Socio-Economic Interpretation of Multiple Agents Decision Making by Game Theory

Abstract

The equivalence of the matrix game problem and the programming problem has been pointed out since an early stage of development in game theory (Dantzig 1951, Dorfman 1951, Gale 1960, etc.). Recently much interest is increasingly focused upon interrelations between programming problems and game problems, because problem formulations as mathematical programming provide efficient solution techniques for game problems, and thus increase applicability of game theory. However, comparable criteria for alternative solutions have not presented, which will be found by examining socio-economic interpretation of multiple agents decision making attained as solutions of games. On the other hand, it has been well-known that duality of mathematical programming provides some evaluation combined with optimal resource allocation. The multiobjective interpretation of the dual optimal vector has been presented (Seo 1978, 1980). The purpose of this paper is to extend this research and to provide some evaluation criteria by examining socio-economic meaning of the dual optimal solutions obtained in mathematical programming problems formulated for game theory. This examination will contribute to check acceptability of solutions for games obtained in alternative concepts.KeywordsDual ProblemMixed StrategyDual VariableDuality TheoremGrand CoalitionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.