Economic Models - Convex Optimization

Cheap-talk Multiple Equilibria and Pareto 117
outcome. This property hinges crucially on the fact that the private sector
is atomistic, and thus, that the single agents do not anticipate the collative
impact of their individual decisions. Moreover, it requires a relatively
benevolent regulator, whose objective function does not differ too drastically
from the one of the private agents.
To introduce dynamics, we assumed that the proportion of believers
and non-believers in the economy changes over time as a function of the
difference in profits for the two types of firms. The change obeys a word-ofmouth
process driven by the relative success of the one or the other private
strategy, to believe or to predict. It is supposed that the regulator recognizes
its ability to influence the word-of-month dynamics, by an appropriate
choice of actions and is interested not only in its instantaneous but also
in its future losses. It is shown that, when the firms react fast enough to the
difference in profits of Bs and NBs, a sufficiently patient regulator may use
incorrect announcements to Pareto-improve the economic outcome compared
to the situation where all firms are non-believers that perfectly predict
the regulator’s actions. A particularly interesting case arise, when a stable
Pareto-superior equilibrium with a positive fraction of believers co-exists
with the (likewise stable) perfect prediction but inferior equilibrium where
all firms are non-believers.
In this case, the optimal policy of the regulator (to converge towards
the one or the other equilibrium) depends upon the initial proportion of
believers in the population. This history dependence of the solution suggests
a promising meta-analysis of the importance of good reputation based on the
previous good governance, in situations where the same macro-economic
policy-maker is confronted with recurrent, distinct decision-making issues.
These results of this paper are obtained under the assumption that the
non-believers do not exploit the fact that the regulator announced tax differs
from the equilibrium announcement for the static game. Likewise, in the
model, the non-believers do not attempt to predict the dynamics of the number
of believers.We leave to future research, the non-trivial task of exploring
the consequences of a relaxation, of these two restrictive hypotheses.
References
Abrego, L and C Perroni (1999). Investment subsidies and time-consistent environmental
policy. Discussion Paper, Coventry: University of Warwick, 1–35.
Barro, R and D Gordon (1983). Rules, discretion and reputation in a model of monetary
policy. Journal of Monetary Economics 12, 101–122.