Mathematical Economics

We have been further occupied with Brouwer's FPT providing an example that showed that it cannot generally hold in infinite dimensional spaces. We have subsequently examined an application of Brouwer's FPT application for the verification of the existence of Nash equilibria in a class of finite non-co-operative games, in a restricted setting that avoids the use of its generalization to correspendences, i.e. Kakutani's FPT. Our restrictive setting essentially ensures that the best response correspondence is actually a function. You can find notes on the above here.

We have also examined an application of Dudley's Theorem in the verification of the continuity of almost all of the sample paths of a standard Wiener process. You can find notes of this here (as noted in the lecture the particular application of Dudley's Theorem will not be a part of your exam material).