A Game Theoretical Model of Interaction Between Taxpayers and the Tax Authority

The hierarchical game, in which the tax authority and finite number of taxpayers are players, is considered. The tax authority interacts to each taxpayer as "principal-to-agent". The players are supposed to be risk neutral. Every taxpayer can declare his income's level as equal or less, than the true level of his income. Tax and penalty rates are defined as constants. The tax authority makes audit with individual probability for every taxpayer. It is assumed that these probabilities are known by the taxpayers. Audit is supposed to reveal 100% of evasions. The taxpayer must pay a tax on his evasion level and a penalty, which depends on this level, as a result of audit, that revealed a tax evasion. Different cases of penalties are considered. Players' payoff fuctions and strategies are defined. The aim of every player is to maximize his payoff function.
Thus, the game theoretical model of taxation for finite number of taxpayers is considered. The Nash equilibrium in the corresponding game is found.