Economic Models - Convex Optimization

Cheap-talk Multiple Equilibria and Pareto 115
Whenever π 0 π s lies in the following
fact: The “deviation costs” that the regulator will have to accept initially in
order to steer the system towards the more favorable E U are so high that the
net benefit of going to E U would be less than the one obtained by letting
the system optimally converge towards the inferior E L .
The above results suggest that the policy of an environmental regulator
maybe very different depending on the fraction of the population that trusts
it when it initiates a new policy. If the initial confidence is high, the costs of
building a large fraction of Bs are compensated in the long-run by accrued
benefits. However, if the regulator’s trustworthiness is low from the onset,
its interest is to exploit its initial credibility for making short-term gains,
although this ultimately leads to an inferior situation where nobody trusts
the regulator.
As already mentioned, the dynamics of the canonical system Eqs. (6)–
(23) at the unstable middle equilibrium E M form a spiral. Therefore, the
threshold value π s is typically close to, but distinct from π M (i.e., π M ̸= π s )
and the threshold takes the particularly challenging form of a Skiba point.
No local analytical expression exists that characterizes a Skiba point. Thus,
Skiba points must be computed numerically. This was not done in this paper.
For a reference article on thresholds and Skiba points in economic models,
see Deissenberg et al. (2004).
5. Sensitivity Analysis and Bifurcations Towards
a Unique Equilibrium
Numerical analyses show that an increase in the firms’ flexibility (i.e., an
increase in β) shifts the stable equilibrium E U to the right and the unstable