Game theory provides a mathematical framework for analysing strategic situations involving at least two players. Normal-form games model situations where the players simultaneously pick their moves. In this thesis we explore the strategic structure of finite normal-form games.
We look at three notions of isomorphisms between games, the structural properties that they preserve and under what conditions they are met. We also look at various notions of symmetric games, under what conditions they are met, the structural properties that these notions capture, how to identify them and how to construct them.
Author(s): Nicholas Ham
Year: 2011
Language: English
Pages: 25
Tags: Game Theory, Symmetric Games, Game Automorphisms. MSC: 91A05, 91A06, 91A10, 91A30, 91A70, 91B16.
Introduction......Page 4
Functions and Correspondences......Page 5
Relations and Matchings......Page 6
Groupoids......Page 7
Definition of a Game......Page 8
Table Representation of a Game......Page 9
Nash Equilibria......Page 10
Game Bijections......Page 11
Properties of Game Isomorphisms......Page 12
Notions of Equivalence......Page 15
Symmetry Groups......Page 17
Notions of Symmetry......Page 18
Properties of Symmetric Games......Page 19
Classifying a Game......Page 20
Examples of Symmetric Games......Page 21
Equilibria in Symmetric Games......Page 23
