Inequality and network structure

Inequality and network structure
Garud Iyengar, Willemien Kets, Rajiv Sethi, and Samuel Bowles

One of the more powerful implications of network analysis is that structure is an explanation. How things are connected to each other can effect the the distribution of resources or cooperative behavior. Here we have a paper that explores this idea in strictly mathematical terms - wow, it takes me back to advanced analysis. I haven't had to consider the behavior convex functions* in quite awhile.

The authors build off work by Myerson (1977) on cooperation on graphs. So, the way their model works is that each player in the network generates "value" if they are connected to other players. In addition the players can break off and define their own network, in which case their value is distributed only with their own network and they may or may not cut off some players' connections to other players. A player will only break off if they gain from it. The gains are relative to some function that determines value based on the number of individuals in the network 'clique'**.

The main implications of this model is that network structure is important, but the traditional measures of centrality, like betweenness and degree, are not. For instance the authors show examples of networks where the player with the highest betweenness and degree is the least valued. They also show an example of two networks with the same number of players, but the one with the more unequal degree distribution is actually more egalitarian in distributing value. They extend and continue having fun with their new model showing that all bipartite networks have a unique extremal distribution and extend the model allowing groups of players within k-distance of each other to break off.

This was just a discussion paper, but it does bring up some interesting points. For instance, if value is determined by those you interact with then it is certainly possible that someone several steps disconnected from me can disconnect me from value creation. Because each player has the choice of defecting to their own network if it benefits them we find the most central player, contrary to much network theory, is not the wealthiest. However, as the authors point out, this model is far too abstract to be empirically verified. It's value is in the theory and method, methinks.

* - in mathese that means you can draw a straight line and intersect the function at two points.

** - clique is defined totally differently than what I'm used to... sigh.