The paper develops a version of Pontryagin's maximum principle for optimal control problems with monotonicity constraints on control variables. Whereas the literature handles such constraints by imposing an assumption of piecewise smoothness on the control variable and treating the slope of this...

Online marketplaces, such as Amazon, Alibaba, or Google Shopping, allow sellers to promote their products by charging them for the right to be displayed on top of organic search results. In this paper, we study the problem of designing auctions for promoted products and highlight some new...