School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Bundoora, Australia.
PLoS One. 2010 Apr 26;5(4):e10331. doi: 10.1371/journal.pone.0010331.
A new treatment to determine the Pareto-optimal outcome for a non-zero-sum game is presented. An equilibrium point for any game is defined here as a set of strategy choices for the players, such that no change in the choice of any single player will increase the overall payoff of all the players. Determining equilibrium for multi-player games is a complex problem. An intuitive conceptual tool for reducing the complexity, via the idea of spatially representing strategy options in the bargaining problem is proposed. Based on this geometry, an equilibrium condition is established such that the product of their gains over what each receives is maximal. The geometrical analysis of a cooperative bargaining game provides an example for solving multi-player and non-zero-sum games efficiently.
提出了一种用于确定非零和博弈帕累托最优结果的新治疗方法。这里将任何博弈的平衡点定义为玩家策略选择的集合，使得任何单个玩家选择的改变都不会增加所有玩家的总收益。确定多人游戏的平衡点是一个复杂的问题。通过在讨价还价问题中空间表示策略选项的想法，提出了一种直观的概念工具来降低复杂性。基于该几何图形，建立了一个平衡条件，使得它们的收益与各自收益的乘积最大化。合作讨价还价博弈的几何分析为有效解决多人博弈和非零和博弈提供了一个示例。
