Levy flights are a special class of random walk whose step lengths follow a power-law tailed distribution. There are plenty of empirical evidences that movement patterns are compatible with Levy flights in many different contexts where efficiency matters. In particular, Levy flights appear recurrently in the description of the motion of animals in real space. Animals explore the environment mainly for searching food resources, and it is therefore plausible to ascribe the optimality of their search strategies to a selective evolutionary process. There is still a lack of knowledge about the statistical properties of search processes performed by humans, and it is not clear weather humans adopt search strategies similar to those of animals or not. We report, for the first time in the literature, empirical evidence that Levy flights describe searches performed, in mental abstractions of the physical space, by humans in online games. We analyze the bid histories of online auctions and show that players, when looking for unknown winning bid values, follow trajectories in the bid space that can be statistically described as Levy flights. The power-law scaling can be measured over several order of magnitude. Differently from previous studies regarding biological and mobility systems where two orders of magnitude of scaling can represent a luxury, the power-law decay in bid space explorations can be clearly observed even over four orders of magnitude. The reason is that the space is not strictly physical and movements of arbitrary length can be performed at the same price: players explore the bid space in a effectively super-diffusive fashion, and steps are made at infinite velocity. Moreover, we provide a game theoretical model for the exploration of prices in the auctions.
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