# RDP 2009-03: Competition Between Payment Systems: Results Appendix A: Model Notation

Table A1: List of Model Notation
Variable Description
Consumer market segments (fractions)
Ωc Set of all consumers
Subset (fraction) of consumers who choose not to hold any cards
Subset (fraction) of consumers who choose to hold card i
Subset (fraction) of consumers who choose to hold card i but not card j
Subset (fraction) of consumers who choose to hold both cards i and j
Subset (fraction) of consumers who choose to hold both cards and who prefer to use card i over card j whenever merchants accept both
Merchant market segments (fractions)
Ωm Set of all merchants
Subset (fraction) of merchants that choose not to accept any cards
Subset (fraction) of merchants that choose to accept card i
Subset (fraction) of merchants that choose to accept card i but not card j
Subset (fraction) of merchants that choose to accept both cards i and j
Platform fees
Flat fee charged to consumers to subscribe to card i
The flat fee converted to per-transaction terms for a consumer in or (that is, the quantity /)
The flat fee converted to per-transaction terms for a consumer in (that is, the quantity )
Per-transaction fee charged to merchants by platform i
Platform costs
ci Cost incurred by platform i for each transaction processed over the platform
gi Flat cost to platform i of signing up each consumer
Other
C (M) Total number of consumers (merchants)
τi Maximum per-transaction benefit received by any consumer on platform i
μi Maximum per-transaction benefit received by any merchant on platform i
Per-transaction benefit received by a given consumer on platform i
Per-transaction benefit received by a given merchant on platform i
Πi Total profit earned by platform i
Notes: For simplicity, where there is analogous notation for both platforms only that for platform i is shown. Consumer (merchant) market fractions represent the proportion of all consumers (merchants) that are members of the corresponding set.