Commit d7b8402c authored by Nick Ham's avatar Nick Ham

added some references

parent 02a6c4a3
......@@ -7,6 +7,24 @@
publisher={Greenwood Publishing Group}
}
@book
{
laffont1993theory,
title={A theory of incentives in procurement and regulation},
author={Laffont, Jean-Jacques and Tirole, Jean},
year={1993},
publisher={MIT press}
}
@book
{
laffont2009theory,
title={The theory of incentives: the principal-agent model},
author={Laffont, Jean-Jacques and Martimort, David},
year={2009},
publisher={Princeton university press}
}
@book
{
VNM,
......
\section{Introduction} \label{sec:intro}
The notion of a game being fair may be made more precise with the concept of symmetry. Broadly speaking we will consider a game fair when the players are indifferent between which position they play, however there are several distinct notions of symmetry that are possible which lead to variations in structure and fairness. For example, the players may or may not care about the arrangement of their opponents.
This paper surveys the numerous notions of symmetry for finite strategic-form games that are present in the literature, whilst also filling various holes and opening several further directions of research in the area. This is important to our understanding of the theory of symmetric games and fairness, which is fundamental when it comes to the theory of games, artificial intelligence, biology, computer science, economic theory, legal systems, logic, philosophy, political science, along with social choice and voting theory to name just a few examples. A few specific examples where a better understanding of symmetry and fairness is ideal includes but is definitely not limited by Arrow's impossibility theorem \cite{arrow1950difficulty, arrow2012social}, financial contagion \cite{dungey2005contagion}, human misery \cite{margolis2003misery} and human trafficking \cite{aronowitz2009human}. Note that this paper does not survey the literature on notions of symmetry, though the reader may find it a useful reference if undertaking such an endeavour.
This paper surveys the numerous notions of symmetry for finite strategic-form games that are present in the literature, whilst also filling various holes and opening several further directions of research in the area. This is important to our understanding of the theory of symmetric games and fairness, which is fundamental when it comes to the theory of games, artificial intelligence, biology, computer science, economic theory, legal systems, logic, philosophy, political science, along with social choice and voting theory to name just a few examples. A few specific examples where a better understanding of symmetry and fairness is ideal includes but is definitely not limited by Arrow's impossibility theorem \cite{arrow1950difficulty, arrow2012social}, financial contagion \cite{dungey2005contagion}, human misery \cite{margolis2003misery}, human trafficking \cite{aronowitz2009human} and incentive theory \cite{laffont1993theory, laffont2009theory}. Note that this paper does not survey the literature on notions of symmetry, though the reader may find it a useful reference if undertaking such an endeavour.
......
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