# The Generalized Nash Bargaining Solution for Transfer Price Negotiations Under Incomplete Information

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## Abstract

In our model two divisions negotiate over type-dependent contracts to determine an intrafirm transfer price for an intermediate product. Since the upstream division’s (seller’s) costs and downstream division’s (buyer’s) revenues are supposed to be private information, we formally consider cooperative bargaining problems under incomplete information. This means that the two divisions consider allocations of expected utility generated by mechanisms that satisfy (interim) individual rationality, incentive compatibility and/or ex post efficiency. Assuming two possible types for buyer and seller each, we first establish that the bargaining problem is regular, regardless whether or not incentive and/or efficiency constraints are imposed. This allows us to apply the generalized Nash bargaining solution to determine *fair* transfer payments and transfer quantities. In particular, the generalized Nash bargaining solution tries to balance divisional profits, while incentive constraints are still in place. In that sense a fair profit division is generated. Furthermore, by means of illustrative examples we derive general properties of this solution for the transfer pricing problem and compare the model developed here with the models existing in the literature. We demonstrate that there is a tradeoff between ex post efficiency and fairness.

## Keywords

Cooperative bargaining Generalized Nash bargaining solution Transfer pricing Incomplete information## JEL Classification

C78 D82 M41## Notes

### Acknowledgements

This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Centre “On-The-Fly Computing” (SFB 901). We are grateful to an anonymous referee and an associate editor for constructive suggestions and comments. We would like to thank the participants of the Conference on Economic Design 2013, July 23–27, 2013, in Lund, Sweden and the Workshop on Game Theory and Economic Applications, July 25–31, 2014, in São Paulo, Brazil, for their comments. An earlier version of this article can be found as Working Paper No. 2013-07, CIE Center for International Economics Working Papers, University of Paderborn.

### Funding

Funding was provided by Deutsche Forschungsgemeinschaft (Grant No. SFB901).

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