Finding the best player via multi-player comparisons

Consider a model where there are n n items, with item i i having an unknown value v i . v_i. At any time, we can can either stop and declare which item has the largest value or else choose a subset of items to compare. If subset S S is chosen, then i ∈ S i \in S will be preferred with probability v i / ∑ j ∈ S v j v_i/\sum _{j \in S} v_j . Assuming a Bayesian prior on the values, and subject to the proviso that the policy employed will make the correct choice with probability at least α \alpha , we are looking for a policy that needs a relatively small mean number of comparisons before making a decision. Some heuristic policies are presented and analyzed.