Eigen-distribution on random assignments for game trees

In this Letter, we investigate a special distribution, called eigen-distribution, on random assignments for a class of game trees . There are two cases, where the assignments to leaves are independently distributed (ID) and correlated distributed (CD). In the ID case, we prove that the distributional probability ϱ belongs to , and ϱ is a strictly increasing function on rounds k∈[1,∞). In the CD case, we propose a reverse assigning technique (RAT) to form two particular sets of assignments, 1-set and 0-set, then show that the E1-distribution (namely, a particular distribution on the assignments of 1-set such that all the deterministic algorithms have the same complexity) is the unique eigen-distribution for in the global distribution.