We study the effect of increased flexibility–increasing the number of ac- tions available to an agent–on an agent’s value for information. Adding a sin- gle action makes information more valuable if and only if the new action is either weakly dominated or extremal, i.e., a (partial) substitute for at most one action. This result extends naturally to the situation in which multiple new actions are made available to the agent. We apply these findings to a monop- olistic screening problem in which the good is information and to delegation with information acquisition.

For an increasing upper order hemi-continuous correspondence F selfmapping sigma-complete lattice A, we first provide tight fixed-point bounds for sufficiently large iterations on F starting from any initial point a in A. We use this result for conducting iterative fixed-point comparative statics, and then apply our results to monotone games and economies. For games of strategic complementarities, we improve the correspondence principle based results of Echenique (2002) by allowing for divergent learning processes, unstable fixed points, equilibrium indeterminacies, and unordered perturbations. We also apply our results to the comparative statics of stationary equilibria in large economies and the set of recursive equilibria in macroeconomic models with indeterminacies.

Firms and statistical agencies that publish or collect data face practical and legal
requirements to protect the privacy of individuals. Increasingly, these organizations
meet these standards by using publication mechanisms that satisfy
differential privacy
.
We consider the problem of choosing such a mechanism so as to maximize the value of
its output to end users. We show that this is a constrained information design problem,
and characterize its solution. When the underlying database is drawn from a symmetric
distribution — for instance, if individuals’ data are i.i.d. — we show that the problem’s
dimensionality can be reduced, and that its solution belongs to a simpler class of mech-
anisms. When, in addition, data users have supermodular payoffs, we show that the
simple
geometric mechanism
is always optimal by using a novel comparative static that
ranks information structures according to their usefulness in supermodular decision
problems

We use the money metric of McKenzie (1957) and Samuelson (1974) to de- rive new theorems about normality of some or all goods for a consumer. The main tool we use is the Saddlepoint Theorem of Khan-Schlee (2022), which shows that a consumer’s demand can be described as a solution of an unconstrained optimization problem—maximize the difference between the money metric and expenditure—even when the consumer’s preferences are incomplete or intransi- tive. Our theorems on normality differ in three ways from those available in the literature, for example, in Quah (2007) or Barthel-Sabarwal (2018). First, we do not assume that preferences are complete or transitive; second our theorems give conditions for one or all goods to be normal at a given price, but possibly not at others—that is, for price-dependent normality; and one of our theorems (Theorem 3) permits all but one good to be discrete.