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 wellcovered 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 

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 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/72425 