You can make an auction for the private key of 34dqaqvQNWMgbMJmmxVa8LeGz7St6ATT97 addy...
he has already done that in a much better way which is to place the reward as a high transaction fee. the 0.27 bitcoin is currently worth nearly $2500 which he could increase in the same manner (bumping the fee).
if a miner wanted to accept the offer they could just include the transaction in their next block they mine and claim its fee. others that aren't miners can't do anything about it.