Visa Inc. and MasterCard Inc., the world’s biggest payment networks, won dismissal of a price- fixing lawsuit brought by a group representing operators of automated teller machines.

U.S. District Judge Amy Berman Jackson in Washington today also threw out two related suits, ruling that all the plaintiffs failed to show the companies conspired to restrict independent ATM operators from charging varying prices for customers using alternative networks such as STAR, Shazam Inc. or TransFund.

“Plaintiffs have not set forth sufficient facts to support their claim that there was a horizontal conspiracy,” Jackson wrote in her 39-page opinion. “Notably absent from each of the complaints are facts showing the existence of an agreement, the essential element of any conspiracy.”

The allegations in the lead case were made by the National ATM Council Inc., a trade group based in Jacksonville, Florida, and 13 operators of ATMs in nine states. Under a uniform agreement, the operators can’t charge less for transactions over a network that competes with Visa and MasterCard, according to the complaint.

The ATM operators claim that the “overwhelming” majority of so-called PIN debit cards used for ATM transactions are branded by Visa or MasterCard.

In order to accept one of these cards, an ATM operator must have access to the Visa and MasterCard networks. Independent or non-bank operators must be sponsored by a financial institution that is a member of the Visa and MasterCard networks.

James Issokson, a spokesman for MasterCard, based in Purchase, New York, said in an e-mail that the company was pleased with the ruling.

Will Valentine, a spokesman for San Francisco-based Visa, didn’t immediately respond to a telephone message seeking comment on the decision. A lawyer for the ATM group, Daniel Small of Cohen Millstein Sellers & Toll Pllc in Washington, didn’t immediately respond to a phone message.

The lead case is National ATM Council v. Visa Inc., 11-cv- 1803, U.S. District Court, District of Columbia (Washington).

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