting end-user prices (e.g. not allowing negative prices) may lead to excess profits to schemes
