The Strategy of Tax Control in Conditions of Possible Mistakes and Corruption of Inspectors

A generalization of the game-theoretical model of tax control adjusted for possible corruption and inspectors mistakes is considered. The hierarchical model has a three-level structure: at the highest level of a hierarchy is an administration of tax authority, in the middle is an inspector, subordinated to tax administration, and at the lowest level are $n$ taxpayers. It is supposed, that an interaction between risk-neutral players of different levels of a hierarchy corresponds to scheme “principal-to-agent”.
The model is studied for the case when the penalty is proportional to the level of evasion. It is supposed that a tax inspector may turn out a bribetaker or make ineffective tax audit, i.e. make a mistake and don't reveal an existing tax evasion.
In the case of corruption a tax control supposed to be effective, i.e. reveals existing tax evasions always. As in previous models, it is supposed that fact of corruption is very difficult to reveal and an inspector is punished only for negligent audit.
In the case of ineffective auditing it is assumed that the tax inspector can mistake and miss an existing evasion with the probability, which can be considered as a part of negligent inspectors of their total number.
For every possible situation the players profit functions and optimal strategies are found.