QCSP on Reflexive Tournaments

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.