“…2 See Vickrey (1961) for participation costs, Spenner and Freeman (2012) for attracting participants, Pathak and Sönmez (2008) for leveling the playing field, and Wilson (1987) and Bergemann and Morris (2005) for a designer's informational requirements. 3 Examples include auctions (Vickrey (1961), Riley and Samuelson (1981), Myerson (1981)), voting (Arrow (1963)), school choice (Abdulkadiroglu and Sönmez (2003)), organ exchange (Roth, Sönmez, and Ünver (2004)), course allocation (Sönmez and Ünver (2010), Budish and Cantillon (2012)), and refugee resettlement (Jones and Teytelboym (2016), Delacrétaz, Kominers, and Teytelboym (2016)). 4 Direct mechanisms are not necessarily simple, and hence the revelation principle does not extend to simple extensive-form games; cf.…”