Optimal rank-order tournaments have traditionally been studied using a first-order approach. The present analysis relies instead on the construction of an ”upper envelope” over all incentive compatibility conditions. lt turns out that the first-order approach is not innocuous. For example, in contrast to the traditional understanding, tournaments may be dominated by piece rates even if workers ...

We give a complexity dichotomy for the Quantified Constraint Satisfaction Problem QCSP(H) when H is reflexive tournament. It well-known that tournaments can be split into sequence of strongly connected components H_1,...,H_n so there exists an edge from every vertex H_i to H_j if and only i<j. prove has both its initial final component (possibly equal) size 1, then in NL otherwise NP-hard.