This paper studies the optimal design of second-best corrective regulation, when some agents or activities cannot be perfectly regulated. We show that policy elasticities and Pigouvian wedges are sufficient statistics to characterize marginal welfare impact regulatory policies in a large class environments. is determined by subset elasticities: leakage elasticities, value relaxing constraints. ...

We introduce an extension of Strategy Logic for the imperfect-information setting, called SL ii and study its model-checking problem. As this logic naturally captures multi-player games with imperfect information, problem is undecidable; but we a syntactical class “hierarchical instances” which, intuitively, as one goes down syntactic tree formula, strategy quantifications are concerned finer o...

A new concept of “an imperfect singular solution” is defined as an approximate solution which becomes a singular solution by adding a suitable small perturbation to the original equations. A numerical method is presented for proving the existence of imperfect singular solutions of nonlinear equations with guaranteed accuracy. A few numerical examples are also presented for illustration. key wor...

In the setting of the two-user broadcast channel, where a two-antenna transmitter communicates information to two single-antenna receivers, recent work by Maddah-Ali and Tse has shown that perfect knowledge of delayed channel state information at the transmitter (perfect delayed CSIT) can be useful, even in the absence of any knowledge of current CSIT. Similar benefits of perfect delayed CSIT w...