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The pivotal mechanism revisited: some evidence on group manipulation

Abstract

This paper studies the vulnerability of the pivotal mechanism with respect to manipulation by groups. In a lab experiment, groups decide on the implementation of various alternatives, some of which imply opposite interests for the two subgroups. We investigate the occurrence of tacit and explicit collusion by allowing for communication within subgroups in one treatment and prohibiting it in another. Even though all agents’ preferences are common knowledge and there exists a simple symmetric collusive strategy for one subgroup, we find little evidence for tacit collusion. Only when explicit communication is allowed, collusion is established. A behavioral model using quantal response equilibrium in which subjects have beliefs over the correlation of errors of same-type subjects helps explain the main features of our data.

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Notes

  1. 1.

    Groves (1973), as well as Groves and Loeb (1975), and much earlier Vickrey (1961) independently also discovered such incentive compatible demand revealing mechanisms for environments with separable utility functions. Green and Laffont (1977) showed that the class of mechanisms proposed by Groves includes all these mechanisms, and furthermore that any efficient and strategy-proof direct revelation mechanism is isomorphic to a Groves mechanism.

  2. 2.

    One of the early experiments by Tideman (1983) already suggested this possibility. However, this experiment was a kind of field experiment with little control over the factors that impact decisions, thus misrevelation could not be quantified.

  3. 3.

    Note that in computer science applications, the class of Vickrey-Groves-Clarke mechanisms is widely used, e.g. in resolving task and resource allocation problems that occur in multi-agent systems (see e.g. Dash et al. 2003, 2004).

  4. 4.

    The steps of 10 may render the reports space rather sparse, however, the dimensions of our payoff tables were already quite large with 13 columns and 49 rows. Extending it by only one more step in each direction would have immediately added 16 additional cells.

  5. 5.

    From the payoff tables one can see that agents are indifferent between stating their true valuation and the next higher valuation for all alternatives, e.g. for M-types, the same payoff is reached for Alpha by reporting 30 or 40, for Beta with −20 and −10, etc. This is simply an artifact of the discrete space of reports, which implies that each agent has two weakly dominant strategies in the pivotal mechanism. For the choice of the socially efficient outcome it does not matter which of these two strategies is selected.

  6. 6.

    Agents of different type have no incentive to collude by virtue of their opposed preferences for alternatives Beta and Delta.

  7. 7.

    This shall serve as main benchmark. In the section describing the experimental results, we will also discuss the case where agents bundle the alternatives.

  8. 8.

    In the section on behavior below, we will discuss whether {Alpha,Beta} is a frequent outcome because it is socially optimal or whether this is due to behavior that arises from other incentives here.

  9. 9.

    For example, in the Fehr and Schmidt (1999) model of inequality aversion this would be the preferred choice of an N-type agent if the parameter β, which measures the weight the agent puts on others’ monetary payoffs when he is behind, is sufficiently high.

  10. 10.

    Recall that the pivotal mechanism provides two weakly dominant strategies for an individual in this experiment if we consider only non-collusive behavior: reporting the true valuation and reporting its next-highest value.

  11. 11.

    This observation finds some support in the literature: Haan et al. (2009) found that tacit collusion is found to some extent for industries with only two firms. In the experiment of Kwasnica and Sherstyuk (2007), collusion occurs only in markets with two bidders; with five bidders no collusion was observed. Experience increased the incidence of collusion in the 2-bidder-market, while it did not help when experience was gained in the 5-bidder-market.

  12. 12.

    Note that four dots in Fig. 4 represent these choices in the Delta-Beta-space: (10,−10), (10,−20), (20,−10) and (20,−20).

  13. 13.

    We are grateful to an anonymous referee for suggesting this approach for the interpretation of our data.

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Correspondence to Anita Gantner.

Additional information

We gratefully acknowledge financial support by the Austrian Science Fund (FWF) through Project No. S10307-G14 and by the University of Innsbruck though grant “Nachwuchsförderung”. We wish to thank two anonymous referees and an editor for their helpful suggestions, and Karl Seiringer for excellent research assistance.

Appendix: Payoff tables

Appendix: Payoff tables

Fig. 7
figure7

M’s payoff tables for alternatives Alpha and Beta

Fig. 8
figure8

M’s payoff tables for alternatives Gamma and Delta

Fig. 9
figure9

N’s payoff tables for alternatives Alpha and Beta

Fig. 10
figure10

N’s payoff tables for alternatives Gamma and Delta

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Feri, F., Gantner, A., Höchtl, W. et al. The pivotal mechanism revisited: some evidence on group manipulation. Exp Econ 16, 23–51 (2013). https://doi.org/10.1007/s10683-012-9331-y

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Keywords

  • Collective decision making
  • Pivotal mechanism
  • Collusion
  • Communication
  • QRE

JEL Classification

  • D71
  • D61
  • C92