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.
Author(s): Nicholas Ham
Series: na
Year: 05/05/2019
Language: English
Pages: 34
Tags: Game Theory, Symmetric Games, Game Automorphisms. MSC: 91A05, 91A06, 91A10, 91A30, 91A70, 91B16.
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
