A type-adjustable mechanism where the designer may obtain more payoffs by optimally controlling distributions of agents' types

Wu, Haoyang (2022): A type-adjustable mechanism where the designer may obtain more payoffs by optimally controlling distributions of agents' types.

Abstract

In a mechanism, a designer may reveal some information to influence agents' private types in order to obtain more payoffs. In the literature, the information is usually represented as random variables, the value of which are realized by the nature. However, this representation of information may not be proper in some practical cases. In this paper, we propose a type-adjustable mechanism where the information sent by the designer is modeled as a solution of her optimization problem. From the designer's perspective, the probability distributions of agents' private types may be optimally controlled. By constructing a type-adjustable first-price sealed-bid auction, we show that the seller may obtain more expected payoffs than what she could obtain at most in the traditional optimal auction model. Interestingly, to the satisfaction of all, each agent's \emph{ex-ante} expected payoffs may be increased too. In the end, we compare the type-adjustable mechanism with other relevant models.

• Item Type: MPRA Paper
• Language: English
• Keywords: Mechanism design; Optimal auction; Bayesian implementation.
• Subjects: D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; Associations

References

A. Mas-Colell, M.D. Whinston and J.R. Green. Microeconomic Theory, Oxford University Press, 1995.

R. Serrano. The Theory of Implementation of Social Choice Function, SIAM Review, vol.46, No.3, 377-414, 2004.

Y. Narahari et al. Game Theoretic Problems in Network Economics and Mechanism Design Solutions, Springer, 2009.

M. Engers and B. McManus, Charity Auctions, International Economic Review, vol.48, No.3, 953-994, 2007.

R. Myerson. Optimal Auction Design, Mathematics of Operations Research, vol.6, No.1, 58-73, 1981.

Maschler et al. Game Theory, Cambridge University Press, 2013.

D. Bergemann and J. V$\ddot{a}$lim$\ddot{a}$ki. Information in mechanism design. In: Blundell, Richard, Newey, Whitney, Persson, Torsten (Eds.), Proceedings of the 9th World Congress of the Econometric Society. Cambridge University Press, Cambridge, pp.186–221, 2006.

V. Krishna. Auction Theory (Second Edition), Academic Press, 2010.

P. Milgrom and R. Weber. A Theory of Auctions and Competitive Bidding, Econometrica, vol.50, 1089-1122, 1982.

Kamenica and Gentzkow. Bayesian persuasion, The American Economic Review, vol.101, 2590-2615, 2011.

D. Bergemann and J. V$\ddot{a}$lim$\ddot{a}$ki. Dynamic Mechanism Design: An Introduction. Journal of Economic Literature, vol.57, 235–274, 2019.

A. Pavan, I. Segal, and J. Toikka. Dynamic Mechanism Design: A Myersonian Approach. Econometrica, vol.82, 601-653, 2014.

E. Kamenica. Bayesian Persuasion and Information Design. Annual Review of Economics, vol.11, 249-272, 2019.

D. Bergemann and S. Morris. Information design: A unified perspective. Journal of Economic Literature, vol.57, 44-95, 2019.

J. Hedlund. Persuasion with communicationn costs. Games and Economic Behavior, vol.92, 28-40, 2015.

D. Fudenberg and J. Tirole. Game Theory, MIT Press, 1990.

A. Nguyen and T. Tan. Bayesian persuasion with costly messages, Journal of Economic Theory, vol.193, 105212, 2021.

J. Kleinberg and M. Raghavan. How Do Classifiers Induce Agents to Invest Effort Strategically? ACM Trans. Econ. Comput., vol.8, 2020.

N. Szech. Optimal disclosure of costly information packages in auctions. Journal of Mathematical Economics, vol.47, 462-469, 2011.

D. Bergemann and M. Pesendorfer. Information structures in optimal auctions. Journal of Economic Theory, vol.137, 580-609, 2007.

A. Gershkov. Optimal auctions and information disclosure. Rev. Econ. Design., vol.13, 335-344, 2009.

N. Szech. Optimal advertising of auctions, Journal of Economic Theory, vol.146, 2596-2607, 2011.

R. Fang, X. Li. Advertising a second-price auction. Journal of Mathematical Economics, vol.61, 246-252, 2015.