Two-agent Nash implementation: A new result

[J. Moore and R. Repullo, \emph{Econometrica} \textbf{58} (1990) 1083-1099] and [B. Dutta and A. Sen, \emph{Rev. Econom. Stud.} \textbf{58} (1991) 121-128] are two important papers on two-agent Nash implementation. Recently, [H. Wu, Quantum mechanism helps agents combat "bad" social choice rules. \emph{International Journal of Quantum Information}, 2010 (accepted). abs/1002.4294 ] broke through traditional results on Nash implementation with three or more agents. In this paper, we will investigate two-agent Nash implementation by virtue of Wu's quantum mechanism. The main result is: A two-agent social choice rule that satisfies Condition $\mu2$ will no longer be Nash implementable if an additional Condition $\lambda'$ is satisfied. Moreover, according to a classical two-agent algorithm, this result holds not only in the quantum world, but also in the macro world.Comment: 15 pages, 4 figure

Two-agent Nash implementation: A new result

[Moore and Repullo, \emph{Econometrica} \textbf{58} (1990) 1083-1099] and [Dutta and Sen, \emph{Rev. Econom. Stud.} \textbf{58} (1991) 121-128] are two fundamental papers on two-agent Nash implementation. Both of them are based on Maskin's classic paper [Maskin, \emph{Rev. Econom. Stud.} \textbf{66} (1999) 23-38]. A recent work [Wu, http://arxiv.org/abs/1002.4294, \emph{Inter. J. Quantum Information}, 2010 (accepted)] shows that when an additional condition is satisfied, the Maskin's theorem will no longer hold by using a quantum mechanism. Furthermore, this result holds in the macro world by using an algorithmic mechanism. In this paper, we will investigate two-agent Nash implementation by virtue of the algorithmic mechanism. The main result is: The sufficient and necessary conditions for Nash implementation with two agents shall be amended, not only in the quantum world, but also in the macro world.Quantum game theory; Mechanism design; Nash implementation.

Nash implementation with partially honest individuals

We investigate the problem of Nash implementation in the presence of "partially honest" individuals. A partially honest player is one who has a strict preference for revealing the true state over lying when truthtelling does not lead to a worse outcome (according to preferences in the true state) than that which obtains when lying. We show that when there are at least three individuals, the presence of even a single partially honest individual (whose identity is not known to the planner) can lead to a dramatic increase in the class of Nash implementable social choice correspondences. In particular, all social choice correspondences satisfying No Veto Power can be implemented. We also provide necessary and sufficient conditions for implementation in the two-person case when there is exactly one partially honest individual and when both individuals are partially honest. We describe some implications of the characterization conditions for the two-person case. Finally, we extend our three or more individual result to the case where there is an individual with an arbitrary small but strictly positive probability of being partially honest

Nash Implementation with Partially Honest Individuals

We investigate the problem of Nash implementation in the presence of "partially honest" individuals. A partially honest player is one who has a strict preference for revealing the true state over lying when truthtelling does not lead to a worse outcome (according to preferences in the true state) than that which obtains when lying. We show that when there are at least three individuals, the presence of even a single partially honest individual (whose identity is not known to the planner) can lead to a dramatic increase in the class of Nash implementable social choice correspondences. In particular, all social choice correspondences satisfying No Veto Power can be implemented. We also provide necessary and sufficient conditions for implementation in the two-person case when there is exactly one partially honest individual and when both individuals are partially honest. We describe some implications of the characterization conditions for the two-person case. Finally, we extend our three or more individual result to the case where there is an individual with an arbitrary small but strictly positive probability of being partially honest.

Two-agent Nash implementation with partially-honest agents: Almost Full Characterizations

In a two-agent society with partially-honest agents, we extend Dutta and Sen (2009)'s results of Nash implementation to the domain of weak orders. We identify the class of Nash implementable social choice correspondences with a "gap" between necessary and sufficient conditions, both when exactly one agent is partially-honest and when both agents are partially-honest. We also show that, on the domain of linear orders, the "gap" between our conditions gets closed and they become equivalent to those devised by Dutta and Sen. New implementing mechanisms are devised. In line with earlier works, the classic condition of monotonicity is no longer required, whereas a weak version of the standard punishment condition is required even when both agents are known to be partially-honest. We derive simpler sufficient conditions that are satisfied in a wide range of applications.Two-agent Nash implementation, intrinsic preferences for honesty, permissive results

Partially-honest Nash implementation: Characterization results

This paper studies implementation problems in the wake of a recent new trend of implementation theory which incorporates a non-consequentialist flavor of the evidence from experimental and behavioral economics into the issues. Specifically, following the seminal works by Matsushima (2008) and Dutta and Sen (2009), the paper considers implementation problems with partially honest agents, which presume that there exists at least one individual in the society who concerns herself with not only outcomes but also honest behavior at least in a limited manner. Given this setting, the paper provides a general characterization of Nash implementation with partially-honest individuals. It also provides the necessary and sufficient condition for Nash implementation with partially-honest individuals by mechanisms with some types of strategy-space reductions. As a consequence, it shows that, in contrast to the case of the standard framework, the equivalence between Nash implementation and Nash implementation with strategy space reduction no longer holds.

Partially-honest Nash implementation: Characterization results

This paper studies implementation problems in the wake of a recent new trend of implementation theory which incorporates a non-consequentialist flavor of the evidence from experimental and behavioral economics into the issues. Specifically, following the seminal works by Matsushima (2008) and Dutta and Sen (2009), the paper considers implementation problems with partially honest agents, which presume that there exists at least one individual in the society who concerns herself with not only outcomes but also honest behavior at least in a limited manner. Given this setting, the paper provides a general characterization of Nash implementation with partially-honest individuals. It also provides the necessary and sufficient condition for Nash implementation with partially-honest individuals by mechanisms with some types of strategy-space reductions. As a consequence, it shows that, in contrast to the case of the standard framework, the equivalence between Nash implementation and Nash implementation with strategy space reduction no longer holds.Nash implementation, canonical-mechanisms, s-mechanisms, self-relevant mechanisms, partial-honesty, permissive results.

Technology Transfers and the Clean Development Mechanism in a North-South General Equilibrium Model

This paper analyzes the potential welfare gains of introducing a technology transfer from Annex I to non-Annex I in order to mitigate greenhouse gas emissions. Our analysis is based on a numerical general equilibrium model for a world economy comprising two regions, North (Annex I) and South (non-Annex I). As our model allows for labor mobility between the formal and informal sectors in the South, we are also able to capture additional aspects of how the transfer influences the Southern economy. In a cooperative equilibrium, a technology transfer from the North to the South is clearly desirable from the perspective of a ‘global social planner’, since the welfare gain for the South outweighs the welfare loss for the North. However, if the regions do not cooperate, then the incentives to introduce the technology transfer appear to be relatively weak from the perspective of the North; at least if we allow for Southern abatement in the pre-transfer Nash equilibrium. Finally, by adding the emission reductions associated with the Kyoto agreement to an otherwise uncontrolled market economy, the technology transfer leads to higher welfare in both regions.Climate Policy, Technology Transfer, Kyoto Protocol, General Equilibrium, Clean Development Mechanism

Do conventions need to be common knowledge?

Do conventions need to be common knowledge? David Lewis builds this requirement into his definition of a convention. This paper explores the extent to which his approach finds support in the game theory literature. The knowledge formalism developed by Robert Aumann and others militates against Lewis’s approach, because it demonstrates that it is almost impossible for something to become common knowledge in a large society. On the other hand, Ariel Rubinstein’s Email Game suggests that coordinated action is equally hard for rational players. But an unnecessary simplifying assumption in the Email Game turns out to be doing all the work, and the paper concludes that common knowledge is better excluded from a definition of the conventions that we use to regulate our daily lives