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. Introduction......Page 1 Background......Page 2 Permutations Acting On Strategy Profiles......Page 10 Notions of Anonymity......Page 12 Notions of Fairness (work in progress)......Page 13 Notions of Symmetry......Page 14 Morphisms Between Games......Page 16 Game Bijections......Page 17 Bijections Acting on Strategy Profiles......Page 18 Strategy Triviality and Matchings......Page 19 Notions of Symmetry......Page 21 Fairness Discussion......Page 22 Parameterised Symmetric Games......Page 26 Further examples......Page 28