Game modeling of collusion and influential factors under uniform taxpayer distribution

Today, tax is the most important and at the same time the most stable source of income for countries and its significant importance indicates that the higher the proportion of taxes to government expenses, the more it remarkably hinders the occurrence of undesirable economic effects. This article addresses the modeling of the game between taxpayers and tax investigating groups in two scenarios - willing and unwilling to collusion - and analyzes the results for each of the two players. Among the most important findings are the inverse relationship between the diagnostic tax function of each group of taxpayers and their declared taxes of the same type, as well as the direct correlation between the diagnostic tax function and the declared taxes of the other group of taxpayers. Furthermore, declared taxes have a direct relationship with tax fine rates, the relevant tax investigating group for the taxpayer, and an inverse correlation with the ratio of the other tax investigating group. If the number of taxpayers increases, the declared taxes of both the willing and unwilling to collusion groups will be equal. The income function of the tax affairs organization is also decreasing toward to the number of willing to collusion taxpayers, the investigating group willing to collusion, and undesirability and increasing toward to the investigating group unwilling to collusion and the increasing number of taxpayers. Finally, it is suggested that the tax affairs organization and relevant tax authorities use the results of this research to neutralize collusion and identify factors influencing diagnostic and declared taxes.