Nash's Theorem is a famous and widely used result in non-cooperative game theory which can be applied to games where each player's mixed strategy payoff function is defined as an expectation. Current proofs of this Theorem neither justify why this constraint is necessary or satisfactorily identifies its origins. In this Thesis we change this and prove Nash's Theorem for abstract games where, in particular, the payoff functions can be replaced by total orders. The result of this is a combinatoric proof of Nash's Theorem. We also construct a generalised simplicial complex model and demonstrate a more general form of Nash's Theorem holds in this setting. This leads to the realisation Nash's Theorem is not a consequence of a fixed-point theorem but rather a combinatoric phenomenon existing in a much more general mathematical model.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:500758 |
| Date | January 2008 |
| Creators | Egan, Sarah |
| Contributors | Vorobjov, Nicolai |
| Publisher | University of Bath |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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