Pareto-efficient strategies in 2-person games in staircase-function continuous and finite spaces

Abstract

A tractable method of solving noncooperative 2-person games in which strategies are staircase functions is suggested. The solution is meant to be Pareto-efficient. The method considers any 2-person staircase-function game as a succession of 2-person games in which strategies are constants. For a finite staircase-function game, each constant-strategy game is a bimatrix game whose size is sufficiently 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 found by holding it the farthest from the pair of the most unprofitable payoffs.