Cooperative game theory considers simple games and influence games as essential classes of games. A simple game can be viewed as a model of voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. An influence game is a cooperative game in which a team of players (or coalition) succeeds if it is able to convince sufficiently many agents to participate in a task. Furthermore, influence decision models allow to represent discrete system dynamics as graphs whose nodes are activated according to an influence spread model. It let us to depth in the social network analysis. All these concepts are applied to a wide variety of disciplines, such as social sciences, economics, marketing, cognitive sciences, political science, biology, computer science, among others. In this survey we present different advances in these topics, joint work with M. Serna.

These advances include representations of simple games, the definition of influence games, and how to characterize different problems on influence games (measures, values, properties and problems for particular cases with respect to both the spread of influence and the structure of the graph). Moreover, we also present equivalent models to the simple games, the computation of satisfaction and power in collective decision-making models, and the definition of new centrality measures used for social network analysis. In addition, several interesting computational complexity results have been found.

合作博弈理论将简单博弈和影响博弈视为博弈的基本类别。简单的游戏可以看作是投票系统的模型，其中单一的替代方案（例如法案或修正案）与现状相抵触。影响力游戏是一种合作游戏，其中，如果一个团队（或联盟）能够说服足够多的特工参加任务，则该游戏成功。此外，影响决策模型允许将离散的系统动力学表示为图，其节点根据影响扩散模型被激活。它让我们深入社交网络分析。所有这些概念都被广泛应用于各种学科，例如社会科学，经济学，市场营销，认知科学，政治科学，生物学，计算机科学等等。

这些进步包括简单博弈的表示，影响博弈的定义，以及如何表征影响博弈中的不同问题（针对影响扩展和图形结构的特定情况下的度量，值，属性和问题）。此外，我们还提供了简单游戏的等效模型，集体决策模型中满意度和权力的计算以及用于社交网络分析的新集中度度量的定义。此外，还发现了一些有趣的计算复杂性结果。