A Three-Party Scheme consists of three main parties as described in the above diagram.
In this model, the issuer (having the relationship with the cardholder) and the acquirer (having the relationship with the Merchant) is the same entity. This means that there is no need for any charges between the issuer and the acquirer. Since it is a franchise setup, there is only one franchisee in each market, which is the incentive in this model. There is no competition within the brand; rather you compete with other brands.
Examples of Three-Party Schemes are Diners Club, Discover Card, American Express and other closed loop system like restaurant checks.
See Payment Card Networks, Four Party Schemes, Credit Card Payment Schemes, eftpos Cards and eftpos