The Core A Methodological Toolkit to Reform Payment Systems Game Theory World Bank, Washington DC, November 5th, 2003

The Core 2 ¶ The need for Game Theory in payment systems reforms. ¶ Basic concepts. ¶ Applications to payment systems. ¶ Conclusions. CONTENTS

The Core 3 GAME THEORY AND PAYMENT SYSTEMS REFORMS Game theory analyzes the interaction between several agents (players) to understand what strategy (or set of strategies) each player chooses and what is the outcome generated Plenty of interactions and consequent conflicts arise over payment systems, especially when a reform has to be decided and implemented

The Core 4 CONFLICTS IN PAYMENT SYSTEMS Conflicts between Large and Small Banks over the access of small banks to systematically important payment systems Conflicts between dealers/brokers and banks and other non bank financial institutions over the access of the former to large value systems and securities settlement systems Banks and other non bank financial institutions over the access to ACH and large value systems Example of potential conflict Issue Access Conflicts between Public Authorities: ­ Central Bank vs. Competition Authority over respective roles in competition issues ­ Central Bank vs. Legislative Authority over legislative role ­ Central Bank as the payment system overseer and other regulators (e.g. Securities Commission and Committee Supervisors) Power

The Core 5 CONFLICTS IN PAYMENT SYSTEMS (cont.) Vertical conflicts between all the stakeholders, over the technology to be used Horizontal conflicts between: ­ Different service providers (different incumbents, incumbent vs. entrants) ­ Different participants (different incumbents, incumbent vs. entrants) Example of potential conflictIssue Service provision Vertical conflicts between all the stakeholders, over the price to be used Horizontal conflicts between: ­ Different service providers (different incumbents, incumbent vs. entrants) ­ Different participants (different incumbents, incumbent vs. entrants) Pricing

The Core 6 CONFLICTS IN PAYMENT SYSTEMS (cont.) Example of potential conflict Issue Conflicts between system providers and system participants over the participants’ compliance of the rules of the payment system Conflicts between regulators and system providers over the system’s ability to deliver efficiency and safety Compliance Conflicts between national and international public institutions and private sector over who should fund a payment system reform and to what conditions Funding

The Core 7 ¶ The need for Game Theory in payment systems reforms. ¶ Basic concepts. ¶ Applications to payment systems. ¶ Conclusions. CONTENTS

The Core 8 Gibbons, R., “Game Theory for Applied Economists”, Princeton University Press, 1992 Osborne, M. and Rubinstein, A., “A Course in Game Theory, MIT Press, 1994 BIBLIOGRAPHY

The Core 9 KEY ELEMENTS OF A GAME A player’s payoffs must depend on other players’ payoffs Strategies There must be at least two players to have a game There must be at least two strategies available for each player to have a game Payoffs Players

The Core 10 BATTLE OF SEXES Husband Wife Basket- ball Opera (3,1) Basketball (0,0)Opera (0,0)(1,3)

The Core 11 All Games TYPES OF GAME Incomplete Information Dynamic Complete Information Static Dynamic Static

The Core 12 NASH EQUILIBRIUM To solve a static game with complete information Nash Equilibrium (NE) is the equilibrium concept It is defined as a set of strategies, one for each player, so that, given the other players’ strategies, no player has any incentive to change her own strategy

The Core 13 PRISONER’S DILEMMA Prisoner 2 Priso- ner 1 Confess No (-1,-1) Confess (-5,0)No (0,-5)(-3,-3) The pair of strategies of P1 and P2 (Confess, Confess) is the NE of the game Both players, given the other player’s strategy, always prefer Confess

The Core 14 FEATURES OF EQUILIBRIA In the Battle of Sexes two pure strategy NE: (B,B) and (O,O) Husband Wife B O (3,1) B (0,0)O (1,3) 1. Multiplicity of equilibria may occur

The Core 15 FEATURES OF EQUILIBRIA (cont.) In the Prisoner’s Dilemma the unique NE (Confess, Confess) is a sub-optimal outcome P.2 P.1 Confess No (-1,-1) Confess (-5,0)No (0,-5)(-3,-3) 2. NE outcomes might not be Pareto efficient

The Core 16 FEATURES OF EQUILIBRIA (cont.) In the Matching Pennies game on the right, there is no NE in pure strategies P2 P1 H T (-1,1) H (1,-1)T (-1,1) 3. There might not be any NE in pure strategies

The Core 17 All Games TYPES OF GAME Incomplete Information Dynamic Complete Information Static Dynamic Static

The Core 18 SUBGAME PERFECT EQUILIBRIUM To solve a dynamic game with complete information Subgame Perfect Equilibrium (SPE) is the equilibrium concept It is defined as a set of strategies for each player so that, for all subgames (given all history paths), the strategy profile is a NE of the game It has to be solved (if finite) through backward induction (starting from the terminal nodes of the game)

The Core 19 EXAMPLE P2 P1 (2,1) The only SPE is (L,r) Notice: the pair (R,l) is not a SPE because P2 will always play r once it should become its turn to play RL lr (0,0) (1,2)

The Core 20 REPEATED GAMES AND COOPERATION If the prisoner’s dilemma above described is repeated several times there is room for a SPE where players cooperate The following strategy is a SPE of the prisoner’s dilemma repeated for several periods and for sufficiently high values of discount rates for both players: ­ Play No as long as the other player does so ­ Play Confess forever on after the stage when the other player plays confess

The Core 21 ¶ The need for Game Theory in payment systems reforms. ¶ Basic concepts. ¶ Applications to payment systems. Access game: small banks in S.I.P.S. Pricing game (vertical). ¶ Conclusions. CONTENTS

The Core 22 A National Payment Council (NPC) must decide de facto – through pricing and level of sophistication of the system – whether small banks should access directly systematically important payment system (SIPS) or through the intermediation of large banks The assessment is taken through voting: majority wins Small banks and large banks are both represented by their own association in the NPC. The leader of the NPC (and other voter) is the Central Bank. CONTEXT

The Core 23 PLAYERS AND STRATEGIES Strategies Each player can either support a system design which favors the access of small banks to SIPS (In) or be against it (Out) by voting simultaneously Central Bank (CB) Large Banks (L) Small Banks (S) Players Static game

The Core 24 OUTCOMES CB: Out S L In OutIn OutOUT CB: In S L In Out OUT In Out IN IN (price war) OUT IN

The Core 25 PAYOFFS CB: Out (0,0,0) CB: In (0,0,0) (-3,3,4) S L In OutIn Out(0,0,0)(-5,1,3) (-3,3,5) S L In OutIn Out

The Core 26 There are two pure strategy NE: (In, In, In) and (Out, Out, Out) The Central Bank can cause the NE (In, In, In), by: ­ Changing the voting systems ­ Committing in advance to the vote In ­ Pushing on large banks. It could state for example that, even if the outcome of the vote is Out, it would either create a huge pressure on them to reduce their fees, or it would oblige them to set very low fees to end-users. NASH EQUILIBRIA

The Core 27 ¶ The need for Game Theory in payment systems reforms. ¶ Basic concepts. ¶ Applications to payment systems. Access game: small banks in S.I.P.S. Pricing game (vertical). ¶ Conclusions. CONTENTS

The Core 28 A fee system, composed of fees to the participants and fees to the end-users has to be designed within the National Payment Council (NPC), and the various stakeholders of the NPC must agree upon it The Central Bank is also the system provider CONTEXT

The Core 29 PLAYERS AND STRATEGIES Strategies CB: set fees to participants P: set fees to end-users E: set the number of transactions Players Central Bank (CB) Participants (P) End-users (E) Static game

The Core 30 PAYOFFS E Variables affecting payoffs P Payoffs of system provider Payoffs of participants Payoffs of end-users Number of transactions Fees to end-users Number of transactions Fees to participants (F P ) Fees to end-users (F E ) CB Player

The Core 31 NASH EQUILIBRIUM FPFP FEFE F P (F E ) NE of the game F E (F P ) In F P (F E ) on the figure CB sets its own optimal F P for any given F E set by P Analogously in F P (F E ) P set their own optimal F E for any given F P set by CB Point A is the NE of the game It is possible to improve upon A by imposing costs / subsidizing participants / end-users A

The Core 32 ¶ The need for Game Theory in payment systems reforms. ¶ Basic concepts. ¶ Applications to payment systems. ¶ Conclusions. CONTENTS

The Core 33 FINAL REMARKS Game theory can be definitely a useful tool for payments systems reforms: it could be adopted initially within the National Payment Council It requires two conditions to be respected (too cumbersome game otherwise) ­ Honesty by the players (as much as possible) ­ Simple assumptions (80:20 approach)