Abstract
Computationally Feasible Automated Mechanism Design (CFAMD) combines manual mechanism design and optimization.
In CFAMD, we focus on a parameterized family of strategy-proof mechanisms, and then optimize within the family by adjusting the parameters. This transforms mechanism design (functional optimization) into value optimization, as we only need to optimize over the parameters.
Under CFAMD, given a mechanism (characterized by a list of parameters), we need to be able to efficiently evaluate the mechanism’s performance. Otherwise, parameter optimization is computationally impractical when the number of parameters is large.
We propose a new technique for speeding up CFAMD for worst-case objectives. Our technique builds up a set of worst-case type profiles, with which we can efficiently approximate a mechanism’s worst-case performance. The new technique allows us to apply CFAMD to cases where mechanism performance evaluation is computationally expensive.
We demonstrate the effectiveness of our approach by applying it to the design of competitive VCG redistribution mechanism for public project problem. This is a well studied mechanism design problem. Several competitive mechanisms have already been proposed. With our new technique, we are able to achieve better competitive ratios than previous results.
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- 1.
In terms of the number of agents.
- 2.
For example, when it comes to revenue-maximizing combinatorial auction design, we do not have an easy-to-work-with characterization of all combinatorial auctions that are strategy-proof and individually rational.
- 3.
By performance, we mean how well the mechanism performs with respect to the mechanism design objective. For example, if our objective is to maximize the expected revenue, then a mechanism’s performance is the expected revenue under it.
- 4.
Even if it is achievable, the overall process may still be computationally expensive.
- 5.
Naroditskiy et al. [18] proved that it is without loss of generality to assume that every agent’s type is bounded above by the project cost, as any competitive mechanism can be easily generalized to cases without this constraint, and still keeps the same competitive ratio.
- 6.
For our setting, it is without loss of generality to focus on anonymous mechanisms [9].
- 7.
The name “VCG redistribution mechanisms” emphasizes on the fact that a non-deficit Groves mechanism can be interpreted as a two step process, where we first allocate and charge payments according to the VCG mechanism (aka, the Clarke mechanism), and then we redistribute the VCG payments back to the agents. An agent’s redistribution does not depend on her own bid, which ensures that the redistribution amount does not affect an agent’s incentives. We also need to ensure that the agents’ total redistribution received is never more than the total VCG payment collected, which is to ensure the non-deficit property.
- 8.
It should be noted that this mechanism is only used as a benchmark. The competitive ratio can be interpreted as the ratio between “best social welfare for selfish agents” and “best social welfare for unselfish agents”.
- 9.
Guo [3] proposed only one mechanism, which is based on averaging the VCG payments. Therefore, we call the proposed mechanism average-based redistribution (ABR) mechanism.
- 10.
For example, on a i7-4770 desktop, for \(n=3\), it takes a few seconds to obtain a mechanism with competitive ratio at least 0.66, but it takes a lot longer to push for more significant digits.
References
Conitzer, V., Sandholm, T.: Complexity of mechanism design. In: Proceedings of the 18th Annual Conference on Uncertainty in Artificial Intelligence (UAI), Edmonton, Canada, pp. 103–110 (2002)
Gujar, S., Narahari, Y.: Redistribution mechanisms for assignment of heterogeneous objects. J. Artif. Intell. Res. 41, 131–154 (2011)
Guo, M.: Competitive VCG redistribution mechanism for public project problem. In: Baldoni, M., Chopra, A.K., Son, T.C., Hirayama, K., Torroni, P. (eds.) PRIMA 2016. LNCS, vol. 9862, pp. 279–294. Springer, Cham (2016). doi:10.1007/978-3-319-44832-9_17
Guo, M., Conitzer, V.: Worst-case optimal redistribution of VCG payments in multi-unit auctions. Games Econ. Behav. 67(1), 69–98 (2009)
Guo, M., Conitzer, V.: Computationally feasible automated mechanism design: General approach and case studies. In: Proceedings of the National Conference on Artificial Intelligence (AAAI), Atlanta, GA, USA, pp. 1676–1679 (2010). NECTAR track
Guo, M., Conitzer, V.: Optimal-in-expectation redistribution mechanisms. Artif. Intell. 174(5–6), 363–381 (2010)
Guo, M., Conitzer, V.: Strategy-proof allocation of multiple items between two agents without payments or priors. In: Proceedings of the Ninth International Joint Conference on Autonomous Agents and Multi-Agent Systems (AAMAS), Toronto, Canada, pp. 881–888 (2010)
Guo, M., Conitzer, V.: Better redistribution with inefficient allocation in multi-unit auctions. Artif. Intell. 216, 287–308 (2014)
Guo, M., Markakis, E., Apt, K.R., Conitzer, V.: Undominated groves mechanisms. J. Artif. Intell. Res. 46, 129–163 (2013)
Guo, M., Naroditskiy, V., Conitzer, V., Greenwald, A., Jennings, N.R.: Budget-balanced and nearly efficient randomized mechanisms: Public goods and beyond. In: Proceedings of the Seventh Workshop on Internet and Network Economics (WINE), Singapore (2011)
Holmström, B.: Groves’ scheme on restricted domains. Econometrica 47(5), 1137–1144 (1979)
Likhodedov, A., Sandholm, T.: Methods for boosting revenue in combinatorial auctions. In: Proceedings of the National Conference on Artificial Intelligence (AAAI), San Jose, CA, USA, pp. 232–237 (2004)
Likhodedov, A., Sandholm, T.: Approximating revenue-maximizing combinatorial auctions. In: Proceedings of the National Conference on Artificial Intelligence (AAAI), Pittsburgh, PA, USA (2005)
Mas-Colell, A., Whinston, M., Green, J.R.: Microeconomic Theory. Oxford University Press, New York (1995)
Moore, J.: General Equilibrium and Welfare Economics: An Introduction. Springer, Heidelberg (2006). doi:10.1007/978-3-540-32223-8
Moulin, H.: Axioms of Cooperative Decision Making. Cambridge University Press, Cambridge (1988)
Moulin, H.: Almost budget-balanced VCG mechanisms to assign multiple objects. J. Econ. Theor. 144(1), 96–119 (2009)
Naroditskiy, V., Guo, M., Dufton, L., Polukarov, M., Jennings, N.R.: Redistribution of VCG payments in public project problems. In: Proceedings of the Eighth Workshop on Internet and Network Economics (WINE), Liverpool (2012)
Acknowledgment
This work is supported by Research Initiative Grant of Sun Yat-Sen University under Project 985 and Australian Research Council Discovery Project DP150104871.
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Guo, M., Shen, H. (2017). Speed up Automated Mechanism Design by Sampling Worst-Case Profiles: An Application to Competitive VCG Redistribution Mechanism for Public Project Problem. In: An, B., Bazzan, A., Leite, J., Villata, S., van der Torre, L. (eds) PRIMA 2017: Principles and Practice of Multi-Agent Systems. PRIMA 2017. Lecture Notes in Computer Science(), vol 10621. Springer, Cham. https://doi.org/10.1007/978-3-319-69131-2_8
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