Envelope theorems are established for locally differentiable Stackelberg equilibria of a general class of finite horizon differential games with an open-loop information structure. It is shown that the follower's envelope results agree in form with those of any player in an open-loop Nash...

Intercommunity disease spread can be modeled using a collection of discrete community “patches” with continuous population flow between them. In a susceptible–infected–susceptible (SIS) model residents of a community may either be classified as susceptible or infected. Infected...

The intrinsic comparative statics properties of a general rate-of-return regulated, profitmaximizing model of a monopolist facing a command-and-control pollution constraint are derived. Recent advances in the theory of comparative statics are used to derive the basic comparative statics of the...

Necessary and sufficient conditions from optimal control theory that are typically used when studying finite and infinite horizon natural resource economics problems are stated. In the finite horizon case their use is demonstrated by deriving an explicit solution of a model describing the...

The comparative dynamics of locally differentiable feedback Nash equilibria are derived for the ubiquitous class of autonomous and exponentially discounted infinite horizon differential games. The resulting refutable implications are intrinsic to the said class of differential games, and thus...

The envelope theorem is extended to cover the class of discounted and autonomous infinite horizon differential games that possess locally differentiable Nash equilibria. The theorems cover open-loop and feedback information structures and are applied to an analytically solvable linear-quadratic...

A new comparative statics formalism using generalized compensated derivatives is presented that, in contrast to existing methodologies, directly yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. The formalism provides a natural and powerful...