Private Sector Participation: A Theoretical Justification of the Brazilian Position

The Brazilian position on the issue of private sector participation in the efforts to forestall and resolve emerging markets crises is that there should be an approach of contacting and convincing a large number, but not the totality, of private creditors. They should be convinced that the international public sector loans will allow a transition to stability that is overfinanced in case they voluntarily join in by maintaining their exposure to the country, at the spreads they choose, and with the counterparts they wish to have as clients. We model private sector participation by means of a game. We show that the traditional argument that there is a coordination problem among the private creditors does not exist is in a model without Knightian uncertainty, because there is only one Pareto dominant Nash equilibrium which involves participation. By introducing Knigthian uncertainty, we show that if the degree of uncertainty, as measured by the uncertainty aversion, is high enough, then there is only one Nash equilibrium under uncertainty, which involves nonparticipation. Finally, we show that if there is a large enough number of private creditors who decrease their uncertainty aversion, then again private participation becomes the unique Pareto dominant Nash equilibrium under Knightian uncertainty. If we interpret the approach and convincing of the private creditors as decreasing their uncertainty aversion, then this last result is a justification of the Brazilian position. In fact, the private creditors would voluntarily choose to maintain their exposures, because private sector participation is the unique Pareto dominant Nash equilibrium under uncertainty of the game.

Thermal and Magnetic Quantum Discord in Heisenberg models

We investigate how the quantum correlations (quantum discord) of a two-qubit one dimensional XYZ Heisenberg chain in thermal equilibrium depends on the temperature (T) of the bath and also on an external magnetic field B. We show that the behavior of the thermal quantum discord (QD) differs in many unexpected ways from the thermal entanglement. For example, we show situations where QD increases with T when entanglement decreases, cases where QD increases with T even in regions with zero entanglement, and that QD signals a quantum phase transition even at finite T. We also show that by properly tuning B or the interaction between the qubits we get non-zero QD for any T and we present a new effect not seen for entanglement, the regrowth of thermal QD.Comment: 4 pages, 5 figures, RevTex, double column; v2: published versio