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Incentive compatible market design with applications

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Abstract

This paper studies markets for heterogeneous goods using mechanism-design theory. For each combination of desirable properties, we derive an assignment process with these properties in the form of a corresponding direct-revelation game, or we show that it does not exist. Each participant’s utility is quasi-linear in money, and depends upon the allocation that he gets and his privately known multidimensional ‘type.’ The key properties are incentive compatibility, individual rationality, efficiency, and budget balance. The main results characterize mechanisms that are ex post incentive compatible in combination with other properties.

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Notes

  1. In the case of private values, ex post incentive compatibility is equivalent to dominant strategy incentive compatibility for direct mechanisms. Dominant strategy incentive compatibility states that each agent prefers truth-telling regardless of what other agents report. This is an additional desirable property of mechanisms since it allows agents to optimize without forming any beliefs about the behavior of others.

  2. When we write individual rationality, budget feasibility, and budget balance without any qualifier, we mean “ex post.”

  3. Recall that Cramton et al. (1987) considers Bayesian implementation only.

  4. No distributional assumptions on the type space are needed for the analysis since all mechanism properties are ex post. In other words, there can be arbitrary correlation of types.

  5. Finiteness of \(\mathcal {A}^f\), continuity of \(u_i\), and connectedness of \(\Theta _i\) are assumed to get a revenue equivalence result for the current setting (Lemma 1). Some of these assumptions can be relaxed, perhaps by strengthening others, via the characterization of revenue equivalence in Heydenreich et al. (2009). However, checking the antisymmetry of the distance function for the associated allocation graph of our setup is complicated, see Theorem 1 of Heydenreich et al. (2009). Alternatively, instead of finiteness of \(\mathcal {A}^f\), we can consider probability distributions over finite sets, but, in return we have to use a stronger connectedness assumption (Chung and Olszewski 2007).

  6. The choice of modeling is inspired by Sönmez (1999). He studies a general market without monetary transfers and analyzes when (Pareto) efficient, individually rational, and dominant strategy incentive compatible allocation functions exist. In comparison, we study all implementable allocation functions in markets with transferable utilities for which transfers (via budget balance) plays a critical role.

  7. See Carbajal and Ely (2013) for an analysis of environments when revenue equivalence fails.

  8. With some abuse of notation, \(\theta _{-i_1,\ldots ,i_j}\) is the vector of types for agents other than \(i_1,\ldots ,i_j\). For \(j=0\), \(\theta _{-i_1,\ldots ,i_j}=\theta \).

  9. For example, see Krishna and Maenner (2001); and Milgrom and Segal (2002).

  10. Thus, it follows the idea of efficient mechanism design by Vickrey (1961), Clarke (1971), and Groves (1973).

  11. More precisely, ex post incentive compatibility implies interim incentive compatibility and ex post individual rationality implies interim individual rationality.

  12. See Crémer and McLean (1985), Maskin (1992) for a similar implementation in the special case when the item is completely owned by a single agent.

  13. Yenmez (2012) studies efficient dissolution of a multi-partnership for agents with private values. He shows that efficient dissolution of multi-partnerships is possible for a convex set that he characterizes.

  14. See Moldovanu (2002) for a survey of efficient partnership dissolution literature and Jehiel and Pauzner (2006) for a setup in which only one agent is informed.

  15. In general the mechanism satisfying (4) has to be a Groves mechanism but not the VCG mechanism.

  16. Shapley and Scarf (1974) introduce the housing market without the possibility of making transfers. Miyagawa (2001) characterizes allocation functions that are dominant strategy incentive compatible, individually rational, budget balanced, and “collusion-proof” when transfers are allowed. We do not study collusion-proofness but characterize environments for which the efficient allocation function can be implemented with other properties.

  17. Gale and Shapley (1962) introduce the roommates problem without the possibility of making transfers.

  18. Two sets \(A\) and \(B\) are separated in \(X\) if each is disjoint from the other’s closure.

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Acknowledgments

This paper is a part of my dissertation submitted to Stanford University, and it has been circulated as a part of “Incentive Compatible Market Design with an Application to Matching with Wages”. I would like to thank the co-editor, Vijay Krishna, and two anonymous referees. I am grateful to my advisors Michael Ostrovsky, Andrzej Skrzypacz, and Robert Wilson for continuous guidance and support. I thank Jeremy Bulow, Itay Fainmesser, Yossi Feinberg, Alexander Frankel, John Hatfield, Onur Kesten, John Lazarev, John Ledyard, Hongyi Li, Naz Nami, Muriel Niederle, Michael Schwarz, Daniel Taylor, Ali Yurukoglu, and seminar participants at various institutions for helpful comments. The author acknowledges the financial support of the SIEPR Leonard W. Ely & Shirley R. Ely Graduate Student Fellowship. Part of this research was conducted at Microsoft Research New England.

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  1. Tepper School of Business, Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA, 15213, USA

    M. Bumin Yenmez

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Yenmez, M.B. Incentive compatible market design with applications. Int J Game Theory 44, 543–569 (2015). https://doi.org/10.1007/s00182-014-0444-8

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