Social interactions within a dynamic competitive economy
The paper considers social interactions and investigates how far the properties of moderate social influence and of diminishing returns foster the uniqueness and stability of a dynamic competitive economy. The corresponding optimal control problem is examined. It is shown that besides the standard outcome of a unique saddle-point steady state, multiple equilibria are possible, depending on whether the objective function is concave or not. In the case of competitive equilibrium, it is shown that a steady state can have one of the following generic local properties: saddlepoint stability, instability (either node or focus) and stable (either node or focus) according to the properties of social interactions.
scientific article; zbMATH DE number 5346072