Diplomacy
Author:
trollgeir
Last Updated:
11 years ago
License:
Creative Commons CC BY 4.0
Abstract:
test
\begin
Discover why over 20 million people worldwide trust Overleaf with their work.
\begin
Discover why over 20 million people worldwide trust Overleaf with their work.
\documentclass[a4paper]{article} % a4paper option recommended
\usepackage[english]{babel}
\usepackage{uureport}
\usepackage{cite}
\usepackage{hyperref}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{pgfplots}
\bibliographystyle{alpha}
\title{Diplomacy}
\type{Report}
\course{Games \& Agents}
\author{A. Berland, B. Reigersberg, E. Koens, \\J. de Groot, K. van Katwijk, T. de Goey}
\begin{document}
supIntolerance = $S$ 0.0005\\
supFavor = $\sigma$ \\
time = $t$ \\
Trust = $T$ \\
Decay = $D$ = 1.1 \\
Paranoia = $P$ \\
incTrust = $\tau$ = 0.002\\
For defecting a treaty:
\large
$$ T'_p = T_p - \frac{D^{-t}} {10} $$
\center
\begin{tikzpicture}
\begin{axis}[
width = 450,
height = 300,
xlabel= time $t$,
ylabel={Trust alteration $T'_p$},
xtick = {0,5,10,15},
ytick = {0.1},
xmin = 0,
ymin = 0,
xmax = 16,
ymax = 0.1,
domain = 0:15
]
\addplot {(1.1^(-x)/10};
\addplot {0.002*x};
\legend{Defect penalty (-), Treaty maintenance (+)};
\end{axis}
\end{tikzpicture}
\large
\[ P_p = \left\{
\begin{array}{l l}
1 - \Big( D^{-t} \cdot T_p \Big) & \quad \text{for $T > 0$} \\
1 & \quad \text{for $T = 0$}
\end{array} \right.\]
\\
\center
\begin{tikzpicture}
\begin{axis}[
width = 450,
height = 300,
xlabel= time $t$,
ylabel={Paranoia $P_p$},
xtick = {0,5,10,15},
ytick = {1},
xmin = 0,
ymin = 0,
xmax = 16,
ymax = 1,
domain = 0:15
]
\addplot {1-((1.1^(-x))*(0.5))};
\end{axis}
\end{tikzpicture}
\large
\[ T'_p = T_p + \left\{
\begin{array}{l l}
(S \cdot \sigma)^2 & \quad \text{if $\sigma > 0$ \& ACCEPT}\\
-(S \cdot \sigma)^2 & \quad \text{if $\sigma < 0$ \& REJECT}\\
\text{0} & \quad \text{if ($\sigma \le 0$ \& ACCEPT) or ($\sigma \geq 0$) \& REJECT)}
\end{array} \right.\]
\\
\centering
\begin{tikzpicture}
\begin{axis}[
width = 450,
height = 300,
axis x line = middle,
axis y line = middle,
xlabel= supFavor $\sigma$,
ylabel={Trust alteration $T'$},
xtick = {-15,-10,-5,0,5,10,15},
ytick = {-0.1,0,0.1},
xmin = -15,
ymin = -0.1,
xmax = 15,
ymax = 0.1,
domain = -15:15
]
\addplot [blue] [line width=2pt] {(x/abs(x))*((0.0005*x^2)};
\end{axis}
\end{tikzpicture}
\end{document}