Your Network or Mine? The Economics of Routing Rules

1. Your Network or Mine?The Economics of Routing Rules Benjamin E. Hermalin & Michael L. Katz University of California, Berkeley

2. The Issue • Two parties A and B want to complete a transaction that requires a network (e.g., a debit-card transaction). • In some situations, there is more than one network to which A and B commonly belong. • Which network carries the transaction in such a case is determined by the operative routing rule. • This paper studies the economics of routing rule choice.

3. An Example: PIN Debit Cards • In US, many debit cards can run over multiple PIN debit networks and many merchants belong to multiple networks • Can be seen as a game between the issuing bank, A, and a merchant, B. • Possible routing regimes: • Issuer chooses (common in US) • Merchant chooses • Network chooses • Networks don’t permit multiple bugging (impose exclusivity)

4. Other Examples

5. Yet Another Example: Choice of Word Processing Program for Writing Joint Paper on Routing Rules LaTEX Word

6. A Model • A and B are two sides of market • X and Y are two networks • Gross consumption benefits for A & B are az& bz, respectively if transaction conducted on network z. • They are zero if no transaction is completed. • Consumption benefits are randomly distributed • A and B’s benefits are independently determined • Each side’s benefits have full support on the relevant rectangle in +2.

7. Timing A and B choose the networks to join and, where they have the right, specify routing choices Network set per-transaction charges, pzk, where z = X or Y and k = A or B Payoffs Networks simultaneously choose routing regimes. A and B learn their consumption benefits (types). A party’s type is his or her private information Parties meet to conduct a transaction

8. Connection Continuation Game • Lemma 1: In equilibrium: • If k gains surplus from neither network, then k joins neither network. • If k gains surplus from only one network, then k must join that network and must not join the other. • If k gains surplus from both networks, then k must join at least one network.

9. One-Side-Chooses Routing • Conflict arises if networks assign routing choice to different sides; here we assume they’ve chosen a common side. • Suppose we have A-chooses routing. • Because A has choice and B might tremble, A should join any network that yields her positive surplus.

10. A’s Strategy

11. B’s Strategy

12. Network Routing (2-sided exclusivity) • Network stipulates that, whenever possible, transactions be carried on it. • Because they risk being in breach of contract, A and B can join only one network when both networks stipulate network routing. • Two cases to consider • Both networks adopt network routing • Only one network adopts network routing (choice of other is irrelevant)

13. A Party’s strategy when networks both adopt network routing Note   (0°,90°).

14. One Network Stipulates Network Routing • Suppose X is only network to stipulate network routing. • Doesn’t matter what routing regime Y chooses.

15. A party’s strategy when only one stipulates network routing

16. Which Network Gets Trade • Corollary 1: Suppose network X stipulates network routing, but Y does not. If X and Y charge the same prices and distribution of user types are uniform on the unit square, then the equilibrium probability that trade is on Y is greater than the probability it is on X. • Network routing appears disadvantageous against a rival network with a different routing regime.

17. One-Sided Exclusivity • Exclusivity looks like network routing if … • … either network requires exclusivity of both sides; or • …one network requires exclusivity of one side and the other network requires exclusivity of the other. • Case to consider is if exclusivity required of just one side (by both or only one network). • Suppose that side is A. • Possibility of trembles B should be on a network if and only it provides him positive surplus.

18. B’s Strategy

19. A’s Strategy

20. Normal-Form Game for Routing Regime Choice

21. Normal-Form Game for Routing Regime Choice

22. Conclusions of Main Model • Networks should give choice of routing to one side of the market. • Privately optimal • Socially optimal • Some results at odds with actual debit-card experience in US. Suggests need to • consider inter-merchant competition • consider a dynamic model of growth & penetration • consider one side (merchants) perceive no differentiation other than price (i.e., bX = bY).

23. Extension: Video Games & Application Software • Can think of game consoles or OS’s imposing one-sided exclusivity on consumers. • Should console makers or OS companies impose one-sided exclusivity on developers?

24. Other Extensions (Future Versions) • Random routing • Conflicts in routing rules could be modeled as resolved via random routing. • Deciding party pays • Often when A or B has choice of routing, he or she is the only one charged for using the network. • While known to be inefficient, common in practice. • Hence, worth considering consequences for pricing game and routing-choice game. • Membership fees