Abstract
We consider an infinite horizon dynamic mechanism design problem with interdependent valuations. In this setting the type of each agent is assumed to be evolving according to a first order Markov process and is independent of the types of other agents. However, the valuation of an agent can depend on the types of other agents, which makes the problem fall into an interdependent valuation setting. Designing truthful mechanisms in this setting is non-trivial in view of an impossibility result which says that for interdependent valuations, any efficient and ex-post incentive compatible mechanism must be a constant mechanism, even in a static setting. Mezzetti (Econometrica 72(5):1617–1626, 2004) circumvents this problem by splitting the decisions of allocation and payment into two stages. However, Mezzetti’s result is limited to a static setting and moreover in the second stage of that mechanism, agents are weakly indifferent about reporting their valuations truthfully. This paper provides a first attempt at designing a dynamic mechanism which is efficient, strict ex-post incentive compatible and ex-post individually rational in a setting with interdependent values and Markovian type evolution.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
The naming of the equilibrium concept is subtle due to the two stage nature in each round. The term ‘ex-post’ is conventionally used in the context of single stage mechanisms, i.e., where the decisions of allocation and transfer are decided simultaneously (see, e.g., Jehiel et al. (2006)) and it denotes that truthful reporting is optimal for every realization of the other agents’ types even if the agent knew the other agents’ types. In the context of two-stage mechanisms that we consider here, we feel that it would be more appropriate to refer to such an equilibrium involving full observability as a ‘subgame perfect’ equilibrium. This is the equilibrium concept used in the static two stage mechanism by Mezzetti (2004), and we discuss the difference between the two equilibrium concepts in detail in the next section.
References
Associated-Press (2004) Some US hospitals outsourcing work. http://www.msnbc.msn.com/id/6621014
Athey S, Segal I (2007) An efficient dynamic mechanism, working paper, Stanford University, earlier version circulated in 2004
Bergemann D, Välimäki J (2010) The dynamic pivot mechanism. Econometrica 78:771–789
Bertsekas DP (1995) Dynamic programming and optimal control, vol I. Athena Scientific, Belmont
Blackwell D (1965) Discounted dynamic programming. Ann Math Stat 36(1):226–235
Cavallo R, Parkes DC, Singh S (2006) Optimal coordinated planning amongst self-interested agents with private state. In: Proceedings of the twenty-second annual conference on uncertainty in artificial intelligence (UAI 2006), pp 55–62
Cavallo R, Parkes DC, Singh S (2009) Efficient mechanisms with dynamic populations and dynamic types. Technical report, Harvard University
Clarke E (1971) Multipart pricing of public goods. Public Choice 8:19–33
Groves T (1973) Incentives in teams. Econometrica 41(4):617–631
Gupta A, Goyal RK, Joiner KA, Saini S (2008) Outsourcing in the healthcare industry: information technology, intellectual property, and allied aspects. Inf Resour Manag J (IRMJ) 21(1):1–26
Jehiel P, Moldovanu B (2001) Efficient design with interdependent valuations. Econometrica 69:1237–1259
Jehiel P, Meyer-ter Vehn M, Moldovanu B, Zame WR (2006) The limits of ex-post implementation. Econometrica 74(3):585–610
Mezzetti C (2004) Mechanism design with interdependent valuations: efficiency. Econometrica 72(5):1617–1626
Mezzetti C (2007) Mechanism design with interdependent valuations: surplus extraction. Econ Theory 31:473–488
Nath S, Zoeter O (2013) A strict ex-post incentive compatible mechanism for interdependent valuations. Econ Lett 121(2):321–325
Nicholson PJ (2004) Occupational health services in the UK—challenges and opportunities. Occup Med 54:147–152. doi:10.1093/occmed/kqg125
Puterman ML (2014) Markov decision processes: discrete stochastic dynamic programming. Wiley
Vickrey W (1961) Counterspeculation, auctions, and competitive sealed tenders. J Finance 16(1):8–37
Ye Y (2005) A new complexity result on solving the Markov decision problem. Math Oper Res 30:733–749
Acknowledgments
We are grateful to Ruggiero Cavallo, David C. Parkes, two anonymous referees and the associate editor for useful comments on the paper. This work was done when the first author was a student at the Indian Institute of Science and was supported by Tata Consultancy Services (TCS) Doctoral Fellowship. This work is part of a collaborative project between Xerox Research and Indian Institute of Science on incentive compatible learning.
Author information
Authors and Affiliations
Corresponding author
Additional information
A preliminary version of this work was presented in the conference on Uncertainty in Artificial Intelligence, 2011.
Rights and permissions
About this article
Cite this article
Nath, S., Zoeter, O., Narahari, Y. et al. Dynamic mechanism design with interdependent valuations. Rev Econ Design 19, 211–228 (2015). https://doi.org/10.1007/s10058-015-0177-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10058-015-0177-6
Keywords
- Dynamic mechanism design
- Interdependent value
- Dynamic pivot mechanism
- Markov decision problem
- Dynamic games
- Nash equilibrium
- Social choice
- Collective action