Goodwin's models through viability analysis: some lights for contemporary political economics regulations

Our contribution aims to revisit the most famous Goodwin's models in macroeconomics by the light of set-valued analysis taking into account state and regulation constraints in a viability program. Goodwin 67 and Goodwin 90 models deal with dynamic interactions between employment and salary levels. They provide endogenous explanations of cyclical trends in dynamical economy. Viability methods enable investigating model properties and revealing appropriate regulation allowing the evolution to fulfill some prescribed qualitative objective. Then, applying computational methods derived from the Viability Kernel Algorithm, one can lash the traditional Goodwin model analysis up to the institutional framework of the economy including monetary and budgetary aspects of the regulatory policy from the public authorities, namely the state government, the central bank and eventually the rivalry between the two boards thanks to dynamical games and discriminant analysis