The main objective of this work is to describe games which fall under title of Potential and simplify the conditions for class of aggregative games. Games classified as aggregative are ones in which, in addition to the player's own action, the payoff for each player depends on an aggregate of all the players' decision variables. In this study, we developed a method based on payoff functions to determine if a given game is potential. Then, in order to identify the Aggregative Games that fall under this class we simplified the criteria for the class of Aggregative Games. A $3$-player Cournot game, also known as an Aggregative Potential Game, is used to test the characterization criteria for Potential Games. A $4$-player Cournot game is also utilized to test the form of potential function we obtained for class of general potential games.

翻译：本研究的主要目标是描述属于势博弈范畴的博弈，并简化一类聚合博弈的条件。聚合博弈是指除玩家自身行动外，每个玩家的收益还取决于所有玩家决策变量聚合值的博弈。本研究基于收益函数提出了一种判定给定博弈是否为势博弈的方法。随后，为了识别属于该类别的聚合博弈，我们简化了聚合博弈的判定准则。采用一个$3$玩家的古诺博弈（又称聚合势博弈）来检验势博弈的特征刻画标准，并利用一个$4$玩家的古诺博弈来验证针对一般势博弈类别所得到的势函数形式。