From 1a2a33ab27b939e357e47209311729a3bad62426 Mon Sep 17 00:00:00 2001 From: Andrew Date: Sun, 23 Feb 2025 04:56:36 +0000 Subject: [PATCH] [CT421]: Week 06 --- .../03. Artificial Life/GT_Auctions.pdf | Bin 0 -> 166089 bytes year4/semester2/CT421/notes/CT421.pdf | Bin 773799 -> 779323 bytes year4/semester2/CT421/notes/CT421.tex | 26 ++++++++++++++++++ 3 files changed, 26 insertions(+) create mode 100644 year4/semester2/CT421/materials/03. Artificial Life/GT_Auctions.pdf diff --git a/year4/semester2/CT421/materials/03. Artificial Life/GT_Auctions.pdf b/year4/semester2/CT421/materials/03. 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b/year4/semester2/CT421/notes/CT421.tex @@ -509,6 +509,32 @@ In many domains, novelty search has out-performed searching directly for an obje The standard approach to novelty search involves maintaining an archive of previously-found novel solutions. To decide are the size of the archive, the similarity measure, and the balance between novelty \& fitness. +\section{Game Theory} +\subsection{Reasoning about Interactions} +Assume that we have just two agents, $i$ and $j$, and that these agents are self-interested. +Let there be a set of ``outcomes'' $\Omega = \{ \Omega_1, \Omega_2, \dots, \Omega_n \}$ over which the agents have preferences. +Preferences are expressed by utility functions: +\begin{align*} + u_i& : \Omega \rightarrow \mathbb{R} \\ + u_j& : \Omega \rightarrow \mathbb{R} \\ +\end{align*} + +These functions lead naturally to preference orderings over outcomes: +\begin{align*} + \Omega \geq u_i \Omega' \rightarrow u_i(\Omega) \geq u_i(\Omega') +\end{align*} + +We need a model of the environment in which agents can act. +Let us assume agents act simultaneously to choose an action to perform, and as a result of the actions an outcome will result. +The actual outcome depends on the combination of actions. +This can be represented as a \textbf{state transformation function}: +\begin{align*} + \tau: \text{Action}_i \times \text{Action}_j \rightarrow \Omega +\end{align*} + +For the time being, we will make the simplifying assumption that an agent can make one of two actions: to co-operate $C$ or to defect $D$. +We say a certain move is \textbf{rational} if the outcomes that arise through the action are better than all outcomes that arise from the alternative action. +