Groves Mechanism vs. Profit Sharing for Corporate Budgeting – An Experimental Analysis with Preplay Communication

Abstract

This paper experimentally explores the efficiency of the Groves mechanism and a profit sharing scheme in a corporate budgeting context. Specifically, it examines the effects of anonymous communication on both incentive schemes. The results show that although the Groves mechanism is analytically superior to the profit sharing scheme, the latter turns out to be advantageous for headquarters in our experiment. This is essentially due to the effects of communication on both incentive schemes. Under the profit sharing scheme, communication improves coordination and reduces inefficient resource allocation. Under the Groves mechanism, however, it leads to stable collusion strategies of the participants, and thus increases compensation costs.

Acknowledgements

We thank participants of the EAA 2006 annual meeting and the EFM Symposium 2006, seminar participants at the University of Vienna, two reviewers, Salvador Carmona (Editor), Mathias Erlei, Thomas Pfeiffer, Rudolf Vetschera and particularly Robert M. Gillenkirch for many helpful comments. We also thank Stefan Geisler for his excellent assistance with the technical implementation of the experiment.

Notes

1. In fact, the literature about centralization and delegation of decision authority usually relies upon the assumption of self-enforcing contracts when analyzing coalitions (Mookherjee, 2006).

2. In general, the more direct the contact is between the players during the communication, the better the cooperation (Frohlich and Oppenheimer, 1998; Brosig et al., 2003). Bochet et al. (2006) find that communication in a chat room is nearly as efficient in inducing cooperation as face-to-face interaction. For the effects of communication in social dilemma experiments, see also, for example, Sally (1995).

3. For coordination through communication, see, for example, Farrell (1987) and Farrell and Rabin (1996) for a theoretical perspective and Cooper et al. (1989, 1994) for experimental results.

4. Another important issue with respect to the Groves mechanism is its effectiveness for combined hidden information and hidden action problems (Kanodia, 1993; Hofmann and Pfeiffer, 2003). We abstract from this problem in our experiment and will discuss it in more detail in Section 5. See also Cohen and Loeb (1984) for the profit sharing scheme under hidden action.

5. Technically, this assumption is necessary to induce multiple Pareto efficient Nash equilibria in the profit sharing treatments. With Δ = 0 the only Pareto efficient equilibrium in pure strategies would be truth-telling. The ex ante information asymmetry thus prevents participants' focusing on this equilibrium during the experiment. For Pareto efficiency as a natural focal point see, for example, Schelling (1966, Appendix C), Harsanyi and Selten (1988, chap. 3), also Cooper et al. (1990) and Van Huyck et al. (1990) for experimental results.

6. However, the players were never told that the resource allocation scheme represents the optimal allocation given truthful reporting.

7. The players were forbidden from revealing their identity or making arrangements beyond the game in the laboratory. If so, they would have lost their entire variable compensation from the experiment. In the analysis of the communication, no evidence could be found for rule breaking.

8. As the range for [Pcirc]_i is 1.3–2.2 under profit sharing, RELDEV_i is correspondingly adjusted in these treatments.

9. We did not directly compare Π_HQ ([Pcirc]_i, ˆ P_j) in the different treatments, as due to the randomization of the productivity parameters, headquarters' net earnings for truth-telling were slightly larger in the profit sharing treatments than in the Groves treatments. Thus, using actual net earnings would favor profit sharing even if the efficiency losses under Groves and profit sharing were equal.

10. The experimental data presented here were gathered in two studies. In the first study, we implemented the Groves treatments with and without communication, and in the second study we performed the profit sharing treatments with and without communication. However, as we had different participants in these two studies and did not change the instructions or the procedure (except for the adjustments necessary to account for the special characteristics of every treatment), there is no relevant difference between these two studies, and thus, we will not differentiate between them in the following. The data from the two Groves treatments are also used in Arnold and Ponick (2006).

11. For example, for the absolute misrepresentation, we use .

12. There are also three cases in the non-communication treatment where ABSDEV_i equals ABSDEV_j and is larger than 0.1 or lower than − 0.1. However, we do not include them in Table 3 as deviations from truth-telling with absolute values larger than 0.1 do not lead to an equilibrium with certainty (i.e. for all P_i) in the non-communication treatment. In the communication treatment however, the corresponding cases are included in Table 3 if participants agreed upon these reports during the communication.

13. When analyzing the communication, we found strong evidence that participants are indeed aware of the fact that only the resource allocation influences their compensation but not the exact magnitude of the deviations from truth-telling. For example, after two participants have truthfully exchanged their actual productivity parameters of P_i = 1.6 and P_j = 1.7 and player j has proposed to report [Pcirc]_i = 1.6 and [Pcirc]_j = 1.9, player i notes (translated from German): ‘As long as you report a larger productivity you get more resource units. Thus, we can report 1.6:1.7 or 1.6:1.9, that makes no difference.’

14. See also Güth et al. (1983), Attiyeh et al. (2000) and Kawagoe and Mori (2001) for difficulties of experiment participants with other forms of this mechanism.

15. Note that setting G_i ([Pcirc]_j) larger than 1 in order to make manager i's evaluation measure independent of a variation of [Pcirc]_j is not possible, as ∂ (Π_i + Πˆ_j)/∂ [Pcirc]_j will generally depend on P_i which is not known to headquarters. See also Green and Laffont (1979) and Crémer (1996) for lacking coalition robustness of the Pivot mechanism for binary public good decisions.