Pandit, Parthe and Kulkarni, Ankur
(2016):
*Refinement of the Equilibrium of Public Goods Games over Networks: Efficiency and Effort of Specialized Equilibria.*

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## Abstract

Recently Bramoulle and Kranton presented a model for the provision of public goods over a network and showed the existence of a class of Nash equilibria called specialized equilibria wherein some agents exert maximum effort while other agents free ride. We examine the efficiency, effort and cost of specialized equilibria in comparison to other equilibria. Our main results show that the welfare of a particular specialized equilibrium approaches the maximum welfare amongst all equilibria as the concavity of the benefit function tends to unity. For forest networks a similar result also holds as the concavity approaches zero. Moreover, without any such concavity conditions, there exists for any network a specialized equilibrium that requires the maximum weighted effort amongst all equilibria. When the network is a forest, a specialized equilibrium also incurs the minimum total cost amongst all equilibria. For well-covered forest networks we show that all welfare maximizing equilibria are specialized and all equilibria incur the same total cost. Thus we argue that specialized equilibria may be considered as a refinement of the equilibrium of the public goods game. We show several results on the structure and efficiency of equilibria that highlight the role of dependants in the network.

Item Type: | MPRA Paper |
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Original Title: | Refinement of the Equilibrium of Public Goods Games over Networks: Efficiency and Effort of Specialized Equilibria |

Language: | English |

Keywords: | Network games; public goods; specialized equilibria; independent sets; linear complementarity problems |

Subjects: | C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games |

Item ID: | 72425 |

Depositing User: | Prof Ankur Kulkarni |

Date Deposited: | 07 Jul 2016 15:12 |

Last Modified: | 05 Oct 2019 07:41 |

References: | J. A. Bondy and U. S. R. Murty. Graph theory with applications, volume 290. Macmillan London, 1976. Y. Bramoullé and R. Kranton. Public goods in networks. Journal of Economic Theory, 135(1):478– 494, 2007. R. W. Cottle, J.-S. Pang, and R. E. Stone. The Linear Complementarity Problem. Academic Press, Inc., Boston, MA, 1992. W. W. Hogan. Point-to-set maps in mathematical programming. SIAM Review, 15(3):591–603, July 1973. A. A. Kulkarni and U. V. Shanbhag. On the variational equilibrium as a refinement of the generalized Nash equilibrium. Automatica, 48(1):45–55, 2012. J. F. Nash. Equilibrium points in N-person games. Proceedings of National Academy of Science, 1950. P. Pandit and A. A. Kulkarni. A linear complementarity based characterization of the weighted inde- pendence number and the independent domination number in graphs. Discrete Applied Mathematics, under review, http://arxiv.org/abs/1603.05075 , 2016. M. D. Plummer. Well-covered graphs: a survey. Quaestiones Mathematicae, 16(3):253–287, 1993. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/72425 |