Collusion proof transfer payment schemes with multiple agents

Most of the current studies on transfer pricing under asymmetric information focus on a single principal and a single agent. Under a separating management and ownership assumption, transfer pricing is at minimum a three-person problem involving one principal and two agents. This paper considers a transfer pricing problem with two agents who possess private information and seek to maximize their net cash flows, instead of divisional accounting profits. The objectives of this paper are: (1) to derive a direct-revelation mechanism that induces truth telling and efficient allocation; (2) to study the agents' collusion behaviors under the direct-revelation mechanism. The findings indicate that when agents have the option to quit after contracting, it is optimal for the center to produce less than the first-best output level unless the costs for both divisions are at their lowest levels. The optimal amount of underproduction varies according to the demand condition. In addition, two sets of transfer functions, named as identical and nonidentical functions, are derived to induce truth-telling and yield optimal equilibrium output. The two sets of transfer functions are subject to collusion. However, the functions induce different collusion behaviors among agents, that is, the collusion sets for both functions are not common sets. This property enables us to eliminate any collusion between agents, particularly prior to their observation of private information.