Situation Distribution on a Symmetrical 3-Person 0-1 Game with Entropy

In order to study the probability of every pure situation occurring in a symmetrical 3-peron game to satisfy the conditions: (1) every player has exactly the two pure actions 0 and 1, (2) marginal distributions of the considered Aumann´s correlated equilibria are exactly the given Nash equilibrium with the same components b, a positive pure decimal, (3) all the players prefer situation distributions with the smallest Shannon entropy, and (4) if l of the two players uses(use) the action 1, then when the other uses 1 and 0 respectively, the difference between his/her utilities is proportional to b to the l-th power times b minus 1 to the 2 minus l, a formula to find situation distribution is obtained by mathematics and MATLAB. An example shows that the conclusions derived from the formula are in line with reality.