Symmetric mechanism design

Designers of economic mechanisms can often benefit by using discriminatory mechanisms which treat agents asymmetrically. This paper studies the extent to which a policy prohibiting biased mechanisms is effective in achieving fair outcomes. Our main result is a characterization of the class of social choice functions that can be implemented by symmetric mechanisms. When the solution concept used is Bayes-Nash equilibrium, symmetry is typically not very restrictive and discriminatory social choice functions can be implemented by symmetric mechanisms. Our characterization in this case is based on a 'revelation principle' type of result, where we show that a social choice function can be symmetrically implemented if and only if a particular kind of (indirect) symmetric mechanism implements it. When implementation in dominant strategies is considered, only symmetric social choice functions can be implemented by symmetric mechanisms. We illustrate our results in environments of voting with private values, voting with a common value, and assignment of indivisible goods.