Marginal-able correlated equilibria for A 3-person 0–1 game in form(ΔS(0), ΔS(1), ΔS(2))

The author studies 3-person games in normal form satisfy the conditions. (1) Every player's utility has nothing to do with his number, called symmetry. (2) Every player has exactly two pure actions 0 and 1. (3) There exists exactly one NE (i.e. Nash equilibrium) and none of the three players' actions in NE is pure. (4) Every player's gain is different if he uses 1 or 0 and none, one or two of the two other players use 1. (5) The difference of every player's gains is different if he uses 1 or 0 and none, one or two of the two other players use 1. In order to study the smaller and refiner correlated equilibria, the author confines the set of correlated equilibria (CE) such that marginal distribution of its element is exactly the NE, called set of marginal-able correlated equilibria (MCE). Some formulas to compute CE are given. Not liking general CE, MCE is computable and it and NE are more closely linked. The conclusion (i.e. key result) is that MCE in the game is a closed segment in 8-dimensional Euclidean space.