pareto-efficient situations in infinite and finite pure-strategy staircase-function games

A computationally tractable method is suggested for solving n-person games in which players’ pure strategies are staircase functions. the solution is meant to be pareto-efficient. owing to the payoff subinterval-wise summing, the n-person staircase-function game is considered as a succession of subinterval n-person games in which strategies are constants. in the case of a finite staircase-function game, each constant-strategy game is an n-dimensional-matrix game whose size is relatively far smaller 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 multiple pareto-efficient situations, the best efficient situation is one which is the farthest from the most unprofitable payoffs. in terms of 0-1-standardization, the best efficient situation is the farthest from the zero payoffs.