1. Shared ATM networks and banking competition Matutes, Carmen and Padilla Jorge. 1. Introduction 2. Model 3. Equilibrium compatibility agreements 4. Public Regulation of ATM compatibility clubs 5. Conclusion Bibliography: Oz, Shy (2001), The Economics of Network Industry, Cambridge University Press, United States. Freixas, Xavier, and Jean-Charles Rochet (1997), Microeconomics of Banking, MIT, Cambridge, MA.

2. Introduction ATM networks is a competitive device in retail banking During 1970‘s invested on own networks. 1990‘s started a consolidation process through sharing (compatibility) agreements. Depositors value a larger ATM network for two reasons: Network effect Substitution effect Trade-off between these two effects in two stages: First agree on (full/partial/total in)compatibility regime Secondly, (simultaneously and independently) compete in deposit rates.

3. Introduction Different scenarios are proposed to study the compatibility: „Plain Vanilla“ Withdrawal fees Interchange fees Switching costs ATM compatibility features: Number of ATMs determines the relevant size of the network as opposed to the number of users. Sharing agreements involve important competitive effects which are independent of the relative size of the proprietary networks.

4. Model Three banks: A, B and C symmetrically located in a circle, each bank with a single ATM machine. City is divided in three neighbourhoods. Each bank competes for the deposits of individuals located in two of these neighbourhoods. A BC

5. Model There is a continuous [0,1] of depositors (each with $1 to deposit). Bank quoting r i attracts  i depositors, then, profits are given by:  i = (R-r i )  i. No bankruptcy risk and depositors always prefer higher interest rates on the deposits. Depositor visits regularly the bank for two purposes: To withdraw cash (can be done with any compatible bank), with associated cost T. Other activities (can be done only where funds are deposited), with associated cost t.

6. Model k i = k(n i ) : expected cost of having access to one‘s funds during unexpected occasions. k i = p * s * E[distance] where, p = probability travelling around the city s = opportunity costs of time and associated unit transportation d = expected travelling distance Depositor‘s utility: If bank A incompatible: r A -k(1) – d A If bank A & B compatible: r A -k(2)–td A –T min(d A,d B ).

7. Model K = k(1)-k(2) represents a network externality. Marginal depositor located at x satisfies: r A -k(2)–tx–T min(d A,d B ) = r B -k(2)–t(1-x)– T min(x,1-x). Marginal depositor between compatible and incompatible bank located at x: r A -k(2)–tx= r C -k(1)–(1-x)

8. Equilibrium compatibility agreements Competition for deposits Recall: 3 possible ATM network configurations: full/partial/in compatibility. First scheme: partial competition (A and B sharing, C incompatible). Then, bank A sets a deposit rate r A to maximise its total profits:  A =  C = As K increases, market equilibrium tend to exclude incompatible banks.

9. Equilibrium compatibility agreements Competition for deposits Analyisis of competition under total compatibility and independent networks is straightforward. Bank‘s equilibrum profits are equal to (1,1,1) = 1/3 and (3,0)=t/3. Equilibrium profits under different structures we have: min((1,1,1), (2,0)) >= (3,0) for all t,K then, universal compatibility cannot be an equilibrium outcome. The next question: whether at least two banks would be willing to share their ATMs under certain conditions? Need to compare the equilibrium profits under incompatibility and partial compatibility.

10. Equilibrium compatibility agreements Competition for deposits Define (K,t) = (2,0)-(1,1,1) t K  (Incompatibility)  (Partial Compatibility) 

11. Equilibrium compatibility agreements Compatibility agreements Partial compatibility is the unique Perfect Coalition-Proof Nash Equilibrium for large K and large t. Otherwise, incompatibility is the unique PCNE outcome. In the general case, profits under incompability: 1/n are greater than full compatibilitiy: t/n. Then, there is always at least one bank willing to deviate from the full compatibility agreement. Compatibility agreements can be used to exclude rivals from the market. As K increases, incompatible markets ar forced out of the market. ((1,2)<=0)

12. Equilibrium compatibility agreements Withdrawal fees Withdrawal fee w>=0. It is charged to the depositors of other compatible banks for the use of ones‘ own ATM. This fee diminishes depositors‘ valuation for a larger network, and thus reduces teh size of network externality (recall: „local“ networks are of the same size). Contrary to the previous case:  W (3,0) >=  W (1,1,1) In this case, equilibrium is attained at complete compatibility.

13. Equilibrium compatibility agreements Interchange fees Interchange fee: f>0. Paid by a bank to its compatible rivals when its customers use the other bank‘s ATMs. Assume full compatibility, then:  A = (R-r A ) A + f {( A –  B ) + ( A –  C )} p/3 + f (1/3 -  A ) Larger market share ( A ) implies larger payments of interchange fees to compatible banks. Similarly to withdrawal fees:  f (3,0) >=  f (1,1,1) Moreover:  f (3,0) >=  W (3,0)

14. Equilibrium compatibility agreements Switching costs Locked-in depositors: (1-) in (0,1). Depositors face an important costs of swithcing banks. As a consequence, the increase in market share that can be obtained through compatibility is reduced, then, banks behave more aggressively. If most depositors are locked-i, compatibility would be trivially achieved since there would not exist real competition between banks.

15. Equilibrium compatibility agreements Switching costs t K  (Incompatibility)  (Compatibility) As decreases

16. Public Regulation of ATM compatibility clubs Full compatibility represents the first-best ATM structure. But it is not an equilibrium. Second-best is attained when K is sufficiently large. First best can be attained through legislation enforcing compatibility. According to the model, this solution will yield incompatibility as the unique equilibrium outcome. Similar result is when regulating the access fees. Deposit rate Ceilings. Limits excessive competition in rates, but could increase through branch and/or ATM proliferation.

17. Conclusions. Results are consistent with the existing evidence: Full compatibility is not observed Compatibility is easier among banks competing in different geographical markets: „Share but not Compete“ Compatibility generates a competitive effect independent from the network size. Compatibility makes entry of new firms more difficult.