Bidding against competitors

Consideration is given to a system of n competitors, where if a competitor selects its bids equally likely from a given set of bid values, its probability of winning is guaranteed to be 1/n , regardless of the bid values selected by other competitors in the system. A discussion is presented of several variations of this basic scheme, namely, bidding with unequal weights, bidding with more than one winner, and bidding with an unknown number of competitors. Two economical, but approximate, bidding schemes are discussed. In the first scheme, the competitors select their bids from a set with a constant size, and in the second, each competitor selects only one bid even though the total number of competitors is not known a priori. It is shown how to use these bidding schemes to construct solutions to several problems in distributed systems, including the mutual exclusion problem and the dining philosophers problem