New algorithm for checking Pareto optimality in bimatrix games

Abstract Bimatrix games have had theoretical importance and important applications since the very beginning of game theory to date. Pareto optimal strategy vectors represent a reasonable frequently applied solution concept (basically in cooperative approach). Particularly, it often arises whether non-cooperative can be improved sense, i.e. is or not. However, concrete cases may hard determine at least check optimality given vector. In present paper, pairs general n × m ( $$n = 2,3, \ldots$$ n = 2 , 3 … ; $$m m ) bimatrix studied. First all an elementary proof provided for theorem, which makes proposed checking algorithm simpler. Then nonlinear transform proposed, even more convenient case 2 (and certain other cases). Two numerical examples practical applicability algorithm. The problem solved by hand. For larger games, numerous computational tools are available practice apply exact approximate way.