scholarly journals Public Goods in Endogenous Networks

2017 ◽  
Vol 9 (3) ◽  
pp. 187-212 ◽  
Author(s):  
Markus Kinateder ◽  
Luca Paolo Merlino
Keyword(s):  
Public Good ◽  
Local Public Good ◽  
The Public ◽  
Heterogeneous Players ◽  
Multipartite Graphs ◽  
Complete Multipartite Graphs ◽  
Endogenous Networks ◽  
Split Graphs ◽  
Complete Multipartite ◽  
The Cost

We study a local public good game in an endogenous network with heterogeneous players. The source of heterogeneity affects the gains from a connection and hence equilibrium networks. When players differ in the cost of producing the public good, active players form pyramidal complete multipartite graphs; yet, better types need not have more neighbors. When players differ in the valuation of the public good, nested split graphs emerge in which production need not be monotonic in type. In large societies, few players produce a lot; furthermore, networks dampen inequality under cost heterogeneity and increase it under heterogeneity in valuation. (JEL D63, D85, H41)

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

Games ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 55
Author(s):  
Markus Kinateder ◽  
Luca Paolo Merlino
Keyword(s):  
Public Good ◽  
Nash Equilibria ◽  
Potential Game ◽  
Public Good Provision ◽  
Local Public Good ◽  
Steady State Distribution ◽  
State Distribution ◽  
Long Run ◽  
Split Graphs ◽  
Good Provision

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.

scholarly journals On DRC-covering of K(n) t λ by cycles

2009 ◽  
Vol 6 (2) ◽  
pp. 229-237 ◽  
Author(s):  
Zhihe Liang
Keyword(s):  
Lower Bound ◽  
Wdm Networks ◽  
Optimal Solutions ◽  
Multipartite Graphs ◽  
Complete Multipartite Graphs ◽  
Number Of Cycles ◽  
Complete Multipartite

This paper considers the cycle covering of complete multipartite graphs motivated by the design of survivable WDM networks, where the requests are routed on sub-networks which are protected independently from each other. The problem can be stated as follows: for a given graph G, find a cycle covering of the edge set of K (n) t ? , where V( Kt (n))=V(G), such that each cycle in the covering satisfies the disjoint routing constraint (DRC). Here we consider the case where G=Ctn, a ring of size tn and we want to minimize the number of cycles ? (nt, ?) in the covering. For the problem, we give the lower bound of ? (nt, ?), and obtain the optimal solutions when n is even or n is odd and both ? and t are even.

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