Analysis of the Tax Gap and Its Affecting Factors Using Game Theory Approach

The tax gap can be considered as the criterion and principle of the effectiveness and efficiency of the tax system. Inadequate collection of taxes as well as non-realization of tax revenues is called tax gap, which is one of the factors that aggravate the budget deficit. In this paper, the issue of tax gap is investigated with two approaches. The first approach is a situation where two groups of investigators who are willing and unwilling to collude with two groups of taxpayers who are willing and unwilling to collude with a uniform distribution are placed in the game. The second approach also shows a situation where the probability of not discovering a taxpayer's violation is shown by a mathematical function and the quality of investigating groups for taxpayers who are uniformly distributed is unknown. The results of the first approach show that with the increase in the number of taxpayers unwilling to collude and the increase in the number of groups willing to collude with taxpayers, the tax gap decreases. Also, with the reduction of the tax rate and the increase in the number of groups unwilling to collude, the tax gap increases. The results of the second approach show that the tax gap increases with the increase in the number of investigators and also the increase in the probability of dishonesty of the taxpayer.