When Jeff Jordan learned last May that Web-search leader Google Inc. was building its own Internet-payment service, he reacted swiftly.

Mr. Jordan, who is president of eBay Inc.'s PayPal online-payments unit, immediately asked employees to unearth information about the Google service. Soon, PayPal employees were monitoring blogs, news reports and other data for information about Google's progress in payments. PayPal staffers even gleaned details about Google's plans during regular calls to customers who were eager to dish...