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.