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When do firms use one set of books in an international tax compliance game?

This study examines how a strategic tax auditor affects a multinational firm's transfer pricing in an incomplete information tax compliance game. Our model uses a divisionalized firm, in both a low-tax and a high-tax country, that decides to implement a transfer-pricing regime with either one or two sets of books. After observing its unit costs, the firm reports a compliant or non-compliant tax transfer price. In a regime with one set of books, the single transfer price coordinates the quantity decision and determines the tax payments. In a regime with two sets, different transfer prices serve those tasks. In contrast to previous studies, our analysis incorporates a strategic tax auditor, who observes the tax transfer price and decides whether to audit the firm. Real-world regulations suggest larger penalties for detected non-compliance under a two-sets-of-books transfer-pricing regime. Our analysis identifies the mixed strategy equilibria and examines how variations in the tax regulation affect the firm's tax aggressiveness. We show that a firm acts less tax aggressively with a higher tax rate difference. Additionally, the model predicts that the firm either increases or decreases the probability of keeping one set of books for a smaller penalty advantage.