Puzzle: the AI circus: (puzzle in honor of Tuomas Sandholm's 50th birthday)

Please send solutions to the author by e-mail, with the title of this puzzle in the subject header. By agreement with the editors, the best solution will be published in the next issue of SIGecom Exchanges, provided that that solution is of sufficiently high quality. Quality is judged by the author, taking into account at least soundness, completeness, and clarity of exposition. A solution may be published even if it does not solve all cases.