Is ghettoisation a collateral damge of "ballot box democracy" in the developing world

In contrast with the evolving racial segregation in the US and Europe over the centuries, the latest phenomenon of urban segregation in the developing world is mostly based on what is commonly known as segregation by income. These urban ghettos are informally built settlements, mostly in the outskirts of large cities, the formation of which is often driven by rural to urban migration as poor migrants cannot afford to pay the premium price for the formal urban housing. Segregation in the developing world has created an unusual dichotomy as, on one side, we see the chaotic world of ghettos while on the other side we see the organized and flourishing advanced sector. The stark dichotomy has prompted reactions from regional and local authorities to physically isolate ghettos from the organized parts of urban centres. We argue that the formation and sustenance urban ghettos, or ghettoisation, in developing nations turn on the pivots of peculiar economic advantages and political opportunism and ours will be a first model to blend these economic and political factors to explain the formation of urban ghettos in equilibrium. We construct a simple game with two ghetto overlords who make relevant economic and political decisions in their respective ghettos. Ghetto overlords are rivals and strategically choose the optimal size of their respective ghettos, while the size of a ghetto determines the local supply of labour and thereby drives the informal economy of a ghetto. The size of a ghetto also endows the ghetto overlord with electoral votes of their ghetto dwellers. With these assumptions and simple functional forms, we characterise the Nash equilibrium of the proposed game. Three important observations are in order: first, the game has multiple equilibria and the equilibria can be Pareto-ranked, which gives rise to the problem of what is commonly known as indeterminacy. Secondly, if a dynamic process is superimposed, then it is possible to examine the stability property of each equilibrium. If the dynamic process is simplistically represented by a first-order difference equation, then conditions under which chaos and cycles would occur are characterised. Finally, we find the bifurcation property of a stable Nash equilibrium can render the ghetto’s economic and political outcomes highly fragile and chaotic, which can seriously impinge on the lives of about 500 million ghetto dwellers in developing nations.