Schelling (in Micromotives and Macrobehavior, Norton, New York, 1978) suggested a simple binary choice model to explain the variation of corruption levels across societies. His basic idea was that the expected profitability of engaging in corruption depends on its prevalence. The key result of the so-called Schelling diagram is the existence of multiple equilibria and a tipping point. The present paper puts Schelling’s essentially static approach into an intertemporal setting. We show how the existence of an unstable interior steady state leads to thresholds such that history alone or history in addition to expectations (or coordination) is necessary to determine the long-run outcome. In contrast to the related literature, which classifies these two cases according to whether the unstable equilibrium is a node or a focus, the actual differentiation is more subtle because even a node can lead to an overlap of solution paths such that the initial conditions alone are insufficient to uniquely determine the competitive equilibrium. Another insight is that a (transiently) cycling competitive equilibrium can dominate the direct and monotonic route to a steady state, even if the direct route is feasible.
- Schelling diagram
- intertemporal competitive equilibria
- history versus expectations
Caulkins, J. P., Feichtinger, G., Grass, D., Hartl, R. F., Kort, P. M., Novak, A. J., ... Wirl, F. (2014). A dynamic analysis of Schelling’s binary corruption model: A competitive equilibrium approach. Journal of Optimization Theory and Applications, 161(2), 608-625. https://doi.org/10.1007%2Fs10957-013-0420-7