The Evolution of Networks and Local Public Good Provision: A Potential Approach

Markus Kinateder,Luca Paolo Merlino

doi:10.3390/g12030055

Abstract

In this paper, we propose a game in which each player decides with whom to establish a costly connection and how much local public good is provided when benefits are shared among neighbors. We show that, when agents are homogeneous, Nash equilibrium networks are nested split graphs. Additionally, we show that the game is a potential game, even when we introduce heterogeneity along several dimensions. Using this result, we introduce stochastic best reply dynamics and show that this admits a unique and stationary steady state distribution expressed in terms of the potential function of the game. Hence, even if the set of Nash equilibria is potentially very large, the long run predictions are sharp.

Highlights

IntroductionIndividuals or firms often interact with each other; for example, researchers share their knowledge to produce joint research, and firms collaborate in R&D activities
Individuals or firms often interact with each other; for example, researchers share their knowledge to produce joint research, and firms collaborate in R&D activities. The benefits of these interactions frequently depend on some individual characteristics of the partners involved and on investments such as the effort devoted to a research project or to engage in R&D activities. These investments display the characteristics of a local public good: they are local because they present direct externalities only for agents who are collaborating; they are public because one’s investment benefits all one’s partners; and, once a collaboration is established, the more one invests, the less one’s partner’s incentives are to invest
We studied an environment in which players provide a local public good, that is, which benefits only those players who are directly connected to a provider

Summary

Introduction

Individuals or firms often interact with each other; for example, researchers share their knowledge to produce joint research, and firms collaborate in R&D activities In such instances, the benefits of these interactions frequently depend on some individual characteristics of the partners involved and on investments such as the effort devoted to a research project or to engage in R&D activities. The benefits of these interactions frequently depend on some individual characteristics of the partners involved and on investments such as the effort devoted to a research project or to engage in R&D activities These investments display the characteristics of a local public good: they are local because they present direct externalities only for agents who are collaborating; they are public because one’s investment benefits all one’s partners; and, once a collaboration is established, the more one invests, the less one’s partner’s incentives are to invest. The key insight of these models is that, when agents are allowed to unilaterally establish links, equilibrium networks display core-periphery structures in which few agents are the largest contributors who collaborate with each other (the core), while others link to them to partly or completely free ride on their contributions (the periphery)

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