Nash equilibrium analysis and determination of the main factor of collusion in the game between taxpayers and tax auditors

Abstract Collusive corruption, like tax evasion, is one of the most important and widespread forms of illegal behavior, which brings destructive and irreparable effects in terms of negative externalities, both in the economic and social dimensions. In this paper, the modeling of the collusion game between taxpayers and tax auditors in two states inclined willing and unwilling to collude designed for each of the two mentioned players and the results were analyzed. For this purpose, for each player, two states of willing and unwilling to collude and a total of four possible states have been examined and the equilibrium for each cell has been specially examined and interpreted. The most important results are presented in the form of two theorems, which are: If the amount proposed by the taxpayers is high enough for collusion, then the tax auditors will recognize the expressed tax as equal to the declared tax of the taxpayers! And that, like the Granger causality test, taxpayers' willingness to collude is the main condition for collusion in the game between taxpayers and tax auditors.