The Study And Analysis Of Methods On Multi-objective Games

Deciders usually have not only one objective to consider. Deciders integrate many objectives in decision-making. Multi-objective decision is more consistent with realism than single objective decision and can make decisions precise. Multi-objective game is an effective method to solve reciprocity between many deciders. So, it is important to study multi-objective games.As a branch of game theory, multi-objective game theory has attracted quite a few scholars' interest. A few research achievements appeared and mainly introduced: the concept of equilibrium solution of multi-objective games, qualitative differential games with multiple objectives, multi-objective games with restricted condition, multi-objective Nash bargaining games, fuzzy multi-objective games and so on.Firstly, this paper introduces the most used methods of solving multi-objective games: the method of Pareto vector superior, weighting coefficients, weighting coefficients aggregated multiple objectives and minimum component aggregated multiple objectives. But to this day, some games with multiple objectives which are different in importance or emergency, namely objectives have their own orders are not discussed.Secondly, this paper uses the thought to multi-objective games and gives the concepts of strong satisfied equilibrium solution set and feeble satisfied equilibrium solution set by using Nash equilibrium theory. A concrete case improved Bertrand double oligarchs model is discussed by using the methods of this paper in the example, and successfully explains the phenomena of following and no following in price war.At last, this paper also puts forward a new method to solve multi-objective games: aggregated multi-objective games based on fuzzy comprehensive evaluation. This method overcasts the method of weighting coefficients and extends of weighting coefficients.