We analyze a dynamic game in which agents strategically search for a prize/reward of known value when they cannot observe the search of others. In every period the rivals decide how much to search. The prize goes to the player who finds it first unless there is simultaneous discovery, in which case the reward is destroyed. In the unique symmetric Nash equilibrium all players receive an expected payoff of zero. A third party could however increase welfare and avoid some search duplication by allocating search zones, even if these exclusive search zones are non-binding.