Tax Auditing Models with the Application of Theory of Search

One of the most important aspects of modeling of taxation — tax control — is studied in the network of game theoretical attitude. Realization of systematic tax audits is considered as the interaction of two players – hiding (T – taxpayer) and seeking (A – authority) — in different statements of the search game.
In the problem statement it is assumed, that tax authority knows due to indirect signs, that some taxpayer T evaded from taxation in the given period (it put down lower than real income in the tax declaration). Also it is assumed, that this taxpayer is quite a large company, having many branches. Company can distribute the hidden income among all or some of its branches or can hide it in the income of one of its branches. Different game cases, which conditions are determined by various possibilities of the evading taxpayer and the tax authority, are considered. In the conditions of the games considered, tax authority A solves the problem of maximization of its income, using mixed strategies, which allow making optimal (in sense of evasion search) tax audits. Taxpayers T aspire to hide their income with the help of mixed strategies, allowing to reduce a probability of revealing of their evasion.
Along with search games, in which tax authority is defined as a search unit or, at best, as several search units, the task of tax audits using the theory of search of immobile chain with the help of big search system is considered. This model takes into account, that practically tax authority is hierarchic structure and is solving tasks on different levels (federal, regional, distirct etc.).
In this model tax authority solves the task of maximizing the probability of revealing of evasion with the help of optimal (in given sense) distribution of search efforts on the given period of time. Company solves the opposite task: to distribute evasion in the way, that minimizes probability of revealing of evasion.
Thus, different possibilities of solving the task of tax evasion search are considered.