Wu, Haoyang (2019): A note on the definition of Bayesian Nash equilibrium of a mechanism when strategies of agents are costly actions.
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Abstract
In the framework of mechanism design theory, in order to implement a desired social choice function in Bayesian Nash equilibrium, a designer constructs a mechanism which specifies her favorite outcome for each possible profile of agents' types. Generally speaking, each agent's strategy has two possible formats: an action, or a message. In this paper, we focus on the former case and claim that the definitions of Bayesian Nash equilibrium of a mechanism and Bayesian incentive compatibility should all be based on a profit function instead of a utility function. Next, we derive the main result: Given a social choice function which can be implemented by an indirect mechanism in Bayesian Nash equilibrium, if all strategies of agents are costly actions, then it cannot be inferred that there exists a direct mechanism that can truthfully implement the social choice function in Bayesian Nash equilibrium.
Item Type:  MPRA Paper 

Original Title:  A note on the definition of Bayesian Nash equilibrium of a mechanism when strategies of agents are costly actions 
Language:  English 
Keywords:  Bayesian Nash Equilibrium; Mechanism design; Revelation Principle. 
Subjects:  D  Microeconomics > D7  Analysis of Collective DecisionMaking > D71  Social Choice ; Clubs ; Committees ; Associations D  Microeconomics > D8  Information, Knowledge, and Uncertainty 
Item ID:  93088 
Depositing User:  Haoyang Wu 
Date Deposited:  08 Apr 2019 03:58 
Last Modified:  28 Sep 2019 15:55 
References:  1. A. MasColell, M.D. Whinston and J.R. Green, Microeconomic Theory, Oxford University Press, 1995. 2. R. Myerson, Incentive compatibility and the bargaining problem, Econometrica, vol.47, 6173, 1979. 3. R. Myerson, Optimal coordination mechanisms in generalized principalagent problems, Journal of Mathematical Economics, vol.10, 6781, 1982. 4. Y. Narahari et al, Game Theoretic Problems in Network Economics and Mechanism Design Solutions, Springer, 2009. 5. N. Kartik, Strategic Communication with Lying Costs. The Review of Economic Studies, vol.76, 13591395, 2009. 6. A. Kephart and V. Conitzer, The revelation principle for mechanism design with reporting cost, In Proceedings of the ACM Conference on Electronic Commerce (EC), Maastricht, The Netherlands, 2016. 7. H. Bester and R. Strausz, Contracting with imperfect commitment and the revelation principle: The single agent case. Econometrica, Vol.69, No.4, 10771098, 2001. 8. D. Martimort and L. Stole, The revelation and delegation principles in common agency games. Econometrica, Vol.70, No.4, 16591673, 2002. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/93088 
Available Versions of this Item

The revelation principle does not always hold when strategies of agents are costly. (deposited 06 Aug 2018 13:04)

The revelation principle does not always hold when strategies of agents are costly. (deposited 19 Sep 2018 01:05)

The revelation principle does not always hold when strategies of agents are costly. (deposited 03 Oct 2018 16:24)

The revelation principle does not always hold when strategies of agents are costly. (deposited 18 Oct 2018 13:40)

The revelation principle does not always hold when strategies of agents are costly. (deposited 26 Oct 2018 18:21)
 A note on the definition of Bayesian Nash equilibrium of a mechanism when strategies of agents are costly actions. (deposited 08 Apr 2019 03:58) [Currently Displayed]

The revelation principle does not always hold when strategies of agents are costly. (deposited 26 Oct 2018 18:21)

The revelation principle does not always hold when strategies of agents are costly. (deposited 18 Oct 2018 13:40)

The revelation principle does not always hold when strategies of agents are costly. (deposited 03 Oct 2018 16:24)

The revelation principle does not always hold when strategies of agents are costly. (deposited 19 Sep 2018 01:05)