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

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

George Gardner and Andrew Stone

April 2009

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Table A1: List of Model Notation
Variable	Description
Consumer market segments (fractions)
Ω^c	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)
Ω^m	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
c_i	Cost incurred by platform i for each transaction processed over the platform
g_i	Flat cost to platform i of signing up each consumer
Other
C (M)	Total number of consumers (merchants)
τ_i	Maximum per-transaction benefit received by any consumer on platform i
μ_i	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
Π_i	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.