The statistical method is used to identify the hidden leaders of the corruption structure. The method is based on principal component analysis (PCA), linear regression, and Shannon information. It is applied to study the time series data of corrupt financial activity. Shannon's quantity of information is specified as a function of two arguments: a vector of hidden corruption factors and a subset of corrupt agents. Several optimization problems are solved to determine the contribution of corresponding corrupt agents to the total illegal behavior. An illustrative example is given. A convenient algorithm for computing the covariance matrix with missing data is proposed. arXiv:1707.04461v1 [math.OC]

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The voting process is formalized as a multistage voting model with successive alternative elimination. A finite number of agents vote for one of the alternatives each round subject to their preferences. If the number of votes given to the alternative is less than a threshold, it gets eliminated from the game. A special subclass of repeated games that always stop after a finite number of stages is considered. Threshold updating rule is proposed. A computer simulation is used to illustrate two properties of these voting games.

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