Competition between collective and individual dynamics: Applications to simple economic models

Using Grauwin?s generalization [1] of Schelling's segregation model [2] we study, in a simplified model, some consequences of the
"fiscal war" waged between the states of a federation, and of the ``rate tax" generated by the recent Brazilian Central Bank regulation
of bank credit portability. The system is divided into blocks and all blocks have the same utility function,
which measures the satisfaction of agents living there and depends on the density of agents. We introduce a disorder parameter
in one of the blocks to make it more attractive than the others, so as to mimick the essential igredient of competition between
states or banks.

In the application to the scenario of a fiscal war between the states of a nation,
we interpret blocks as the states of a federation and economic agents as companies that make decisions seeking
to increase their own satisfaction. A vacant state, in order to attract agents already established elsewhere, need to give more
incentives to attract investment because of its low utility. In this work we try to
quantify the costs that states have with this kind of action.

Another analysis of the results can be applied to a bank credit portability model, where we interpret economic agents as customers
and blocks as retail credit banks. The interest rate levied on each bank will depend on the size of the portfolio of that bank.
Having a bank with a differentiated interest rate makes it more attractive than others, and it begins to "steal" customers from other
banks. Studying the selfish scenario (where the government doesn?t discourage a client from taking his/her debt to another bank),
and assuming that the number of customers in the market is sufficiently small, the dynamics leads to a situation where we have just a
few coexisting banks, the others having gone bankrupt.

We study analytically the effects, at the global level, of variations in the density, in the altruism parameter and in the
parameter determining the utiliy function at saturation, as well as the effects of introducing disorder in one or more blocks.
Finally, computer simulations were performed to check that the dynamic behavior in all scenarios was consistent with the
obtained solutions.

[1] S. Grauwin et al., PNAS 106, 20622 (2009).

[2] T. C. Schelling, J. Math. Sociol. 1, 143 (1971).