Groves mechanisms and communication externalities

Efthymios Athanasiou,Santanu Dey,Giacomo Valletta

doi:10.1007/s10058-015-0180-y

Efthymios Athanasiou, Santanu Dey + Show 1 more

Open Access

https://doi.org/10.1007/s10058-015-0180-y

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Abstract

We put forward a model of private goods with externalities. Agents derive benefit from communicating with each other. In order to communicate they need to operate on a common platform. Adopting new platforms is costly. We first provide an algorithm that determines the efficient outcome. Then we prove that no individually rational and feasible Groves mechanism exists. We provide sufficient conditions that determine when an individually rational Groves mechanism runs a deficit and we characterize the individually rational Groves mechanism that minimizes such deficit whenever it occurs. Moreover, for 2-agent economies, we single out the only feasible and symmetrical Groves mechanism that is not Pareto dominated by another strategy-proof, feasible and symmetrical mechanism.

Highlights

Traveling by train across the border between France and Spain used to involve the inconvenience of changing trains
In this paper we study Groves mechanisms in a context of private goods that accounts for the effect of an externality
The pattern of language acquisition that maximizes the sum of utilities involves Igor, Ivan and Natasha learning English. This example capture the nature of the externality that lies in the heart of the problem we study in this paper

Summary

Introduction

Traveling by train across the border between France and Spain used to involve the inconvenience of changing trains. This enables her to communicate with each agent whose native platform is β The net benefit she derives depends on the number of agents she is able to communicate with [this is what Selten and Pool (1991) call ‘communicative benefit’] and the cost she had to face in order to adopt the new platform. The pattern of language acquisition that maximizes the sum of utilities involves Igor, Ivan and Natasha learning English This example capture the nature of the externality that lies in the heart of the problem we study in this paper.

The model

Efficient assignments

Axioms

Individually rational Groves mechanisms

Feasible Groves mechanisms

Concluding remarks