Travel search sites have made it easy to find the lowest available fares ever since the Web’s early Jurassic period, when pioneers like Expedia and Travelocity opened shop. Many others, like Kayak and Hipmunk, have since joined in.

Flightfox uses online competitions to help travelers find the best price for a flight itinerary — which may involve multiple destinations. Travelers with complex travel plans may have noticed, however, that the search results aren’t necessarily consistent. This has created a business opportunity for Flightfox, a start-up company based in Mountain View, Calif., which uses a contest format to come up with the best fare that the crowd — all Flightfox-approved users — can find.