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## Pareto-efficient strategies in 3-person games played with staircase-function strategies | ||

Communications in Combinatorics and Optimization | ||

مقاله 1، دوره 8، شماره 2، شهریور 2023، صفحه 271-304 اصل مقاله (4 M)
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نوع مقاله: Original paper | ||

شناسه دیجیتال (DOI): 10.22049/cco.2022.27434.1261 | ||

نویسنده | ||

Vadim Romanuke^{*}
| ||

^{}Faculty of Mechanical and Electrical Engineering, Polish Naval Academy, Gdynia, Poland | ||

چکیده | ||

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. | ||

کلیدواژهها | ||

game theory؛ payoff functional؛ Pareto efficiency؛ staircase-function strategy؛ trimatrix game | ||

مراجع | ||

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