Optimization of the post-crisis recovery plans in scale-free networks

General Motors or a local business, which one is it better to be stimulated in postcrisis recessions, when government stimulation is meant to overcome recessions? Due to the budget constraints, it is quite relevant to ask how government can increase the chance of economic recovery. One of the key elements to answer this question is to understand metastable features of crises in economic networks and their related hysteresis. The Ising model has been suggested for studying such features. In the homogeneous networks, one needs at least a minimum budget, to force the network to switch its local equilibria, where such a minimum is independent of the network characteristics such as the average degree. In the scale free networks however, when the government aims to push the network to switch to another equilibrium, one may wonder which nodes are to be preferably stimulated in order to minimize the cost. In this paper, it is shown that stimulation of high degree nodes costs less in general. It is also found that in scale free networks, the stimulation cost depends on the networks features such as its assortativity. Although we confine our study to the Ising model in order to tackle a problem in economics, our analysis shines lights on many other problems concerning stimulations of socio-economic systems where dynamical hysteresis appears.