Eigen-distribution on assignments for game trees with random properties

In this paper, we investigate a special distribution, called eigen-distribution, on assignments for game tree Tk 2 with random properties. There are two cases, where the assignments to leaves are independently distributed (ID) and correlated istributed (CD). In ID setting, we prove that the distributional probability % belongs to [√7-1/3, √5-1/2 ], and q is a strictly increasing function on rounds kε² [1,1). In CD setting, we propose a reverse assigning technique (RAT) to form 1-set and 0-set, then show that E1-distribution (namely, a particular distribution on assignments of 1-set such that the complexity of any deterministic algorithm is equal) is the unique eigen-distribution.