Network Structures and Poverty Traps

We build an evolutionary network game of economic agents that choose actions of being either a high-profile or a low-profile economic agent. Those economic agents reside in the vertices of an undirected graph or network given by their types, and their strategic interaction is driven by imitative behavior. Then, the share of types of economic agents form networks described by a mean field formalism which depends on agents' payoff functions, as well as on the current state of the economic network. We show the fact that, in this context of networks, a neighbor is imitated if her strategy outperformed the focal individual's in the previous iterations. The main result is that there are three equilibria (each with a non-degenerate basin of attraction), one completely made up of high profile individuals, one made up of low profile individuals (i.e. the poverty trap), and a mixture. The main parameters from being in one or the other equilibrium are: i) the degree of node, ii) cost of being high-profile, and iii) initial distribution of types. We conclude with simple numerical examples to show that outcome depends on network structures, and on both the education costs, $c$, and the value of $eta$ which is the incentive to choose the high-profile action.