Worst-case mechanism design with undominated strategies ∗ Takuro Yamashita † April 26, 2009 Abstract We consider a way to evaluate mechanisms without assuming mu- tual knowledge of rationality among the agents. More specifically, we assume that each agent can take any undominated strategy un- der a mechanism, and the mechanism is evaluated by its worst-case scenario. First, we provide some characteristics of a mechanism that implements a “strongly monotonic” social choice correspondence in an environment with “single-crossing” preferences. Second, we show that if the mechanism designer is interested in implementation of “individ- ually rational outcome mappings” in a “random valuation” model, any mechanism that is not dominant-strategy incentive compatible (DSIC) is outperformed by a DSIC mechanism. Key words: mechanism design, implementation * I am grateful to Ilya Segal, Matthew O. Jackson, Paul Milgrom, Jon Levin, Koichi Tadenuma, and seminar participants at Stanford University, Hitotsubashi University, and Yokohama National University. † Stanford University. takuroy@stanford.edu 1