Open AccessPareto-efficient strategies in 2-person games in staircase-function continuous and finite spaces
Author(s) -
Vadim Romanuke
Publication year - 2022
Publication title -
decision making. applications in management and engineering/decision making: applications in management and engineering
Language(s) - English
Resource type - Journals
eISSN - 2620-0104
pISSN - 2560-6018
DOI - 10.31181/dmame0316022022r
Subject(s) - pareto principle , constant (computer programming) , mathematical economics , function (biology) , mathematical optimization , game theory , pareto efficiency , mathematics , repeated game , strategy , constant function , non cooperative game , pareto optimal , computer science , multi objective optimization , mathematical analysis , evolutionary biology , piecewise , biology , programming language
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.