中文摘要：

向量空间结构为每个运动员与播放器和策略的固定数字为有限比赛的集合被建议。二个静态的等价被用来减少有限比赛的尺寸。在向量空间结构下面，准确、加权的潜在的游戏的 subspaces 被调查。公式被提供计算他们。然后，有限进化比赛(EGs ) 被考虑。策略侧面动力学用更新规则(SUR ) 的不同策略被获得。某些 SUR，保证轨道的集中到纯纳什平衡，被调查。用向量空间结构，到 subspace 的有限比赛的设计准确(或加权) 比赛被考虑的潜力，和一个简单公式被给计算设计。到电子平衡的近潜在的比赛的集中被学习。进一步更， EGs 的 Lyapunov 函数被定义，它到 EGs 的集中的应用程序被介绍。最后，近潜在的功能为一例如被定义，并且如果，它被证明那近潜在的功能一例如是 Lyapunov 功能， EG 将收敛到纯纳什平衡。一些例子被举说明结果。

英文摘要：

A vector space structure is proposed for the set of finite games with fixed nmnbers of players and strategies for each players. Two statical equivalences are used to reduce tile dimension of finite games. Under the vector space structure the subspaces of exact and weighted potential games are investigated. Formulas are provided to calculate them. Then the finite evolutionary games （EGs） are considered. Strategy profile dynamics is obtained using different strategy updating rules （SURs）. Certain SURs, which assure the convergence of trajectories to pure Nash equilibriums, are investigated. Using the vector space structure, the projection of finite games to the subspace of exact （or weighted） potential games is considered, and a simple formula is given to calculate the projection. The convergence of near potential games to an c-equilibrium is studied. Further more, the Lyapunov function of EGs is defined and its application to the convergence of EGs is presented. Finally, the near potential function for an EG is defined, and it is proved that if the near potential function of an EG is a Lyapunov function, the EG will converge to a pure Nash equilibrium. Some examples are presented to illustrate the results.