Collaborate with strangers to find own preferences

We consider a model with n players and m objects. Each player has a "preference vector" of length m that models his grade for each object. The grades are unknown to the players. A player can learn his grade for an object by probing that object, but performing a probe incurs cost. The goal of a player is to learn his preference vector with minimal cost, by adopting the results of probes performed by other players. To facilitate communication, we assume that players collaborate by posting their grades for objects on a shared billboard: reading from the billboard is free. We consider players whose preference vectors are popular, i.e., players whose preferences are common to many other players. We present distributed and sequential algorithms to solve the problem with logarithmic cost overhead.