Notions of Anonymity, Fairness and Symmetry%0Afor Finite Strategic-Form Games [draft]

In this paper we survey the various notions of anonymity and symmetry for finite strategic-form games that are present in the literature, and discuss notions of fairness; show that game bijections and game isomorphisms form groupoids; introduce matchings as a convenient characterisation of strategy triviality; and outline how to construct and partially order parameterised (symmetric) games with numerous examples that range all combinations of surveyed symmetry notions, which when combined with other results in this paper gives the precise relationship between the various symmetry notions.