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 mechanism design theory, a designer would like to implement a desired social choice function which specifies her favorite outcome for each possible profile of agents' types. To do so, the designer constructs a mechanism which describes each agent's feasible strategy set and the outcome function. 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 notion of Bayesian Nash equilibrium of a mechanism should be based on a threeparameter profit function instead of the conventional twoparameter utility function when strategies of agents are costly actions. 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:  93325 
Depositing User:  Haoyang Wu 
Date Deposited:  18 Apr 2019 08:20 
Last Modified:  08 Oct 2019 15:32 
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/93325 
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)
 A note on the definition of Bayesian Nash equilibrium of a mechanism when strategies of agents are costly actions. (deposited 18 Apr 2019 08:20) [Currently Displayed]

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)

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)