The payoff function is defined on the product of the spaces of mixed strategies that are the spaces of probability measures on compact Hausdorff spaces. The continuity of the payoff function is recently proved by Glycopantis and Muir. Here we give an alternative proof that is essentially based...

The strong Whitney topology on the sets of maps of smooth manifolds induces a topology on the set of preferences in euclidean space. We prove that the obtained space is not connected which implies that there is no continuous social choice function defined on a finite power of this space. We also...