“…Significant progress has been made in developing duality approaches to certify optimality of candidate mechanisms Chone 1998, Daskalakis et al 2017;Cai et al 2016, Carroll 2017. In response to the analytical difficulty, several recent papers study either approximately optimal mechanisms (Li and Yao 2013, Babaioff et al 2014, Cai et al 2016, Hart and Nisan 2017, or worst-case optimal mechanisms (Carroll 2017, Koçyiğit et al 2021, Che and Zhong 2021, Deb and Roesler 2021.…”