A Differential Approach to Gibbard-Satterthwaite Theorem - Ville Korpela (Aboa Centre for Economics (ACE), 2012)
Numerous simple proofs of the celebrated Gibbard-Satterthwaite theorem (Gibbard, 1977, Satterthwaite, 1975) has been given in the literature. These are based on a number of different intuitions about the most fundamental reason for the result. In this paper we derive the Gibbard-Satterthwaite theorem once more, this time in a differentiable environment using the idea of potential games (Rosenthal, 1973, Monderer and Shapley, 1996). Our proof is very different from those that have been given previously.
Keywords: D71; D82; 330; Differentiable function; Gibbard-Satterthwaite theorem; Potential game; Strategy-Proofness