Myopic Decision Rules

Abstract

In a dynamic context a decision maker at any instant t has information about his exogenous economic environment both at time t and at later dates. We represent the environment at t by a vector x(t) of exogenous variables, and their future values by $\left(x\left(t+1\right),x\left(t+2\right),\dots, x\left(t+T\right)\right)$. The horizon T is determined by such considerations as length of life, technology, resource limitations etc.; it might be infinite. A decision rule at time t is a map ψ_t associating with a vector of variables z the variable d representing the choice of the decision maker. We write $d={\psi}_t(z)$. Myopic decision rules refer to those maps of the form $d(t)={\psi}_t\left(x(t)\right)$ in which d(t) depends only upon the values of the exogenous variables at time t, disregarding any information about future conditions of the economic environment. A decision rule is said to be non-myopic if it is of the form $d(t)={\psi}_t\left(x(t),x\left(t=1\right),\dots, x\left(t+T\right)\right)$.