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Some Remarks on Bayesian Mechanism Design

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Social Design

Part of the book series: Studies in Economic Design ((DESI))

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Abstract

Although the problem of revelation of preferences for public goods had already been brought up in several instances, it was surely the merit of Leo Hurwicz to show that providing incentives was a fundamental problem in the design of any institution for collective decision based on decentralized information and control.

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Notes

  1. 1.

    An ex post equilibrium is called a uniform equilibrium in d’Aspremont and Gérard-Varet (1979a) and incentive compatibility is called uniform incentive compatibility by Holmström and Myerson (1983). See Bergemann and Morris (2005) for more discussion and references.

  2. 2.

    If the set of types is large enough (i.e., connected), Groves mechanisms are the only efficient SIC mechanisms. This result does not hold in our discrete types of framework. See Green and Laffont (1977), Walker (1978), and Holmström (1979).

  3. 3.

    This generalizes a result of Maskin (1986), proved in the case of two agents.

  4. 4.

    “C” for “Compatibility condition” the name given by d’Aspremont and Gérard-Varet (1979a) and the star in C* to indicate that it is the “dual” version of the condition. The “primal” version is studied in the next section.

  5. 5.

    For the proof, see d’Aspremont et al. (2004). Forges et al. (2002) call this property “automatic balance.”

  6. 6.

    It is strictly weaker than Chung (1999) weak regularity (hence than Matsushima (1991) regularity condition) and Fudenberg et al. (1994) pairwise identifiability. It is equivalent to Johnson et al. (1990) condition called LINK.

  7. 7.

    Condition B was first defined by d’Aspremont and Gérard-Varet (1982). When n = 2, condition C is equivalent to independence of types, and condition B never holds.

  8. 8.

    We are assuming that the reservation utilities are equal to 0, both in the case of ex ante and interim participation constraints. It is quite easy to prove that this does not entail any loss of generality.

  9. 9.

    This result was first proved in d’Aspremont and Gérard-Varet (1979b) and generalized in Holmström (1977, 1979).

  10. 10.

    Because of the independence of types, we can write p(α −i) instead of \(p\left ( \alpha _{-i}\mid \alpha _{i}\right )\).

  11. 11.

    Note that with independence, we can write p(α −i) without ambiguity as \(p(\alpha _{-i} \mid \alpha _i) = p(\alpha _{-i} \mid \widetilde {\alpha }_i)\) for all \(\alpha _i, \widetilde {\alpha }_{i}, \alpha _{-i}\).

  12. 12.

    To be totally clear, this condition is not necessary in the case of finite sets of types. We are writing it in this way to avoid introducing more notation.

  13. 13.

    See Alchian and Demsetz (1972) and Holmström (1982).

References

  • Alchian, A., & Demsetz, H. (1972). Production, information costs and economic organization. American Economic Review, 62, 777–805.

    Google Scholar 

  • Bergemann, D., & Morris, S. (2005). Robust mechanism design. Econometrica, 73, 1771–1813.

    Article  Google Scholar 

  • Chung, K.-S. (1999). A note on Matsushima’s regularity condition. Journal of Economic Theory, 87, 429–433.

    Article  Google Scholar 

  • Crémer, J., & Khalil, F. (1992). Gathering information before signing a contract. American Economic Review, 82, 566–578.

    Google Scholar 

  • Crémer, J., Khalil, F., & Rochet, J.-C. (1998a). Contracts and productive information gathering. Games and Economic Behavior, 25, 174–193.

    Article  Google Scholar 

  • Crémer, J., Khalil, F., & Rochet, J.-C. (1998b). Strategic information gathering before a contract is offered. Journal of Economic Theory, 81, 163–200.

    Article  Google Scholar 

  • Crémer, J., & McLean, R. P. (1985). Optimal selling strategies under uncertainty for a discriminating monopolist when demands are interdependent. Econometrica, 53, 345–361.

    Article  Google Scholar 

  • Crémer, J., & McLean, R. P. (1988). Full extraction of the surplus in Bayesian and dominant strategy auctions. Econometrica, 56, 1247–1258.

    Article  Google Scholar 

  • d’Aspremont, C., & Crémer, J. (2018). Bayesian incentive compatibility with and without free beliefs (in press).

    Google Scholar 

  • d’Aspremont, C., Crémer, J., & Gérard-Varet, L.-A. (1990). Incentives and the existence of Pareto-optimal revelation mechanisms. Journal of Economic Theory, 51, 233–254.

    Article  Google Scholar 

  • d’Aspremont, C., Crémer, J., & Gérard-Varet, L.-A. (2003). Correlation, independence, and Bayesian incentives. Social Choice and Welfare, 21, 281–310.

    Article  Google Scholar 

  • d’Aspremont, C., Crémer, J., & Gérard-Varet, L.-A. (2004). Balanced Bayesian mechanisms. Journal of Economic Theory, 115, 385–396.

    Article  Google Scholar 

  • d’Aspremont, C., & Gérard-Varet, L.-A. (1979a). Incentives and incomplete information. Journal of Public Economics, 11, 25–45.

    Article  Google Scholar 

  • d’Aspremont, C., & Gérard-Varet, L.-A. (1979b), On Bayesian incentive compatible mechanisms. In J.-J. Laffont (Ed.), Aggregation and Revelation of Preferences (pp. 269–288). Amsterdam: North-Holland.

    Google Scholar 

  • d’Aspremont, C., & Gérard-Varet, L.-A. (1982). Bayesian incentive compatible beliefs. Journal of Mathematical Economics, 10, 25–45.

    Google Scholar 

  • d’Aspremont, C., & Gérard-Varet, L.-A. (1998). Linear inequality methods to enforce partnerships under uncertainty: An overview. Games and Economic Behavior, 25, 311–336.

    Article  Google Scholar 

  • Fan, K. (1956). On systems of linear inequalities. In H. W. Kuhn & A. W. Tucker (Eds.), Linear inequalities and related systems. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Forges, F., Mertens, J.-F., & Vohra, R. V. (2002). The ex ante incentive compatible core in the absence of wealth effects. Econometrica, 70, 1865–1892.

    Article  Google Scholar 

  • Fudenberg, D., Levine, D. K., & Maskin, E. (1994). The folk theorem with imperfect public information. Econometrica, 62, 997–1039.

    Article  Google Scholar 

  • Green, J., & Laffont, J.-J. (1977). Characterization of satisfactory mechanisms for the revelation of preferences for public goods. Econometrica, 45, 427–438.

    Article  Google Scholar 

  • Green, J., & Laffont, J.-J. (1979). Incentives in public decision making. Amsterdam: North-Holland.

    Google Scholar 

  • Harsanyi, J. C. (1967). Games with incomplete information played by “Bayesian” players, I-III. Part I. The basic model. Management Science, 14, 159–182.

    Article  Google Scholar 

  • Harsanyi, J. C. (1968a). Games with incomplete information played by “Bayesian” players, Part II. Bayesian equilibrium points. Management Science, 14, 320–334.

    Article  Google Scholar 

  • Harsanyi, J. C. (1968b). Games with incomplete information played by “Bayesian” players, Part III. The basic probability distribution of the game. Management Science, 14, 486–502.

    Article  Google Scholar 

  • Holmström, B. (1977). On incentive problems in organizations. Ph.D. thesis, Stanford University.

    Google Scholar 

  • Holmström, B. (1979). Groves’ scheme on restricted domains. Econometrica, 47, 1137–1144.

    Article  Google Scholar 

  • Holmström, B. (1982). Moral hazard in teams. Bell Journal of Economics, 13, 324–340.

    Article  Google Scholar 

  • Holmström, B., & Myerson, R. B. (1983). Efficient and durable decision rules with incomplete information. Econometrica, 51, 1799–1819.

    Article  Google Scholar 

  • Hurwicz, L. (1972). On informationally decentralized systems. In C. B. McGuire, R. Radner, & K. J. Arrow (Eds.) Decision and organization: A volume in honor of Jacob Marschak (pp. 297–336). Amsterdam: North-Holland.

    Google Scholar 

  • Johnson, J. W., Pratt, J. W., & Zeckhauser, R. J. (1990). Efficiency despite mutually payoff-relevant private information: The finite case. Econometrica, 58, 873–900.

    Article  Google Scholar 

  • Kosenok, G., & Severinov, S. (2008). Individually rational, budget-balanced mechanisms and allocation of surplus. Journal of Economic Theory, 140, 126–161.

    Article  Google Scholar 

  • Makowski, L., & Mezzetti, C. (1994). Bayesian and weakly robust first best mechanisms: Characterizations. Journal of Economic Theory, 64, 500–519.

    Article  Google Scholar 

  • Maskin, E. S. (1986). Optimal Bayesian mechanisms. In W. P. Heller, R. M. Starr, & D. A. Starrett (Eds.), Essays in honor of Kenneth J. Arrow: Volume 3, uncertainty, information, and communication (pp. 229–238). Cambridge: Cambridge University Press.

    Chapter  Google Scholar 

  • Matsushima, H. (1991). Incentive compatible mechanisms with full transferability. Journal of Economic Theory, 54, 198–203.

    Article  Google Scholar 

  • Matsushima, H. (2007). Mechanism design with side payments: Individual rationality and iterative dominance. Journal of Economic Theory, 133, 1–30.

    Article  Google Scholar 

  • Myerson, R., & Satterthwaite, M. (1983). Efficient mechanisms for bilateral trading. Journal of Economic Theory, 29, 265–281.

    Article  Google Scholar 

  • Szalay, D. (2008). Contracts with endogenous information. Games and Economic Behaviour, 65, 586–625.

    Article  Google Scholar 

  • Vickrey, W. (1961), Counterspeculation, auctions and competitive sealed tenders. Journal of Finance, 72, 44–61.

    Google Scholar 

  • Walker, M. (1978). A note on the characterization of mechanisms for the revelation of preferences. Econometrica, 46, 147–152.

    Article  Google Scholar 

  • Walker, M. (1980). On the nonexistence of a dominant strategy mechanism for making optimal public decisions. Econometrica, 48, 1521–1540.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. CORE, Université Catholique de Louvain, Louvain-la-Neuve, Belgium

    Claude d’Aspremont

  2. Toulouse School of Economics, Toulouse, France

    Jacques Crémer

Authors
  1. Claude d’Aspremont
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  2. Jacques Crémer
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Correspondence to Jacques Crémer .

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Editors and Affiliations

  1. Center for Mathematical Economics (IMW), Bielefeld University, Bielefeld, Germany

    Walter Trockel

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d’Aspremont, C., Crémer, J. (2019). Some Remarks on Bayesian Mechanism Design. In: Trockel, W. (eds) Social Design. Studies in Economic Design. Springer, Cham. https://doi.org/10.1007/978-3-319-93809-7_6

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