Changes in the parameters of an $n$-dimensional system of equations induce changes in its solutions. For a class of such systems, we determine the qualitative change in solutions given certain qualitative changes in parameters. Our methods and results are elementary yet useful. They highlight...

Changes in the parameters of an n-dimensional system of equations induce changes in its solutions. For a class of such systems, we determine the qualitative change in solutions given certain qualitative changes in parameters. Our methods and results are elementary yet useful. They highlight the...

We prove that the English auction (with bidders that need not be ex ante identical and may have interdependent valuations) has an efficient ex post equilibrium. We establish this result for environments where it has not been previously obtained. We also prove two versions of the...

We prove that the English auction (with bidders that need not be ex ante identical and may have interdependent valuations) has an efficient ex post equilibrium. We establish this result for environments where it has not been previously obtained. We also prove two versions of the...