Jonathan Griffin, Michael Pawlak and Chris Iuso all are chasing bargains on foreclosed homes here. It should be easy. Las Vegas is one of the foreclosure capitals of the U.S., with about one in four households behind on house payments or in mortgage foreclosure. Yet all three of these shoppers—a professional real-estate investor, a county official with federal funds designated for stabilizing neighborhoods and an installer of security systems who needs a new place to live—are frustrated. “I thought it would be a heck of a lot easier,” said Mr. Iuso, a renter who wants to buy a home but has been outbid eight times, usually by investors able to pay cash. Bargain hunters here and in many other metropolitan areas are up against a paradox. By far the biggest wave of foreclosures since the Great Depression was expected to be a bonanza for anyone with cash or the ability to get a loan. But prospective home buyers say it is increasingly difficult to find foreclosed homes at attractive prices in desirable neighborhoods.