Multiple equilibria in optimal control models – a research program

Multiple long-run steady states occur in many economic decision processes. The research program we propose in the following intends to investigate the solution structure of dynamic optimization models with multiple equilibria. The existence of Skiba points separating their basins of attraction implies the existence of (at least) two different optimal solutions. A typical example is from public sector Operations Research. As long as damages resulting from environmental pollution, say, are not too heavy, it pays off to aspire to a clean environment. If, however, a certain threshold is surpassed, there is a long-run optimal trade-off between the damage and the costs of control instruments (prevention, abatement and clean-up). While the eradication of the problem leads to a lower boundary equilibrium, the upper long-run equilibrium corresponds to an appeasement policy, in which escalation is suppressed. This example shows why it might be important in practice to recognize whether the problem exhibits a Skiba point, and to identify empirically the position and the shape of the threshold.