The Google matrix analysis of the world trade network (WTN) allows to probe the direct and indirect trade exchange dependencies between countries (see e.g. [1]). Unlike the simple accounting view obtained from the usual import export balance, relying on the total volumes of exchanged commodities between countries, the PageRank-CheiRank trade balance (PCTB) allows to take account of the long range inter-dependencies between world economies. We present a WTN crisis contagion model [2, 3] built upon the iterative measure of the PCTB for each country. 1 Once a country have a PCTB below a threshold , it is declared in a bankruptcy state in which it can no more import commodities excepting some vital one for the industry, eg, petroleum and gas. This state corresponds either to the fact that a country with a very negative trade balance have not enough liquidity to import non essential commodities, or to the decision of a supranational economic authority trying to contain a crisis by placing an unhealthy national economy in bankruptcy. The bankruptcies of economies with PCTB less than induce a rewiring of the world trade network which possibly weaken other economies. In the phase corresponding to a bankruptcy threshold < c, the crisis contagion is rapid and contained since it affects only less than 10% of the world countries and induces a total cost of less than 5% of the total USD volume exchanged in the WTN. This total cost of the crisis drops exponentially with the decrease of . In the phase corresponding to a bankruptcy threshold > c, the cascade of bankruptcies can not be contained and the crisis is global, affecting about 90% of the world countries. In the global crisis phase ( > c), at the first stage of the contagion, myriads of countries with low exchanged volume (ie, low import and export volumes) go to bankruptcy. These countries belong mainly to Sub Saharan Africa, Central and South America, Middle East, and Eastern Europe. In the next stage of the crisis contagion, the conjugated effect of the bankruptcies of these countries contribute to the fall of big exporters, such as the US or Western European countries. As an example, for 2004, 2012, and 2016 WTNs, the bankruptcy of France is solely due to the failure of many low exchanged volume countries, which, here, individually import from France a volume of commodities less than 10 billions USD. Otherwise stated, France failure is caused by the failure of many small importers. Great Britain is a similar case for the 2004, 2008, and 2016 WTNs. Among the big exporters (ie, with a exchanged volume greater than 10 1This contagion model has been already used for the study of crisis in the Bitcoin transactions network [3]. billions USD), European and American countries are the sources of the crisis contagion. The gates from which crisis enters Asia are Japan, Korea, and Singapore. Generally, Asian countries go to bankruptcy at the end of the crisis contagion, with China, India, Indonesia, Malaysia and Thailand, being, with Australia, usually the last economies to fall. We also observe that failures of the four BRIC occur during the last stages of the crisis contagion.
