Techniques are described for facilitating interactions between computing systems, such as via a third-party transaction authorization system that automatically authorizes transactions between parties. In some situations, the transactions are programmatic transactions involving the use of fee-based Web services by executing application programs, with the transaction authorization system authorizing and/or providing payments for transactions between Web service provider and consumer parties in accordance with private authorization instructions previously specified by the parties. The authorization instructions may include predefined instruction rule sets that regulate conditions under which a potential transaction can be authorized, with the instruction rule sets each referenced by an associated reference token. The transaction authorization system can then receive a reference token from each party to a potential transaction, and determine whether to authorize the transaction based on whether the instruction rule sets associated with the reference tokens are compatible or otherwise satisfied.