pareto-efficient strategies in 3-person games played with staircase-function strategies

A tractable method of solving 3-person games in which players’ pure strategies are staircase functions is suggested. the solution is meant to be pareto-efficient. the method considers any 3-person staircase-function game as a succession of 3-person games in which strategies are constants. for a finite staircase-function game, each constant-strategy game is a trimatrix game whose size is likely to be relatively small to solve it in a reasonable time. it is proved that any staircase-function game has a single pareto-efficient situation if every constant-strategy game has a single pareto-efficient situation, and vice versa. besides, it is proved that, whichever the staircase-function game continuity is, any pareto-efficient situation of staircase function-strategies is a stack of successive pareto-efficient situations in the constant-strategy games. if a staircase-function game has two or more pareto-efficient situations, the best efficient situation is one which is the farthest from the triple of the most unprofitable payoffs. in terms of 0-1-standardization, the best efficient situation is the farthest from the triple of zero payoffs.